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  • Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680
20
Lecture #34 Precipitation and Dissolution : Basics and metal solubility (Stumm & Morgan, Chapt.7) Benjamin; Chapter 8.7-8.15 David Reckhow CEE 680 #34 1 Updated: 26 March 2020 Print version

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Page 1: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Lecture 34Precipitation and Dissolution Basics and

metal solubility (Stumm amp Morgan Chapt7)

Benjamin Chapter 87-815

David Reckhow CEE 680 34 1

Updated 26 March 2020 Print version

Topics Hydrolysis

Aquo metal ion gives rise to hydroxo complexes Magnesium and Iron Hydroxide solubility

David Reckhow CEE 680 34 2

Precipitation and Dissolution Environmental Significance

Engineered systems coagulation softening removal of heavy metals

Natural systems composition of natural waters formation and composition of aquatic sediments global cycling of elements

Composition of natural waters SampM 3rd ed figure 151 (pg 873) Benjamin 2nd ed figure 11

David Reckhow CEE 680 34 3

Elemental Abundance in Crust ad

David Reckhow CEE 680 34 4

dfs

David Reckhow CEE 680 34 5

From USGS 2005

Top 8IN EARTHrsquoS CRUST

Abundance of inorganics in fresh water and in earthrsquos crust

David Reckhow CEE 680 35 6

From Stumm amp Morgan 1996 Benjamin 2002 fig 11

Terrestrial water

Solubility Products General Equilibrium

AmBn(s) harr mA+n + nB-m

Solubility Product Equation Kso = [A+n]m[B-m]n

also sometimes written Ksp

Example Calcium Carbonate

sources Smith amp Martell SampM table 71 (pg362-364)

David Reckhow CEE 680 34 7

Solid Cation Anion

Kso and Q Reaction Quotient (Q)

computed value from actual measurements may not be at thermodynamic equilibrium

comparison with Ksp will tell you about tendency toward dissolution or precipitation QgtKso then water will precipitate solid phase QltKso then water will dissolve solid phase

Example Calcium Carbonate solubility Ca+2 = 40 mgL and CO3

-2 = 100 mgL as CaCO3 what is Q if Kso is 10-834 what does this tell us

David Reckhow CEE 680 34 8

Presenter
Presentation Notes
Note GFW for Ca is 40 so Q = 10-6 and system is over saturated and will precipitate CaCO3

Solubility of some simple salts Barium sulfate

BaSO4 = Ba+2 + SO4-2

Kso = 10-996 = [Ba+2][SO4-2]

How much will dissolve and what will the barium and sulfate concentrations be

How much will dissolve in a 1mM solution of Na2SO4

David Reckhow CEE 680 34 9

984

2969

1010

minus

minus

=

=

xx

( )

9667

96963

32

3969

101009712

1041010

101010

minusminus

minusminusminus

minus

minusminus

==

minusplusmnminus=

+=

+=

x

xx

xxxx

Presenter
Presentation Notes
Simplify last equation by neglecting the second ldquoxrdquo in right hand term

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-28 -112 00015848932 28 1124 262 0 0 0 0 0 173780082874938 4168693834703 0 0 0 0 0 0 0
-285 -1115 00014125375 285 1114 257 0 0 0 0 0 138038426460289 3715352290972 0 0 0 0 0 0 0
-29 -111 00012589254 29 1104 252 0 0 0 0 0 109647819614319 3311311214826 0 0 0 0 0 0 0
-295 -1105 00011220185 295 1094 247 0 0 0 0 0 870963589956082 2951209226666 0 0 0 0 0 0 0
-3 -11 0001 3 1084 242 0 0 0 0 0 691830970918939 2630267991895 0 0 0 0 0 0 0
-305 -1095 00008912509 305 1074 237 0 0 0 0 0 549540873857627 234422881532 0 0 0 0 0 0 0
-31 -109 00007943282 31 1064 232 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-315 -1085 00007079458 315 1054 227 0 0 0 0 0 346736850452531 1862087136663 0 0 0 0 0 0 0
-32 -108 00006309573 32 1044 222 0 0 0 0 0 275422870333817 1659586907438 0 0 0 0 0 0 0
-325 -1075 00005623413 325 1034 217 0 0 0 0 0 218776162394955 1479108388168 0 0 0 0 0 0 0
-33 -107 00005011872 33 1024 212 0 0 0 0 0 173780082874938 1318256738556 0 0 0 0 0 0 0
-335 -1065 00004466836 335 1014 207 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-34 -106 00003981072 34 1004 202 0 0 0 0 0 109647819614319 1047128548051 0 0 0 0 0 0 0
-345 -1055 00003548134 345 994 197 0 0 0 0 0 870963589956081 933254300797 0 0 0 0 0 0 0
-35 -105 00003162278 35 984 192 0 0 0 0 0 691830970918938 831763771103 0 0 0 0 0 0 0
-355 -1045 00002818383 355 974 187 0 0 0 0 0 549540873857626 741310241301 0 0 0 0 0 0 0
-36 -104 00002511886 36 964 182 0 0 0 0 0 436515832240168 660693448008 0 0 0 0 0 0 0
-365 -1035 00002238721 365 954 177 0 0 0 0 0 346736850452532 588843655356 0 0 0 0 0 0 0
-37 -103 00001995262 37 944 172 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-375 -1025 00001778279 375 934 167 0 0 0 0 0 218776162394956 467735141287 0 0 0 0 0 0 0
-38 -102 00001584893 38 924 162 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-385 -1015 00001412538 385 914 157 0 0 0 0 0 138038426460289 371535229097 0 0 0 0 0 0 0
-39 -101 00001258925 39 904 152 0 0 0 0 0 109647819614318 331131121483 0 0 0 0 0 0 0
-395 -1005 00001122018 395 894 147 0 0 0 0 0 870963589956081 295120922667 0 0 0 0 0 0 0
-4 -10 00001 4 884 142 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-405 -995 00000891251 405 874 137 0 0 0 0 0 549540873857625 234422881532 0 0 0 0 0 0 0
-41 -99 00000794328 41 864 132 0 0 0 0 0 436515832240167 208929613085 0 0 0 0 0 0 0
-415 -985 00000707946 415 854 127 0 0 0 0 0 346736850452532 186208713666 0 0 0 0 0 0 0
-42 -98 00000630957 42 844 122 0 0 0 0 0 275422870333817 165958690744 0 0 0 0 0 0 0
-425 -975 00000562341 425 834 117 0 0 0 0 0 218776162394956 147910838817 0 0 0 0 0 0 0
-43 -97 00000501187 43 824 112 0 0 0 0 0 173780082874938 131825673856 0 0 0 0 0 0 0
-435 -965 00000446684 435 814 107 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-44 -96 00000398107 44 804 102 0 0 0 0 0 109647819614319 104712854805 0 0 0 0 0 0 0
-445 -955 00000354813 445 794 097 0 0 0 0 0 870963589956083 9332543008 0 0 0 0 0 0 0
-45 -95 00000316228 45 784 092 0 0 0 0 0 691830970918936 8317637711 0 0 0 0 0 0 0
-455 -945 00000281838 455 774 087 0 0 0 0 0 549540873857625 7413102413 0 0 0 0 0 0 0
-46 -94 00000251189 46 764 082 0 0 0 0 0 436515832240167 66069344801 0 0 0 0 0 0 0
-465 -935 00000223872 465 754 077 0 0 0 0 0 346736850452531 58884365536 0 0 0 0 0 0 0
-47 -93 00000199526 47 744 072 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-475 -925 00000177828 475 734 067 0 0 0 0 0 218776162394955 46773514129 0 0 0 0 0 0 0
-48 -92 00000158489 48 724 062 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-485 -915 00000141254 485 714 057 0 0 0 0 0 138038426460289 3715352291 0 0 0 0 0 0 0
-49 -91 00000125893 49 704 052 0 0 0 0 0 109647819614319 33113112148 0 0 0 0 0 0 0
-495 -905 00000112202 495 694 047 0 0 0 0 0 870963589956082 29512092267 0 0 0 0 0 0 0
-5 -9 000001 5 684 042 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-505 -895 00000089125 505 674 037 0 0 0 0 0 549540873857625 23442288153 0 0 0 0 0 0 0
-51 -89 00000079433 51 664 032 0 0 0 0 0 436515832240167 20892961309 0 0 0 0 0 0 0
-515 -885 00000070795 515 654 027 0 0 0 0 0 346736850452532 18620871367 0 0 0 0 0 0 0
-52 -88 00000063096 52 644 022 0 0 0 0 0 275422870333817 16595869074 0 0 0 0 0 0 0
-525 -875 00000056234 525 634 017 0 0 0 0 0 218776162394956 14791083882 0 0 0 0 0 0 0
-53 -87 00000050119 53 624 012 0 0 0 0 0 173780082874938 13182567386 0 0 0 0 0 0 0
-535 -865 00000044668 535 614 007 0 0 0 0 0 138038426460289 11748975549 0 0 0 0 0 0 0
-54 -86 00000039811 54 604 002 0 0 0 0 0 109647819614318 10471285481 0 0 0 0 0 0 0
-545 -855 00000035481 545 594 -003 0 0 0 0 0 870963589956081 09332543008 0 0 0 0 0 0 0
-55 -85 00000031623 55 584 -008 0 0 0 0 0 691830970918937 08317637711 0 0 0 0 0 0 0
-555 -845 00000028184 555 574 -013 0 0 0 0 0 549540873857626 07413102413 0 0 0 0 0 0 0
-56 -84 00000025119 56 564 -018 0 0 0 0 0 436515832240167 0660693448 0 0 0 0 0 0 0
-565 -835 00000022387 565 554 -023 0 0 0 0 0 346736850452531 05888436554 0 0 0 0 0 0 0
-57 -83 00000019953 57 544 -028 0 0 0 0 0 275422870333817 05248074602 0 0 0 0 0 0 0
-575 -825 00000017783 575 534 -033 0 0 0 0 0 218776162394955 04677351413 0 0 0 0 0 0 0
-58 -82 00000015849 58 524 -038 0 0 0 0 0 173780082874938 04168693835 0 0 0 0 0 0 0
-585 -815 00000014125 585 514 -043 0 0 0 0 0 138038426460289 03715352291 0 0 0 0 0 0 0
-59 -81 00000012589 59 504 -048 0 0 0 0 0 109647819614318 03311311215 0 0 0 0 0 0 0
-595 -805 0000001122 595 494 -053 0 0 0 0 0 870963589956081 02951209227 0 0 0 0 0 0 0
-6 -8 0000001 6 484 -058 0 0 0 0 0 691830970918937 02630267992 0 0 0 0 0 0 0
-605 -795 00000008913 605 474 -063 0 0 0 0 0 549540873857625 02344228815 0 0 0 0 0 0 0
-61 -79 00000007943 61 464 -068 0 0 0 0 0 436515832240167 02089296131 0 0 0 0 0 0 0
-615 -785 00000007079 615 454 -073 0 0 0 0 0 346736850452531 01862087137 0 0 0 0 0 0 0
-62 -78 0000000631 62 444 -078 0 0 0 0 0 275422870333817 01659586907 0 0 0 0 0 0 0
-625 -775 00000005623 625 434 -083 0 0 0 0 0 218776162394955 01479108388 0 0 0 0 0 0 0
-63 -77 00000005012 63 424 -088 0 0 0 0 0 173780082874938 01318256739 0 0 0 0 0 0 0
-635 -765 00000004467 635 414 -093 0 0 0 0 0 138038426460289 01174897555 0 0 0 0 0 0 0
-64 -76 00000003981 64 404 -098 0 0 0 0 0 109647819614318 01047128548 0 0 0 0 0 0 0
-645 -755 00000003548 645 394 -103 0 0 0 0 0 87096358995608 00933254301 0 0 0 0 0 0 0
-65 -75 00000003162 65 384 -108 0 0 0 0 0 69183097091894 00831763771 0 0 0 0 0 0 0
-655 -745 00000002818 655 374 -113 0 0 0 0 0 54954087385762 00741310241 0 0 0 0 0 0 0
-66 -74 00000002512 66 364 -118 0 0 0 0 0 43651583224017 00660693448 0 0 0 0 0 0 0
-665 -735 00000002239 665 354 -123 0 0 0 0 0 34673685045253 00588843655 0 0 0 0 0 0 0
-67 -73 00000001995 67 344 -128 0 0 0 0 0 27542287033382 0052480746 0 0 0 0 0 0 0
-675 -725 00000001778 675 334 -133 0 0 0 0 0 21877616239496 00467735141 0 0 0 0 0 0 0
-68 -72 00000001585 68 324 -138 0 0 0 0 0 17378008287494 00416869383 0 0 0 0 0 0 0
-685 -715 00000001413 685 314 -143 0 0 0 0 0 13803842646029 00371535229 0 0 0 0 0 0 0
-69 -71 00000001259 69 304 -148 0 0 0 0 0 10964781961432 00331131121 0 0 0 0 0 0 0
-695 -705 00000001122 695 294 -153 0 0 0 0 0 8709635899561 00295120923 0 0 0 0 0 0 0
-7 -7 00000001 7 284 -158 0 0 0 0 0 6918309709189 00263026799 0 0 0 0 0 0 0
-705 -695 00000000891 705 274 -163 0 0 0 0 0 5495408738576 00234422882 0 0 0 0 0 0 0
-71 -69 00000000794 71 264 -168 0 0 0 0 0 4365158322402 00208929613 0 0 0 0 0 0 0
-715 -685 00000000708 715 254 -173 0 0 0 0 0 3467368504525 00186208714 0 0 0 0 0 0 0
-72 -68 00000000631 72 244 -178 0 0 0 0 0 2754228703338 00165958691 0 0 0 0 0 0 0
-725 -675 00000000562 725 234 -183 0 0 0 0 0 218776162395 00147910839 0 0 0 0 0 0 0
-73 -67 00000000501 73 224 -188 0 0 0 0 0 1737800828749 00131825674 0 0 0 0 0 0 0
-735 -665 00000000447 735 214 -193 0 0 0 0 0 1380384264603 00117489755 0 0 0 0 0 0 0
-74 -66 00000000398 74 204 -198 0 0 0 0 0 1096478196143 00104712855 0 0 0 0 0 0 0
-745 -655 00000000355 745 194 -203 0 0 0 0 0 870963589956 0009332543 0 0 0 0 0 0 0
-75 -65 00000000316 75 184 -208 0 0 0 0 0 691830970919 00083176377 0 0 0 0 0 0 0
-755 -645 00000000282 755 174 -213 0 0 0 0 0 549540873858 00074131024 0 0 0 0 0 0 0
-76 -64 00000000251 76 164 -218 0 0 0 0 0 43651583224 00066069345 0 0 0 0 0 0 0
-765 -635 00000000224 765 154 -223 0 0 0 0 0 346736850453 00058884366 0 0 0 0 0 0 0
-77 -63 000000002 77 144 -228 0 0 0 0 0 275422870334 00052480746 0 0 0 0 0 0 0
-775 -625 00000000178 775 134 -233 0 0 0 0 0 218776162395 00046773514 0 0 0 0 0 0 0
-78 -62 00000000158 78 124 -238 0 0 0 0 0 173780082875 00041686938 0 0 0 0 0 0 0
-785 -615 00000000141 785 114 -243 0 0 0 0 0 13803842646 00037153523 0 0 0 0 0 0 0
-79 -61 00000000126 79 104 -248 0 0 0 0 0 109647819614 00033113112 0 0 0 0 0 0 0
-795 -605 00000000112 795 094 -253 0 0 0 0 0 87096358996 00029512092 0 0 0 0 0 0 0
-8 -6 000000001 8 084 -258 0 0 0 0 0 69183097092 0002630268 0 0 0 0 0 0 0
-805 -595 00000000089 805 074 -263 0 0 0 0 0 54954087386 00023442288 0 0 0 0 0 0 0
-81 -59 00000000079 81 064 -268 0 0 0 0 0 43651583224 00020892961 0 0 0 0 0 0 0
-815 -585 00000000071 815 054 -273 0 0 0 0 0 34673685045 00018620871 0 0 0 0 0 0 0
-82 -58 00000000063 82 044 -278 0 0 0 0 0 27542287033 00016595869 0 0 0 0 0 0 0
-825 -575 00000000056 825 034 -283 0 0 0 0 0 21877616239 00014791084 0 0 0 0 0 0 0
-83 -57 0000000005 83 024 -288 0 0 0 0 0 17378008287 00013182567 0 0 0 0 0 0 0
-835 -565 00000000045 835 014 -293 0 0 0 0 0 13803842646 00011748976 0 0 0 0 0 0 0
-84 -56 0000000004 84 004 -298 0 0 0 0 0 10964781961 00010471285 0 0 0 0 0 0 0
-845 -555 00000000035 845 -006 -303 0 0 0 0 0 087096359 00009332543 0 0 0 0 0 0 0
-85 -55 00000000032 85 -016 -308 0 0 0 0 0 06918309709 00008317638 0 0 0 0 0 0 0
-855 -545 00000000028 855 -026 -313 0 0 0 0 0 05495408739 00007413102 0 0 0 0 0 0 0
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-865 -535 00000000022 865 -046 -323 0 0 0 0 0 03467368505 00005888437 0 0 0 0 0 0 0
-87 -53 0000000002 87 -056 -328 0 0 0 0 0 02754228703 00005248075 0 0 0 0 0 0 0
-875 -525 00000000018 875 -066 -333 0 0 0 0 0 02187761624 00004677351 0 0 0 0 0 0 0
-88 -52 00000000016 88 -076 -338 0 0 0 0 0 01737800829 00004168694 0 0 0 0 0 0 0
-885 -515 00000000014 885 -086 -343 0 0 0 0 0 01380384265 00003715352 0 0 0 0 0 0 0
-89 -51 00000000013 89 -096 -348 0 0 0 0 0 01096478196 00003311311 0 0 0 0 0 0 0
-895 -505 00000000011 895 -106 -353 0 0 0 0 0 0087096359 00002951209 0 0 0 0 0 0 0
-9 -5 0000000001 9 -116 -358 0 0 0 0 0 00691830971 00002630268 0 0 0 0 0 0 0
-905 -495 00000000009 905 -126 -363 0 0 0 0 0 00549540874 00002344229 0 0 0 0 0 0 0
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-92 -48 00000000006 92 -156 -378 0 0 0 0 0 0027542287 00001659587 0 0 0 0 0 0 0
-925 -475 00000000006 925 -166 -383 0 0 0 0 0 00218776162 00001479108 0 0 0 0 0 0 0
-93 -47 00000000005 93 -176 -388 0 0 0 0 0 00173780083 00001318257 0 0 0 0 0 0 0
-935 -465 00000000004 935 -186 -393 0 0 0 0 0 00138038426 00001174898 0 0 0 0 0 0 0
-94 -46 00000000004 94 -196 -398 0 0 0 0 0 0010964782 00001047129 0 0 0 0 0 0 0
-945 -455 00000000004 945 -206 -403 0 0 0 0 0 00087096359 00000933254 0 0 0 0 0 0 0
-95 -45 00000000003 95 -216 -408 0 0 0 0 0 00069183097 00000831764 0 0 0 0 0 0 0
-955 -445 00000000003 955 -226 -413 0 0 0 0 0 00054954087 0000074131 0 0 0 0 0 0 0
-96 -44 00000000003 96 -236 -418 0 0 0 0 0 00043651583 00000660693 0 0 0 0 0 0 0
-965 -435 00000000002 965 -246 -423 0 0 0 0 0 00034673685 00000588844 0 0 0 0 0 0 0
-97 -43 00000000002 97 -256 -428 0 0 0 0 0 00027542287 00000524807 0 0 0 0 0 0 0
-975 -425 00000000002 975 -266 -433 0 0 0 0 0 00021877616 00000467735 0 0 0 0 0 0 0
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-985 -415 00000000001 985 -286 -443 0 0 0 0 0 00013803843 00000371535 0 0 0 0 0 0 0
-99 -41 00000000001 99 -296 -448 0 0 0 0 0 00010964782 00000331131 0 0 0 0 0 0 0
-995 -405 00000000001 995 -306 -453 0 0 0 0 0 00008709636 00000295121 0 0 0 0 0 0 0
-10 -4 00000000001 10 -316 -458 0 0 0 0 0 0000691831 00000263027 0 0 0 0 0 0 0
-1005 -395 00000000001 1005 -326 -463 0 0 0 0 0 00005495409 00000234423 0 0 0 0 0 0 0
-101 -39 00000000001 101 -336 -468 0 0 0 0 0 00004365158 0000020893 0 0 0 0 0 0 0
-1015 -385 00000000001 1015 -346 -473 0 0 0 0 0 00003467369 00000186209 0 0 0 0 0 0 0
-102 -38 00000000001 102 -356 -478 0 0 0 0 0 00002754229 00000165959 0 0 0 0 0 0 0
-1025 -375 00000000001 1025 -366 -483 0 0 0 0 0 00002187762 00000147911 0 0 0 0 0 0 0
-103 -37 00000000001 103 -376 -488 0 0 0 0 0 00001737801 00000131826 0 0 0 0 0 0 0
-1035 -365 0 1035 -386 -493 0 0 0 0 0 00001380384 0000011749 0 0 0 0 0 0 0
-104 -36 0 104 -396 -498 0 0 0 0 0 00001096478 00000104713 0 0 0 0 0 0 0
-1045 -355 0 1045 -406 -503 0 0 0 0 0 00000870964 00000093325 0 0 0 0 0 0 0
-105 -35 0 105 -416 -508 0 0 0 0 0 00000691831 00000083176 0 0 0 0 0 0 0
-1055 -345 0 1055 -426 -513 0 0 0 0 0 00000549541 00000074131 0 0 0 0 0 0 0
-106 -34 0 106 -436 -518 0 0 0 0 0 00000436516 00000066069 0 0 0 0 0 0 0
-1065 -335 0 1065 -446 -523 0 0 0 0 0 00000346737 00000058884 0 0 0 0 0 0 0
-107 -33 0 107 -456 -528 0 0 0 0 0 00000275423 00000052481 0 0 0 0 0 0 0
-1075 -325 0 1075 -466 -533 0 0 0 0 0 00000218776 00000046774 0 0 0 0 0 0 0
-108 -32 0 108 -476 -538 0 0 0 0 0 0000017378 00000041687 0 0 0 0 0 0 0
-1085 -315 0 1085 -486 -543 0 0 0 0 0 00000138038 00000037154 0 0 0 0 0 0 0
-109 -31 0 109 -496 -548 0 0 0 0 0 00000109648 00000033113 0 0 0 0 0 0 0
-1095 -305 0 1095 -506 -553 0 0 0 0 0 00000087096 00000029512 0 0 0 0 0 0 0
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-1105 -295 0 1105 -526 -563 0 0 0 0 0 00000054954 00000023442 0 0 0 0 0 0 0
-111 -29 0 111 -536 -568 0 0 0 0 0 00000043652 00000020893 0 0 0 0 0 0 0
-1115 -285 0 1115 -546 -573 0 0 0 0 0 00000034674 00000018621 0 0 0 0 0 0 0
-112 -28 0 112 -556 -578 0 0 0 0 0 00000027542 00000016596 0 0 0 0 0 0 0
-1125 -275 0 1125 -566 -583 0 0 0 0 0 00000021878 00000014791 0 0 0 0 0 0 0
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-121 -19 0 121 -736 -668 0 0 0 0 0 00000000437 00000002089 0 0 0 0 0 0 0
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-124 -16 0 124 -796 -698 0 0 0 0 0 0000000011 00000001047 0 0 0 0 0 0 0
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-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
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-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
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-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
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-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 2: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Topics Hydrolysis

Aquo metal ion gives rise to hydroxo complexes Magnesium and Iron Hydroxide solubility

David Reckhow CEE 680 34 2

Precipitation and Dissolution Environmental Significance

Engineered systems coagulation softening removal of heavy metals

Natural systems composition of natural waters formation and composition of aquatic sediments global cycling of elements

Composition of natural waters SampM 3rd ed figure 151 (pg 873) Benjamin 2nd ed figure 11

David Reckhow CEE 680 34 3

Elemental Abundance in Crust ad

David Reckhow CEE 680 34 4

dfs

David Reckhow CEE 680 34 5

From USGS 2005

Top 8IN EARTHrsquoS CRUST

Abundance of inorganics in fresh water and in earthrsquos crust

David Reckhow CEE 680 35 6

From Stumm amp Morgan 1996 Benjamin 2002 fig 11

Terrestrial water

Solubility Products General Equilibrium

AmBn(s) harr mA+n + nB-m

Solubility Product Equation Kso = [A+n]m[B-m]n

also sometimes written Ksp

Example Calcium Carbonate

sources Smith amp Martell SampM table 71 (pg362-364)

David Reckhow CEE 680 34 7

Solid Cation Anion

Kso and Q Reaction Quotient (Q)

computed value from actual measurements may not be at thermodynamic equilibrium

comparison with Ksp will tell you about tendency toward dissolution or precipitation QgtKso then water will precipitate solid phase QltKso then water will dissolve solid phase

Example Calcium Carbonate solubility Ca+2 = 40 mgL and CO3

-2 = 100 mgL as CaCO3 what is Q if Kso is 10-834 what does this tell us

David Reckhow CEE 680 34 8

Presenter
Presentation Notes
Note GFW for Ca is 40 so Q = 10-6 and system is over saturated and will precipitate CaCO3

Solubility of some simple salts Barium sulfate

BaSO4 = Ba+2 + SO4-2

Kso = 10-996 = [Ba+2][SO4-2]

How much will dissolve and what will the barium and sulfate concentrations be

How much will dissolve in a 1mM solution of Na2SO4

David Reckhow CEE 680 34 9

984

2969

1010

minus

minus

=

=

xx

( )

9667

96963

32

3969

101009712

1041010

101010

minusminus

minusminusminus

minus

minusminus

==

minusplusmnminus=

+=

+=

x

xx

xxxx

Presenter
Presentation Notes
Simplify last equation by neglecting the second ldquoxrdquo in right hand term

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
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-126 -14 0 126 -836 -718 0 0 0 0 0 00000000044 00000000661 0 0 0 0 0 0 0
-1265 -135 0 1265 -846 -723 0 0 0 0 0 00000000035 00000000589 0 0 0 0 0 0 0
-127 -13 0 127 -856 -728 0 0 0 0 0 00000000028 00000000525 0 0 0 0 0 0 0
-1275 -125 0 1275 -866 -733 0 0 0 0 0 00000000022 00000000468 0 0 0 0 0 0 0
-128 -12 0 128 -876 -738 0 0 0 0 0 00000000017 00000000417 0 0 0 0 0 0 0
-1285 -115 0 1285 -886 -743 0 0 0 0 0 00000000014 00000000372 0 0 0 0 0 0 0
-129 -11 0 129 -896 -748 0 0 0 0 0 00000000011 00000000331 0 0 0 0 0 0 0
-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
-13 -1 0 13 -916 -758 0 0 0 0 0 00000000007 00000000263 0 0 0 0 0 0 0
-1305 -095 0 1305 -926 -763 0 0 0 0 0 00000000005 00000000234 0 0 0 0 0 0 0
-131 -09 0 131 -936 -768 0 0 0 0 0 00000000004 00000000209 0 0 0 0 0 0 0
-1315 -085 0 1315 -946 -773 0 0 0 0 0 00000000003 00000000186 0 0 0 0 0 0 0
-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
-1325 -075 0 1325 -966 -783 0 0 0 0 0 00000000002 00000000148 0 0 0 0 0 0 0
-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
-1395 -005 0 1395 -1106 -853 0 0 0 0 0 0 0000000003 0 0 0 0 0 0 0
-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 3: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Precipitation and Dissolution Environmental Significance

Engineered systems coagulation softening removal of heavy metals

Natural systems composition of natural waters formation and composition of aquatic sediments global cycling of elements

Composition of natural waters SampM 3rd ed figure 151 (pg 873) Benjamin 2nd ed figure 11

David Reckhow CEE 680 34 3

Elemental Abundance in Crust ad

David Reckhow CEE 680 34 4

dfs

David Reckhow CEE 680 34 5

From USGS 2005

Top 8IN EARTHrsquoS CRUST

Abundance of inorganics in fresh water and in earthrsquos crust

David Reckhow CEE 680 35 6

From Stumm amp Morgan 1996 Benjamin 2002 fig 11

Terrestrial water

Solubility Products General Equilibrium

AmBn(s) harr mA+n + nB-m

Solubility Product Equation Kso = [A+n]m[B-m]n

also sometimes written Ksp

Example Calcium Carbonate

sources Smith amp Martell SampM table 71 (pg362-364)

David Reckhow CEE 680 34 7

Solid Cation Anion

Kso and Q Reaction Quotient (Q)

computed value from actual measurements may not be at thermodynamic equilibrium

comparison with Ksp will tell you about tendency toward dissolution or precipitation QgtKso then water will precipitate solid phase QltKso then water will dissolve solid phase

Example Calcium Carbonate solubility Ca+2 = 40 mgL and CO3

-2 = 100 mgL as CaCO3 what is Q if Kso is 10-834 what does this tell us

David Reckhow CEE 680 34 8

Presenter
Presentation Notes
Note GFW for Ca is 40 so Q = 10-6 and system is over saturated and will precipitate CaCO3

Solubility of some simple salts Barium sulfate

BaSO4 = Ba+2 + SO4-2

Kso = 10-996 = [Ba+2][SO4-2]

How much will dissolve and what will the barium and sulfate concentrations be

How much will dissolve in a 1mM solution of Na2SO4

David Reckhow CEE 680 34 9

984

2969

1010

minus

minus

=

=

xx

( )

9667

96963

32

3969

101009712

1041010

101010

minusminus

minusminusminus

minus

minusminus

==

minusplusmnminus=

+=

+=

x

xx

xxxx

Presenter
Presentation Notes
Simplify last equation by neglecting the second ldquoxrdquo in right hand term

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-28 -112 00015848932 28 1124 262 0 0 0 0 0 173780082874938 4168693834703 0 0 0 0 0 0 0
-285 -1115 00014125375 285 1114 257 0 0 0 0 0 138038426460289 3715352290972 0 0 0 0 0 0 0
-29 -111 00012589254 29 1104 252 0 0 0 0 0 109647819614319 3311311214826 0 0 0 0 0 0 0
-295 -1105 00011220185 295 1094 247 0 0 0 0 0 870963589956082 2951209226666 0 0 0 0 0 0 0
-3 -11 0001 3 1084 242 0 0 0 0 0 691830970918939 2630267991895 0 0 0 0 0 0 0
-305 -1095 00008912509 305 1074 237 0 0 0 0 0 549540873857627 234422881532 0 0 0 0 0 0 0
-31 -109 00007943282 31 1064 232 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-315 -1085 00007079458 315 1054 227 0 0 0 0 0 346736850452531 1862087136663 0 0 0 0 0 0 0
-32 -108 00006309573 32 1044 222 0 0 0 0 0 275422870333817 1659586907438 0 0 0 0 0 0 0
-325 -1075 00005623413 325 1034 217 0 0 0 0 0 218776162394955 1479108388168 0 0 0 0 0 0 0
-33 -107 00005011872 33 1024 212 0 0 0 0 0 173780082874938 1318256738556 0 0 0 0 0 0 0
-335 -1065 00004466836 335 1014 207 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-34 -106 00003981072 34 1004 202 0 0 0 0 0 109647819614319 1047128548051 0 0 0 0 0 0 0
-345 -1055 00003548134 345 994 197 0 0 0 0 0 870963589956081 933254300797 0 0 0 0 0 0 0
-35 -105 00003162278 35 984 192 0 0 0 0 0 691830970918938 831763771103 0 0 0 0 0 0 0
-355 -1045 00002818383 355 974 187 0 0 0 0 0 549540873857626 741310241301 0 0 0 0 0 0 0
-36 -104 00002511886 36 964 182 0 0 0 0 0 436515832240168 660693448008 0 0 0 0 0 0 0
-365 -1035 00002238721 365 954 177 0 0 0 0 0 346736850452532 588843655356 0 0 0 0 0 0 0
-37 -103 00001995262 37 944 172 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-375 -1025 00001778279 375 934 167 0 0 0 0 0 218776162394956 467735141287 0 0 0 0 0 0 0
-38 -102 00001584893 38 924 162 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-385 -1015 00001412538 385 914 157 0 0 0 0 0 138038426460289 371535229097 0 0 0 0 0 0 0
-39 -101 00001258925 39 904 152 0 0 0 0 0 109647819614318 331131121483 0 0 0 0 0 0 0
-395 -1005 00001122018 395 894 147 0 0 0 0 0 870963589956081 295120922667 0 0 0 0 0 0 0
-4 -10 00001 4 884 142 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-405 -995 00000891251 405 874 137 0 0 0 0 0 549540873857625 234422881532 0 0 0 0 0 0 0
-41 -99 00000794328 41 864 132 0 0 0 0 0 436515832240167 208929613085 0 0 0 0 0 0 0
-415 -985 00000707946 415 854 127 0 0 0 0 0 346736850452532 186208713666 0 0 0 0 0 0 0
-42 -98 00000630957 42 844 122 0 0 0 0 0 275422870333817 165958690744 0 0 0 0 0 0 0
-425 -975 00000562341 425 834 117 0 0 0 0 0 218776162394956 147910838817 0 0 0 0 0 0 0
-43 -97 00000501187 43 824 112 0 0 0 0 0 173780082874938 131825673856 0 0 0 0 0 0 0
-435 -965 00000446684 435 814 107 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-44 -96 00000398107 44 804 102 0 0 0 0 0 109647819614319 104712854805 0 0 0 0 0 0 0
-445 -955 00000354813 445 794 097 0 0 0 0 0 870963589956083 9332543008 0 0 0 0 0 0 0
-45 -95 00000316228 45 784 092 0 0 0 0 0 691830970918936 8317637711 0 0 0 0 0 0 0
-455 -945 00000281838 455 774 087 0 0 0 0 0 549540873857625 7413102413 0 0 0 0 0 0 0
-46 -94 00000251189 46 764 082 0 0 0 0 0 436515832240167 66069344801 0 0 0 0 0 0 0
-465 -935 00000223872 465 754 077 0 0 0 0 0 346736850452531 58884365536 0 0 0 0 0 0 0
-47 -93 00000199526 47 744 072 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-475 -925 00000177828 475 734 067 0 0 0 0 0 218776162394955 46773514129 0 0 0 0 0 0 0
-48 -92 00000158489 48 724 062 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-485 -915 00000141254 485 714 057 0 0 0 0 0 138038426460289 3715352291 0 0 0 0 0 0 0
-49 -91 00000125893 49 704 052 0 0 0 0 0 109647819614319 33113112148 0 0 0 0 0 0 0
-495 -905 00000112202 495 694 047 0 0 0 0 0 870963589956082 29512092267 0 0 0 0 0 0 0
-5 -9 000001 5 684 042 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-505 -895 00000089125 505 674 037 0 0 0 0 0 549540873857625 23442288153 0 0 0 0 0 0 0
-51 -89 00000079433 51 664 032 0 0 0 0 0 436515832240167 20892961309 0 0 0 0 0 0 0
-515 -885 00000070795 515 654 027 0 0 0 0 0 346736850452532 18620871367 0 0 0 0 0 0 0
-52 -88 00000063096 52 644 022 0 0 0 0 0 275422870333817 16595869074 0 0 0 0 0 0 0
-525 -875 00000056234 525 634 017 0 0 0 0 0 218776162394956 14791083882 0 0 0 0 0 0 0
-53 -87 00000050119 53 624 012 0 0 0 0 0 173780082874938 13182567386 0 0 0 0 0 0 0
-535 -865 00000044668 535 614 007 0 0 0 0 0 138038426460289 11748975549 0 0 0 0 0 0 0
-54 -86 00000039811 54 604 002 0 0 0 0 0 109647819614318 10471285481 0 0 0 0 0 0 0
-545 -855 00000035481 545 594 -003 0 0 0 0 0 870963589956081 09332543008 0 0 0 0 0 0 0
-55 -85 00000031623 55 584 -008 0 0 0 0 0 691830970918937 08317637711 0 0 0 0 0 0 0
-555 -845 00000028184 555 574 -013 0 0 0 0 0 549540873857626 07413102413 0 0 0 0 0 0 0
-56 -84 00000025119 56 564 -018 0 0 0 0 0 436515832240167 0660693448 0 0 0 0 0 0 0
-565 -835 00000022387 565 554 -023 0 0 0 0 0 346736850452531 05888436554 0 0 0 0 0 0 0
-57 -83 00000019953 57 544 -028 0 0 0 0 0 275422870333817 05248074602 0 0 0 0 0 0 0
-575 -825 00000017783 575 534 -033 0 0 0 0 0 218776162394955 04677351413 0 0 0 0 0 0 0
-58 -82 00000015849 58 524 -038 0 0 0 0 0 173780082874938 04168693835 0 0 0 0 0 0 0
-585 -815 00000014125 585 514 -043 0 0 0 0 0 138038426460289 03715352291 0 0 0 0 0 0 0
-59 -81 00000012589 59 504 -048 0 0 0 0 0 109647819614318 03311311215 0 0 0 0 0 0 0
-595 -805 0000001122 595 494 -053 0 0 0 0 0 870963589956081 02951209227 0 0 0 0 0 0 0
-6 -8 0000001 6 484 -058 0 0 0 0 0 691830970918937 02630267992 0 0 0 0 0 0 0
-605 -795 00000008913 605 474 -063 0 0 0 0 0 549540873857625 02344228815 0 0 0 0 0 0 0
-61 -79 00000007943 61 464 -068 0 0 0 0 0 436515832240167 02089296131 0 0 0 0 0 0 0
-615 -785 00000007079 615 454 -073 0 0 0 0 0 346736850452531 01862087137 0 0 0 0 0 0 0
-62 -78 0000000631 62 444 -078 0 0 0 0 0 275422870333817 01659586907 0 0 0 0 0 0 0
-625 -775 00000005623 625 434 -083 0 0 0 0 0 218776162394955 01479108388 0 0 0 0 0 0 0
-63 -77 00000005012 63 424 -088 0 0 0 0 0 173780082874938 01318256739 0 0 0 0 0 0 0
-635 -765 00000004467 635 414 -093 0 0 0 0 0 138038426460289 01174897555 0 0 0 0 0 0 0
-64 -76 00000003981 64 404 -098 0 0 0 0 0 109647819614318 01047128548 0 0 0 0 0 0 0
-645 -755 00000003548 645 394 -103 0 0 0 0 0 87096358995608 00933254301 0 0 0 0 0 0 0
-65 -75 00000003162 65 384 -108 0 0 0 0 0 69183097091894 00831763771 0 0 0 0 0 0 0
-655 -745 00000002818 655 374 -113 0 0 0 0 0 54954087385762 00741310241 0 0 0 0 0 0 0
-66 -74 00000002512 66 364 -118 0 0 0 0 0 43651583224017 00660693448 0 0 0 0 0 0 0
-665 -735 00000002239 665 354 -123 0 0 0 0 0 34673685045253 00588843655 0 0 0 0 0 0 0
-67 -73 00000001995 67 344 -128 0 0 0 0 0 27542287033382 0052480746 0 0 0 0 0 0 0
-675 -725 00000001778 675 334 -133 0 0 0 0 0 21877616239496 00467735141 0 0 0 0 0 0 0
-68 -72 00000001585 68 324 -138 0 0 0 0 0 17378008287494 00416869383 0 0 0 0 0 0 0
-685 -715 00000001413 685 314 -143 0 0 0 0 0 13803842646029 00371535229 0 0 0 0 0 0 0
-69 -71 00000001259 69 304 -148 0 0 0 0 0 10964781961432 00331131121 0 0 0 0 0 0 0
-695 -705 00000001122 695 294 -153 0 0 0 0 0 8709635899561 00295120923 0 0 0 0 0 0 0
-7 -7 00000001 7 284 -158 0 0 0 0 0 6918309709189 00263026799 0 0 0 0 0 0 0
-705 -695 00000000891 705 274 -163 0 0 0 0 0 5495408738576 00234422882 0 0 0 0 0 0 0
-71 -69 00000000794 71 264 -168 0 0 0 0 0 4365158322402 00208929613 0 0 0 0 0 0 0
-715 -685 00000000708 715 254 -173 0 0 0 0 0 3467368504525 00186208714 0 0 0 0 0 0 0
-72 -68 00000000631 72 244 -178 0 0 0 0 0 2754228703338 00165958691 0 0 0 0 0 0 0
-725 -675 00000000562 725 234 -183 0 0 0 0 0 218776162395 00147910839 0 0 0 0 0 0 0
-73 -67 00000000501 73 224 -188 0 0 0 0 0 1737800828749 00131825674 0 0 0 0 0 0 0
-735 -665 00000000447 735 214 -193 0 0 0 0 0 1380384264603 00117489755 0 0 0 0 0 0 0
-74 -66 00000000398 74 204 -198 0 0 0 0 0 1096478196143 00104712855 0 0 0 0 0 0 0
-745 -655 00000000355 745 194 -203 0 0 0 0 0 870963589956 0009332543 0 0 0 0 0 0 0
-75 -65 00000000316 75 184 -208 0 0 0 0 0 691830970919 00083176377 0 0 0 0 0 0 0
-755 -645 00000000282 755 174 -213 0 0 0 0 0 549540873858 00074131024 0 0 0 0 0 0 0
-76 -64 00000000251 76 164 -218 0 0 0 0 0 43651583224 00066069345 0 0 0 0 0 0 0
-765 -635 00000000224 765 154 -223 0 0 0 0 0 346736850453 00058884366 0 0 0 0 0 0 0
-77 -63 000000002 77 144 -228 0 0 0 0 0 275422870334 00052480746 0 0 0 0 0 0 0
-775 -625 00000000178 775 134 -233 0 0 0 0 0 218776162395 00046773514 0 0 0 0 0 0 0
-78 -62 00000000158 78 124 -238 0 0 0 0 0 173780082875 00041686938 0 0 0 0 0 0 0
-785 -615 00000000141 785 114 -243 0 0 0 0 0 13803842646 00037153523 0 0 0 0 0 0 0
-79 -61 00000000126 79 104 -248 0 0 0 0 0 109647819614 00033113112 0 0 0 0 0 0 0
-795 -605 00000000112 795 094 -253 0 0 0 0 0 87096358996 00029512092 0 0 0 0 0 0 0
-8 -6 000000001 8 084 -258 0 0 0 0 0 69183097092 0002630268 0 0 0 0 0 0 0
-805 -595 00000000089 805 074 -263 0 0 0 0 0 54954087386 00023442288 0 0 0 0 0 0 0
-81 -59 00000000079 81 064 -268 0 0 0 0 0 43651583224 00020892961 0 0 0 0 0 0 0
-815 -585 00000000071 815 054 -273 0 0 0 0 0 34673685045 00018620871 0 0 0 0 0 0 0
-82 -58 00000000063 82 044 -278 0 0 0 0 0 27542287033 00016595869 0 0 0 0 0 0 0
-825 -575 00000000056 825 034 -283 0 0 0 0 0 21877616239 00014791084 0 0 0 0 0 0 0
-83 -57 0000000005 83 024 -288 0 0 0 0 0 17378008287 00013182567 0 0 0 0 0 0 0
-835 -565 00000000045 835 014 -293 0 0 0 0 0 13803842646 00011748976 0 0 0 0 0 0 0
-84 -56 0000000004 84 004 -298 0 0 0 0 0 10964781961 00010471285 0 0 0 0 0 0 0
-845 -555 00000000035 845 -006 -303 0 0 0 0 0 087096359 00009332543 0 0 0 0 0 0 0
-85 -55 00000000032 85 -016 -308 0 0 0 0 0 06918309709 00008317638 0 0 0 0 0 0 0
-855 -545 00000000028 855 -026 -313 0 0 0 0 0 05495408739 00007413102 0 0 0 0 0 0 0
-86 -54 00000000025 86 -036 -318 0 0 0 0 0 04365158322 00006606934 0 0 0 0 0 0 0
-865 -535 00000000022 865 -046 -323 0 0 0 0 0 03467368505 00005888437 0 0 0 0 0 0 0
-87 -53 0000000002 87 -056 -328 0 0 0 0 0 02754228703 00005248075 0 0 0 0 0 0 0
-875 -525 00000000018 875 -066 -333 0 0 0 0 0 02187761624 00004677351 0 0 0 0 0 0 0
-88 -52 00000000016 88 -076 -338 0 0 0 0 0 01737800829 00004168694 0 0 0 0 0 0 0
-885 -515 00000000014 885 -086 -343 0 0 0 0 0 01380384265 00003715352 0 0 0 0 0 0 0
-89 -51 00000000013 89 -096 -348 0 0 0 0 0 01096478196 00003311311 0 0 0 0 0 0 0
-895 -505 00000000011 895 -106 -353 0 0 0 0 0 0087096359 00002951209 0 0 0 0 0 0 0
-9 -5 0000000001 9 -116 -358 0 0 0 0 0 00691830971 00002630268 0 0 0 0 0 0 0
-905 -495 00000000009 905 -126 -363 0 0 0 0 0 00549540874 00002344229 0 0 0 0 0 0 0
-91 -49 00000000008 91 -136 -368 0 0 0 0 0 00436515832 00002089296 0 0 0 0 0 0 0
-915 -485 00000000007 915 -146 -373 0 0 0 0 0 0034673685 00001862087 0 0 0 0 0 0 0
-92 -48 00000000006 92 -156 -378 0 0 0 0 0 0027542287 00001659587 0 0 0 0 0 0 0
-925 -475 00000000006 925 -166 -383 0 0 0 0 0 00218776162 00001479108 0 0 0 0 0 0 0
-93 -47 00000000005 93 -176 -388 0 0 0 0 0 00173780083 00001318257 0 0 0 0 0 0 0
-935 -465 00000000004 935 -186 -393 0 0 0 0 0 00138038426 00001174898 0 0 0 0 0 0 0
-94 -46 00000000004 94 -196 -398 0 0 0 0 0 0010964782 00001047129 0 0 0 0 0 0 0
-945 -455 00000000004 945 -206 -403 0 0 0 0 0 00087096359 00000933254 0 0 0 0 0 0 0
-95 -45 00000000003 95 -216 -408 0 0 0 0 0 00069183097 00000831764 0 0 0 0 0 0 0
-955 -445 00000000003 955 -226 -413 0 0 0 0 0 00054954087 0000074131 0 0 0 0 0 0 0
-96 -44 00000000003 96 -236 -418 0 0 0 0 0 00043651583 00000660693 0 0 0 0 0 0 0
-965 -435 00000000002 965 -246 -423 0 0 0 0 0 00034673685 00000588844 0 0 0 0 0 0 0
-97 -43 00000000002 97 -256 -428 0 0 0 0 0 00027542287 00000524807 0 0 0 0 0 0 0
-975 -425 00000000002 975 -266 -433 0 0 0 0 0 00021877616 00000467735 0 0 0 0 0 0 0
-98 -42 00000000002 98 -276 -438 0 0 0 0 0 00017378008 00000416869 0 0 0 0 0 0 0
-985 -415 00000000001 985 -286 -443 0 0 0 0 0 00013803843 00000371535 0 0 0 0 0 0 0
-99 -41 00000000001 99 -296 -448 0 0 0 0 0 00010964782 00000331131 0 0 0 0 0 0 0
-995 -405 00000000001 995 -306 -453 0 0 0 0 0 00008709636 00000295121 0 0 0 0 0 0 0
-10 -4 00000000001 10 -316 -458 0 0 0 0 0 0000691831 00000263027 0 0 0 0 0 0 0
-1005 -395 00000000001 1005 -326 -463 0 0 0 0 0 00005495409 00000234423 0 0 0 0 0 0 0
-101 -39 00000000001 101 -336 -468 0 0 0 0 0 00004365158 0000020893 0 0 0 0 0 0 0
-1015 -385 00000000001 1015 -346 -473 0 0 0 0 0 00003467369 00000186209 0 0 0 0 0 0 0
-102 -38 00000000001 102 -356 -478 0 0 0 0 0 00002754229 00000165959 0 0 0 0 0 0 0
-1025 -375 00000000001 1025 -366 -483 0 0 0 0 0 00002187762 00000147911 0 0 0 0 0 0 0
-103 -37 00000000001 103 -376 -488 0 0 0 0 0 00001737801 00000131826 0 0 0 0 0 0 0
-1035 -365 0 1035 -386 -493 0 0 0 0 0 00001380384 0000011749 0 0 0 0 0 0 0
-104 -36 0 104 -396 -498 0 0 0 0 0 00001096478 00000104713 0 0 0 0 0 0 0
-1045 -355 0 1045 -406 -503 0 0 0 0 0 00000870964 00000093325 0 0 0 0 0 0 0
-105 -35 0 105 -416 -508 0 0 0 0 0 00000691831 00000083176 0 0 0 0 0 0 0
-1055 -345 0 1055 -426 -513 0 0 0 0 0 00000549541 00000074131 0 0 0 0 0 0 0
-106 -34 0 106 -436 -518 0 0 0 0 0 00000436516 00000066069 0 0 0 0 0 0 0
-1065 -335 0 1065 -446 -523 0 0 0 0 0 00000346737 00000058884 0 0 0 0 0 0 0
-107 -33 0 107 -456 -528 0 0 0 0 0 00000275423 00000052481 0 0 0 0 0 0 0
-1075 -325 0 1075 -466 -533 0 0 0 0 0 00000218776 00000046774 0 0 0 0 0 0 0
-108 -32 0 108 -476 -538 0 0 0 0 0 0000017378 00000041687 0 0 0 0 0 0 0
-1085 -315 0 1085 -486 -543 0 0 0 0 0 00000138038 00000037154 0 0 0 0 0 0 0
-109 -31 0 109 -496 -548 0 0 0 0 0 00000109648 00000033113 0 0 0 0 0 0 0
-1095 -305 0 1095 -506 -553 0 0 0 0 0 00000087096 00000029512 0 0 0 0 0 0 0
-11 -3 0 11 -516 -558 0 0 0 0 0 00000069183 00000026303 0 0 0 0 0 0 0
-1105 -295 0 1105 -526 -563 0 0 0 0 0 00000054954 00000023442 0 0 0 0 0 0 0
-111 -29 0 111 -536 -568 0 0 0 0 0 00000043652 00000020893 0 0 0 0 0 0 0
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-112 -28 0 112 -556 -578 0 0 0 0 0 00000027542 00000016596 0 0 0 0 0 0 0
-1125 -275 0 1125 -566 -583 0 0 0 0 0 00000021878 00000014791 0 0 0 0 0 0 0
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-1185 -215 0 1185 -686 -643 0 0 0 0 0 0000000138 00000003715 0 0 0 0 0 0 0
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-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
-13 -1 0 13 -916 -758 0 0 0 0 0 00000000007 00000000263 0 0 0 0 0 0 0
-1305 -095 0 1305 -926 -763 0 0 0 0 0 00000000005 00000000234 0 0 0 0 0 0 0
-131 -09 0 131 -936 -768 0 0 0 0 0 00000000004 00000000209 0 0 0 0 0 0 0
-1315 -085 0 1315 -946 -773 0 0 0 0 0 00000000003 00000000186 0 0 0 0 0 0 0
-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
-1325 -075 0 1325 -966 -783 0 0 0 0 0 00000000002 00000000148 0 0 0 0 0 0 0
-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
-1395 -005 0 1395 -1106 -853 0 0 0 0 0 0 0000000003 0 0 0 0 0 0 0
-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 4: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Elemental Abundance in Crust ad

David Reckhow CEE 680 34 4

dfs

David Reckhow CEE 680 34 5

From USGS 2005

Top 8IN EARTHrsquoS CRUST

Abundance of inorganics in fresh water and in earthrsquos crust

David Reckhow CEE 680 35 6

From Stumm amp Morgan 1996 Benjamin 2002 fig 11

Terrestrial water

Solubility Products General Equilibrium

AmBn(s) harr mA+n + nB-m

Solubility Product Equation Kso = [A+n]m[B-m]n

also sometimes written Ksp

Example Calcium Carbonate

sources Smith amp Martell SampM table 71 (pg362-364)

David Reckhow CEE 680 34 7

Solid Cation Anion

Kso and Q Reaction Quotient (Q)

computed value from actual measurements may not be at thermodynamic equilibrium

comparison with Ksp will tell you about tendency toward dissolution or precipitation QgtKso then water will precipitate solid phase QltKso then water will dissolve solid phase

Example Calcium Carbonate solubility Ca+2 = 40 mgL and CO3

-2 = 100 mgL as CaCO3 what is Q if Kso is 10-834 what does this tell us

David Reckhow CEE 680 34 8

Presenter
Presentation Notes
Note GFW for Ca is 40 so Q = 10-6 and system is over saturated and will precipitate CaCO3

Solubility of some simple salts Barium sulfate

BaSO4 = Ba+2 + SO4-2

Kso = 10-996 = [Ba+2][SO4-2]

How much will dissolve and what will the barium and sulfate concentrations be

How much will dissolve in a 1mM solution of Na2SO4

David Reckhow CEE 680 34 9

984

2969

1010

minus

minus

=

=

xx

( )

9667

96963

32

3969

101009712

1041010

101010

minusminus

minusminusminus

minus

minusminus

==

minusplusmnminus=

+=

+=

x

xx

xxxx

Presenter
Presentation Notes
Simplify last equation by neglecting the second ldquoxrdquo in right hand term

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
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-1165 -235 0 1165 -646 -623 0 0 0 0 0 00000003467 00000005888 0 0 0 0 0 0 0
-117 -23 0 117 -656 -628 0 0 0 0 0 00000002754 00000005248 0 0 0 0 0 0 0
-1175 -225 0 1175 -666 -633 0 0 0 0 0 00000002188 00000004677 0 0 0 0 0 0 0
-118 -22 0 118 -676 -638 0 0 0 0 0 00000001738 00000004169 0 0 0 0 0 0 0
-1185 -215 0 1185 -686 -643 0 0 0 0 0 0000000138 00000003715 0 0 0 0 0 0 0
-119 -21 0 119 -696 -648 0 0 0 0 0 00000001096 00000003311 0 0 0 0 0 0 0
-1195 -205 0 1195 -706 -653 0 0 0 0 0 00000000871 00000002951 0 0 0 0 0 0 0
-12 -2 0 12 -716 -658 0 0 0 0 0 00000000692 0000000263 0 0 0 0 0 0 0
-1205 -195 0 1205 -726 -663 0 0 0 0 0 0000000055 00000002344 0 0 0 0 0 0 0
-121 -19 0 121 -736 -668 0 0 0 0 0 00000000437 00000002089 0 0 0 0 0 0 0
-1215 -185 0 1215 -746 -673 0 0 0 0 0 00000000347 00000001862 0 0 0 0 0 0 0
-122 -18 0 122 -756 -678 0 0 0 0 0 00000000275 0000000166 0 0 0 0 0 0 0
-1225 -175 0 1225 -766 -683 0 0 0 0 0 00000000219 00000001479 0 0 0 0 0 0 0
-123 -17 0 123 -776 -688 0 0 0 0 0 00000000174 00000001318 0 0 0 0 0 0 0
-1235 -165 0 1235 -786 -693 0 0 0 0 0 00000000138 00000001175 0 0 0 0 0 0 0
-124 -16 0 124 -796 -698 0 0 0 0 0 0000000011 00000001047 0 0 0 0 0 0 0
-1245 -155 0 1245 -806 -703 0 0 0 0 0 00000000087 00000000933 0 0 0 0 0 0 0
-125 -15 0 125 -816 -708 0 0 0 0 0 00000000069 00000000832 0 0 0 0 0 0 0
-1255 -145 0 1255 -826 -713 0 0 0 0 0 00000000055 00000000741 0 0 0 0 0 0 0
-126 -14 0 126 -836 -718 0 0 0 0 0 00000000044 00000000661 0 0 0 0 0 0 0
-1265 -135 0 1265 -846 -723 0 0 0 0 0 00000000035 00000000589 0 0 0 0 0 0 0
-127 -13 0 127 -856 -728 0 0 0 0 0 00000000028 00000000525 0 0 0 0 0 0 0
-1275 -125 0 1275 -866 -733 0 0 0 0 0 00000000022 00000000468 0 0 0 0 0 0 0
-128 -12 0 128 -876 -738 0 0 0 0 0 00000000017 00000000417 0 0 0 0 0 0 0
-1285 -115 0 1285 -886 -743 0 0 0 0 0 00000000014 00000000372 0 0 0 0 0 0 0
-129 -11 0 129 -896 -748 0 0 0 0 0 00000000011 00000000331 0 0 0 0 0 0 0
-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
-13 -1 0 13 -916 -758 0 0 0 0 0 00000000007 00000000263 0 0 0 0 0 0 0
-1305 -095 0 1305 -926 -763 0 0 0 0 0 00000000005 00000000234 0 0 0 0 0 0 0
-131 -09 0 131 -936 -768 0 0 0 0 0 00000000004 00000000209 0 0 0 0 0 0 0
-1315 -085 0 1315 -946 -773 0 0 0 0 0 00000000003 00000000186 0 0 0 0 0 0 0
-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
-1325 -075 0 1325 -966 -783 0 0 0 0 0 00000000002 00000000148 0 0 0 0 0 0 0
-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
-1395 -005 0 1395 -1106 -853 0 0 0 0 0 0 0000000003 0 0 0 0 0 0 0
-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 5: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

dfs

David Reckhow CEE 680 34 5

From USGS 2005

Top 8IN EARTHrsquoS CRUST

Abundance of inorganics in fresh water and in earthrsquos crust

David Reckhow CEE 680 35 6

From Stumm amp Morgan 1996 Benjamin 2002 fig 11

Terrestrial water

Solubility Products General Equilibrium

AmBn(s) harr mA+n + nB-m

Solubility Product Equation Kso = [A+n]m[B-m]n

also sometimes written Ksp

Example Calcium Carbonate

sources Smith amp Martell SampM table 71 (pg362-364)

David Reckhow CEE 680 34 7

Solid Cation Anion

Kso and Q Reaction Quotient (Q)

computed value from actual measurements may not be at thermodynamic equilibrium

comparison with Ksp will tell you about tendency toward dissolution or precipitation QgtKso then water will precipitate solid phase QltKso then water will dissolve solid phase

Example Calcium Carbonate solubility Ca+2 = 40 mgL and CO3

-2 = 100 mgL as CaCO3 what is Q if Kso is 10-834 what does this tell us

David Reckhow CEE 680 34 8

Presenter
Presentation Notes
Note GFW for Ca is 40 so Q = 10-6 and system is over saturated and will precipitate CaCO3

Solubility of some simple salts Barium sulfate

BaSO4 = Ba+2 + SO4-2

Kso = 10-996 = [Ba+2][SO4-2]

How much will dissolve and what will the barium and sulfate concentrations be

How much will dissolve in a 1mM solution of Na2SO4

David Reckhow CEE 680 34 9

984

2969

1010

minus

minus

=

=

xx

( )

9667

96963

32

3969

101009712

1041010

101010

minusminus

minusminusminus

minus

minusminus

==

minusplusmnminus=

+=

+=

x

xx

xxxx

Presenter
Presentation Notes
Simplify last equation by neglecting the second ldquoxrdquo in right hand term

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-28 -112 00015848932 28 1124 262 0 0 0 0 0 173780082874938 4168693834703 0 0 0 0 0 0 0
-285 -1115 00014125375 285 1114 257 0 0 0 0 0 138038426460289 3715352290972 0 0 0 0 0 0 0
-29 -111 00012589254 29 1104 252 0 0 0 0 0 109647819614319 3311311214826 0 0 0 0 0 0 0
-295 -1105 00011220185 295 1094 247 0 0 0 0 0 870963589956082 2951209226666 0 0 0 0 0 0 0
-3 -11 0001 3 1084 242 0 0 0 0 0 691830970918939 2630267991895 0 0 0 0 0 0 0
-305 -1095 00008912509 305 1074 237 0 0 0 0 0 549540873857627 234422881532 0 0 0 0 0 0 0
-31 -109 00007943282 31 1064 232 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-315 -1085 00007079458 315 1054 227 0 0 0 0 0 346736850452531 1862087136663 0 0 0 0 0 0 0
-32 -108 00006309573 32 1044 222 0 0 0 0 0 275422870333817 1659586907438 0 0 0 0 0 0 0
-325 -1075 00005623413 325 1034 217 0 0 0 0 0 218776162394955 1479108388168 0 0 0 0 0 0 0
-33 -107 00005011872 33 1024 212 0 0 0 0 0 173780082874938 1318256738556 0 0 0 0 0 0 0
-335 -1065 00004466836 335 1014 207 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-34 -106 00003981072 34 1004 202 0 0 0 0 0 109647819614319 1047128548051 0 0 0 0 0 0 0
-345 -1055 00003548134 345 994 197 0 0 0 0 0 870963589956081 933254300797 0 0 0 0 0 0 0
-35 -105 00003162278 35 984 192 0 0 0 0 0 691830970918938 831763771103 0 0 0 0 0 0 0
-355 -1045 00002818383 355 974 187 0 0 0 0 0 549540873857626 741310241301 0 0 0 0 0 0 0
-36 -104 00002511886 36 964 182 0 0 0 0 0 436515832240168 660693448008 0 0 0 0 0 0 0
-365 -1035 00002238721 365 954 177 0 0 0 0 0 346736850452532 588843655356 0 0 0 0 0 0 0
-37 -103 00001995262 37 944 172 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-375 -1025 00001778279 375 934 167 0 0 0 0 0 218776162394956 467735141287 0 0 0 0 0 0 0
-38 -102 00001584893 38 924 162 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-385 -1015 00001412538 385 914 157 0 0 0 0 0 138038426460289 371535229097 0 0 0 0 0 0 0
-39 -101 00001258925 39 904 152 0 0 0 0 0 109647819614318 331131121483 0 0 0 0 0 0 0
-395 -1005 00001122018 395 894 147 0 0 0 0 0 870963589956081 295120922667 0 0 0 0 0 0 0
-4 -10 00001 4 884 142 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-405 -995 00000891251 405 874 137 0 0 0 0 0 549540873857625 234422881532 0 0 0 0 0 0 0
-41 -99 00000794328 41 864 132 0 0 0 0 0 436515832240167 208929613085 0 0 0 0 0 0 0
-415 -985 00000707946 415 854 127 0 0 0 0 0 346736850452532 186208713666 0 0 0 0 0 0 0
-42 -98 00000630957 42 844 122 0 0 0 0 0 275422870333817 165958690744 0 0 0 0 0 0 0
-425 -975 00000562341 425 834 117 0 0 0 0 0 218776162394956 147910838817 0 0 0 0 0 0 0
-43 -97 00000501187 43 824 112 0 0 0 0 0 173780082874938 131825673856 0 0 0 0 0 0 0
-435 -965 00000446684 435 814 107 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-44 -96 00000398107 44 804 102 0 0 0 0 0 109647819614319 104712854805 0 0 0 0 0 0 0
-445 -955 00000354813 445 794 097 0 0 0 0 0 870963589956083 9332543008 0 0 0 0 0 0 0
-45 -95 00000316228 45 784 092 0 0 0 0 0 691830970918936 8317637711 0 0 0 0 0 0 0
-455 -945 00000281838 455 774 087 0 0 0 0 0 549540873857625 7413102413 0 0 0 0 0 0 0
-46 -94 00000251189 46 764 082 0 0 0 0 0 436515832240167 66069344801 0 0 0 0 0 0 0
-465 -935 00000223872 465 754 077 0 0 0 0 0 346736850452531 58884365536 0 0 0 0 0 0 0
-47 -93 00000199526 47 744 072 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-475 -925 00000177828 475 734 067 0 0 0 0 0 218776162394955 46773514129 0 0 0 0 0 0 0
-48 -92 00000158489 48 724 062 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-485 -915 00000141254 485 714 057 0 0 0 0 0 138038426460289 3715352291 0 0 0 0 0 0 0
-49 -91 00000125893 49 704 052 0 0 0 0 0 109647819614319 33113112148 0 0 0 0 0 0 0
-495 -905 00000112202 495 694 047 0 0 0 0 0 870963589956082 29512092267 0 0 0 0 0 0 0
-5 -9 000001 5 684 042 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-505 -895 00000089125 505 674 037 0 0 0 0 0 549540873857625 23442288153 0 0 0 0 0 0 0
-51 -89 00000079433 51 664 032 0 0 0 0 0 436515832240167 20892961309 0 0 0 0 0 0 0
-515 -885 00000070795 515 654 027 0 0 0 0 0 346736850452532 18620871367 0 0 0 0 0 0 0
-52 -88 00000063096 52 644 022 0 0 0 0 0 275422870333817 16595869074 0 0 0 0 0 0 0
-525 -875 00000056234 525 634 017 0 0 0 0 0 218776162394956 14791083882 0 0 0 0 0 0 0
-53 -87 00000050119 53 624 012 0 0 0 0 0 173780082874938 13182567386 0 0 0 0 0 0 0
-535 -865 00000044668 535 614 007 0 0 0 0 0 138038426460289 11748975549 0 0 0 0 0 0 0
-54 -86 00000039811 54 604 002 0 0 0 0 0 109647819614318 10471285481 0 0 0 0 0 0 0
-545 -855 00000035481 545 594 -003 0 0 0 0 0 870963589956081 09332543008 0 0 0 0 0 0 0
-55 -85 00000031623 55 584 -008 0 0 0 0 0 691830970918937 08317637711 0 0 0 0 0 0 0
-555 -845 00000028184 555 574 -013 0 0 0 0 0 549540873857626 07413102413 0 0 0 0 0 0 0
-56 -84 00000025119 56 564 -018 0 0 0 0 0 436515832240167 0660693448 0 0 0 0 0 0 0
-565 -835 00000022387 565 554 -023 0 0 0 0 0 346736850452531 05888436554 0 0 0 0 0 0 0
-57 -83 00000019953 57 544 -028 0 0 0 0 0 275422870333817 05248074602 0 0 0 0 0 0 0
-575 -825 00000017783 575 534 -033 0 0 0 0 0 218776162394955 04677351413 0 0 0 0 0 0 0
-58 -82 00000015849 58 524 -038 0 0 0 0 0 173780082874938 04168693835 0 0 0 0 0 0 0
-585 -815 00000014125 585 514 -043 0 0 0 0 0 138038426460289 03715352291 0 0 0 0 0 0 0
-59 -81 00000012589 59 504 -048 0 0 0 0 0 109647819614318 03311311215 0 0 0 0 0 0 0
-595 -805 0000001122 595 494 -053 0 0 0 0 0 870963589956081 02951209227 0 0 0 0 0 0 0
-6 -8 0000001 6 484 -058 0 0 0 0 0 691830970918937 02630267992 0 0 0 0 0 0 0
-605 -795 00000008913 605 474 -063 0 0 0 0 0 549540873857625 02344228815 0 0 0 0 0 0 0
-61 -79 00000007943 61 464 -068 0 0 0 0 0 436515832240167 02089296131 0 0 0 0 0 0 0
-615 -785 00000007079 615 454 -073 0 0 0 0 0 346736850452531 01862087137 0 0 0 0 0 0 0
-62 -78 0000000631 62 444 -078 0 0 0 0 0 275422870333817 01659586907 0 0 0 0 0 0 0
-625 -775 00000005623 625 434 -083 0 0 0 0 0 218776162394955 01479108388 0 0 0 0 0 0 0
-63 -77 00000005012 63 424 -088 0 0 0 0 0 173780082874938 01318256739 0 0 0 0 0 0 0
-635 -765 00000004467 635 414 -093 0 0 0 0 0 138038426460289 01174897555 0 0 0 0 0 0 0
-64 -76 00000003981 64 404 -098 0 0 0 0 0 109647819614318 01047128548 0 0 0 0 0 0 0
-645 -755 00000003548 645 394 -103 0 0 0 0 0 87096358995608 00933254301 0 0 0 0 0 0 0
-65 -75 00000003162 65 384 -108 0 0 0 0 0 69183097091894 00831763771 0 0 0 0 0 0 0
-655 -745 00000002818 655 374 -113 0 0 0 0 0 54954087385762 00741310241 0 0 0 0 0 0 0
-66 -74 00000002512 66 364 -118 0 0 0 0 0 43651583224017 00660693448 0 0 0 0 0 0 0
-665 -735 00000002239 665 354 -123 0 0 0 0 0 34673685045253 00588843655 0 0 0 0 0 0 0
-67 -73 00000001995 67 344 -128 0 0 0 0 0 27542287033382 0052480746 0 0 0 0 0 0 0
-675 -725 00000001778 675 334 -133 0 0 0 0 0 21877616239496 00467735141 0 0 0 0 0 0 0
-68 -72 00000001585 68 324 -138 0 0 0 0 0 17378008287494 00416869383 0 0 0 0 0 0 0
-685 -715 00000001413 685 314 -143 0 0 0 0 0 13803842646029 00371535229 0 0 0 0 0 0 0
-69 -71 00000001259 69 304 -148 0 0 0 0 0 10964781961432 00331131121 0 0 0 0 0 0 0
-695 -705 00000001122 695 294 -153 0 0 0 0 0 8709635899561 00295120923 0 0 0 0 0 0 0
-7 -7 00000001 7 284 -158 0 0 0 0 0 6918309709189 00263026799 0 0 0 0 0 0 0
-705 -695 00000000891 705 274 -163 0 0 0 0 0 5495408738576 00234422882 0 0 0 0 0 0 0
-71 -69 00000000794 71 264 -168 0 0 0 0 0 4365158322402 00208929613 0 0 0 0 0 0 0
-715 -685 00000000708 715 254 -173 0 0 0 0 0 3467368504525 00186208714 0 0 0 0 0 0 0
-72 -68 00000000631 72 244 -178 0 0 0 0 0 2754228703338 00165958691 0 0 0 0 0 0 0
-725 -675 00000000562 725 234 -183 0 0 0 0 0 218776162395 00147910839 0 0 0 0 0 0 0
-73 -67 00000000501 73 224 -188 0 0 0 0 0 1737800828749 00131825674 0 0 0 0 0 0 0
-735 -665 00000000447 735 214 -193 0 0 0 0 0 1380384264603 00117489755 0 0 0 0 0 0 0
-74 -66 00000000398 74 204 -198 0 0 0 0 0 1096478196143 00104712855 0 0 0 0 0 0 0
-745 -655 00000000355 745 194 -203 0 0 0 0 0 870963589956 0009332543 0 0 0 0 0 0 0
-75 -65 00000000316 75 184 -208 0 0 0 0 0 691830970919 00083176377 0 0 0 0 0 0 0
-755 -645 00000000282 755 174 -213 0 0 0 0 0 549540873858 00074131024 0 0 0 0 0 0 0
-76 -64 00000000251 76 164 -218 0 0 0 0 0 43651583224 00066069345 0 0 0 0 0 0 0
-765 -635 00000000224 765 154 -223 0 0 0 0 0 346736850453 00058884366 0 0 0 0 0 0 0
-77 -63 000000002 77 144 -228 0 0 0 0 0 275422870334 00052480746 0 0 0 0 0 0 0
-775 -625 00000000178 775 134 -233 0 0 0 0 0 218776162395 00046773514 0 0 0 0 0 0 0
-78 -62 00000000158 78 124 -238 0 0 0 0 0 173780082875 00041686938 0 0 0 0 0 0 0
-785 -615 00000000141 785 114 -243 0 0 0 0 0 13803842646 00037153523 0 0 0 0 0 0 0
-79 -61 00000000126 79 104 -248 0 0 0 0 0 109647819614 00033113112 0 0 0 0 0 0 0
-795 -605 00000000112 795 094 -253 0 0 0 0 0 87096358996 00029512092 0 0 0 0 0 0 0
-8 -6 000000001 8 084 -258 0 0 0 0 0 69183097092 0002630268 0 0 0 0 0 0 0
-805 -595 00000000089 805 074 -263 0 0 0 0 0 54954087386 00023442288 0 0 0 0 0 0 0
-81 -59 00000000079 81 064 -268 0 0 0 0 0 43651583224 00020892961 0 0 0 0 0 0 0
-815 -585 00000000071 815 054 -273 0 0 0 0 0 34673685045 00018620871 0 0 0 0 0 0 0
-82 -58 00000000063 82 044 -278 0 0 0 0 0 27542287033 00016595869 0 0 0 0 0 0 0
-825 -575 00000000056 825 034 -283 0 0 0 0 0 21877616239 00014791084 0 0 0 0 0 0 0
-83 -57 0000000005 83 024 -288 0 0 0 0 0 17378008287 00013182567 0 0 0 0 0 0 0
-835 -565 00000000045 835 014 -293 0 0 0 0 0 13803842646 00011748976 0 0 0 0 0 0 0
-84 -56 0000000004 84 004 -298 0 0 0 0 0 10964781961 00010471285 0 0 0 0 0 0 0
-845 -555 00000000035 845 -006 -303 0 0 0 0 0 087096359 00009332543 0 0 0 0 0 0 0
-85 -55 00000000032 85 -016 -308 0 0 0 0 0 06918309709 00008317638 0 0 0 0 0 0 0
-855 -545 00000000028 855 -026 -313 0 0 0 0 0 05495408739 00007413102 0 0 0 0 0 0 0
-86 -54 00000000025 86 -036 -318 0 0 0 0 0 04365158322 00006606934 0 0 0 0 0 0 0
-865 -535 00000000022 865 -046 -323 0 0 0 0 0 03467368505 00005888437 0 0 0 0 0 0 0
-87 -53 0000000002 87 -056 -328 0 0 0 0 0 02754228703 00005248075 0 0 0 0 0 0 0
-875 -525 00000000018 875 -066 -333 0 0 0 0 0 02187761624 00004677351 0 0 0 0 0 0 0
-88 -52 00000000016 88 -076 -338 0 0 0 0 0 01737800829 00004168694 0 0 0 0 0 0 0
-885 -515 00000000014 885 -086 -343 0 0 0 0 0 01380384265 00003715352 0 0 0 0 0 0 0
-89 -51 00000000013 89 -096 -348 0 0 0 0 0 01096478196 00003311311 0 0 0 0 0 0 0
-895 -505 00000000011 895 -106 -353 0 0 0 0 0 0087096359 00002951209 0 0 0 0 0 0 0
-9 -5 0000000001 9 -116 -358 0 0 0 0 0 00691830971 00002630268 0 0 0 0 0 0 0
-905 -495 00000000009 905 -126 -363 0 0 0 0 0 00549540874 00002344229 0 0 0 0 0 0 0
-91 -49 00000000008 91 -136 -368 0 0 0 0 0 00436515832 00002089296 0 0 0 0 0 0 0
-915 -485 00000000007 915 -146 -373 0 0 0 0 0 0034673685 00001862087 0 0 0 0 0 0 0
-92 -48 00000000006 92 -156 -378 0 0 0 0 0 0027542287 00001659587 0 0 0 0 0 0 0
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-93 -47 00000000005 93 -176 -388 0 0 0 0 0 00173780083 00001318257 0 0 0 0 0 0 0
-935 -465 00000000004 935 -186 -393 0 0 0 0 0 00138038426 00001174898 0 0 0 0 0 0 0
-94 -46 00000000004 94 -196 -398 0 0 0 0 0 0010964782 00001047129 0 0 0 0 0 0 0
-945 -455 00000000004 945 -206 -403 0 0 0 0 0 00087096359 00000933254 0 0 0 0 0 0 0
-95 -45 00000000003 95 -216 -408 0 0 0 0 0 00069183097 00000831764 0 0 0 0 0 0 0
-955 -445 00000000003 955 -226 -413 0 0 0 0 0 00054954087 0000074131 0 0 0 0 0 0 0
-96 -44 00000000003 96 -236 -418 0 0 0 0 0 00043651583 00000660693 0 0 0 0 0 0 0
-965 -435 00000000002 965 -246 -423 0 0 0 0 0 00034673685 00000588844 0 0 0 0 0 0 0
-97 -43 00000000002 97 -256 -428 0 0 0 0 0 00027542287 00000524807 0 0 0 0 0 0 0
-975 -425 00000000002 975 -266 -433 0 0 0 0 0 00021877616 00000467735 0 0 0 0 0 0 0
-98 -42 00000000002 98 -276 -438 0 0 0 0 0 00017378008 00000416869 0 0 0 0 0 0 0
-985 -415 00000000001 985 -286 -443 0 0 0 0 0 00013803843 00000371535 0 0 0 0 0 0 0
-99 -41 00000000001 99 -296 -448 0 0 0 0 0 00010964782 00000331131 0 0 0 0 0 0 0
-995 -405 00000000001 995 -306 -453 0 0 0 0 0 00008709636 00000295121 0 0 0 0 0 0 0
-10 -4 00000000001 10 -316 -458 0 0 0 0 0 0000691831 00000263027 0 0 0 0 0 0 0
-1005 -395 00000000001 1005 -326 -463 0 0 0 0 0 00005495409 00000234423 0 0 0 0 0 0 0
-101 -39 00000000001 101 -336 -468 0 0 0 0 0 00004365158 0000020893 0 0 0 0 0 0 0
-1015 -385 00000000001 1015 -346 -473 0 0 0 0 0 00003467369 00000186209 0 0 0 0 0 0 0
-102 -38 00000000001 102 -356 -478 0 0 0 0 0 00002754229 00000165959 0 0 0 0 0 0 0
-1025 -375 00000000001 1025 -366 -483 0 0 0 0 0 00002187762 00000147911 0 0 0 0 0 0 0
-103 -37 00000000001 103 -376 -488 0 0 0 0 0 00001737801 00000131826 0 0 0 0 0 0 0
-1035 -365 0 1035 -386 -493 0 0 0 0 0 00001380384 0000011749 0 0 0 0 0 0 0
-104 -36 0 104 -396 -498 0 0 0 0 0 00001096478 00000104713 0 0 0 0 0 0 0
-1045 -355 0 1045 -406 -503 0 0 0 0 0 00000870964 00000093325 0 0 0 0 0 0 0
-105 -35 0 105 -416 -508 0 0 0 0 0 00000691831 00000083176 0 0 0 0 0 0 0
-1055 -345 0 1055 -426 -513 0 0 0 0 0 00000549541 00000074131 0 0 0 0 0 0 0
-106 -34 0 106 -436 -518 0 0 0 0 0 00000436516 00000066069 0 0 0 0 0 0 0
-1065 -335 0 1065 -446 -523 0 0 0 0 0 00000346737 00000058884 0 0 0 0 0 0 0
-107 -33 0 107 -456 -528 0 0 0 0 0 00000275423 00000052481 0 0 0 0 0 0 0
-1075 -325 0 1075 -466 -533 0 0 0 0 0 00000218776 00000046774 0 0 0 0 0 0 0
-108 -32 0 108 -476 -538 0 0 0 0 0 0000017378 00000041687 0 0 0 0 0 0 0
-1085 -315 0 1085 -486 -543 0 0 0 0 0 00000138038 00000037154 0 0 0 0 0 0 0
-109 -31 0 109 -496 -548 0 0 0 0 0 00000109648 00000033113 0 0 0 0 0 0 0
-1095 -305 0 1095 -506 -553 0 0 0 0 0 00000087096 00000029512 0 0 0 0 0 0 0
-11 -3 0 11 -516 -558 0 0 0 0 0 00000069183 00000026303 0 0 0 0 0 0 0
-1105 -295 0 1105 -526 -563 0 0 0 0 0 00000054954 00000023442 0 0 0 0 0 0 0
-111 -29 0 111 -536 -568 0 0 0 0 0 00000043652 00000020893 0 0 0 0 0 0 0
-1115 -285 0 1115 -546 -573 0 0 0 0 0 00000034674 00000018621 0 0 0 0 0 0 0
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-1125 -275 0 1125 -566 -583 0 0 0 0 0 00000021878 00000014791 0 0 0 0 0 0 0
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-114 -26 0 114 -596 -598 0 0 0 0 0 00000010965 00000010471 0 0 0 0 0 0 0
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-117 -23 0 117 -656 -628 0 0 0 0 0 00000002754 00000005248 0 0 0 0 0 0 0
-1175 -225 0 1175 -666 -633 0 0 0 0 0 00000002188 00000004677 0 0 0 0 0 0 0
-118 -22 0 118 -676 -638 0 0 0 0 0 00000001738 00000004169 0 0 0 0 0 0 0
-1185 -215 0 1185 -686 -643 0 0 0 0 0 0000000138 00000003715 0 0 0 0 0 0 0
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-1195 -205 0 1195 -706 -653 0 0 0 0 0 00000000871 00000002951 0 0 0 0 0 0 0
-12 -2 0 12 -716 -658 0 0 0 0 0 00000000692 0000000263 0 0 0 0 0 0 0
-1205 -195 0 1205 -726 -663 0 0 0 0 0 0000000055 00000002344 0 0 0 0 0 0 0
-121 -19 0 121 -736 -668 0 0 0 0 0 00000000437 00000002089 0 0 0 0 0 0 0
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-122 -18 0 122 -756 -678 0 0 0 0 0 00000000275 0000000166 0 0 0 0 0 0 0
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-123 -17 0 123 -776 -688 0 0 0 0 0 00000000174 00000001318 0 0 0 0 0 0 0
-1235 -165 0 1235 -786 -693 0 0 0 0 0 00000000138 00000001175 0 0 0 0 0 0 0
-124 -16 0 124 -796 -698 0 0 0 0 0 0000000011 00000001047 0 0 0 0 0 0 0
-1245 -155 0 1245 -806 -703 0 0 0 0 0 00000000087 00000000933 0 0 0 0 0 0 0
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-1255 -145 0 1255 -826 -713 0 0 0 0 0 00000000055 00000000741 0 0 0 0 0 0 0
-126 -14 0 126 -836 -718 0 0 0 0 0 00000000044 00000000661 0 0 0 0 0 0 0
-1265 -135 0 1265 -846 -723 0 0 0 0 0 00000000035 00000000589 0 0 0 0 0 0 0
-127 -13 0 127 -856 -728 0 0 0 0 0 00000000028 00000000525 0 0 0 0 0 0 0
-1275 -125 0 1275 -866 -733 0 0 0 0 0 00000000022 00000000468 0 0 0 0 0 0 0
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-1285 -115 0 1285 -886 -743 0 0 0 0 0 00000000014 00000000372 0 0 0 0 0 0 0
-129 -11 0 129 -896 -748 0 0 0 0 0 00000000011 00000000331 0 0 0 0 0 0 0
-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
-13 -1 0 13 -916 -758 0 0 0 0 0 00000000007 00000000263 0 0 0 0 0 0 0
-1305 -095 0 1305 -926 -763 0 0 0 0 0 00000000005 00000000234 0 0 0 0 0 0 0
-131 -09 0 131 -936 -768 0 0 0 0 0 00000000004 00000000209 0 0 0 0 0 0 0
-1315 -085 0 1315 -946 -773 0 0 0 0 0 00000000003 00000000186 0 0 0 0 0 0 0
-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
-1325 -075 0 1325 -966 -783 0 0 0 0 0 00000000002 00000000148 0 0 0 0 0 0 0
-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
-1395 -005 0 1395 -1106 -853 0 0 0 0 0 0 0000000003 0 0 0 0 0 0 0
-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 6: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Abundance of inorganics in fresh water and in earthrsquos crust

David Reckhow CEE 680 35 6

From Stumm amp Morgan 1996 Benjamin 2002 fig 11

Terrestrial water

Solubility Products General Equilibrium

AmBn(s) harr mA+n + nB-m

Solubility Product Equation Kso = [A+n]m[B-m]n

also sometimes written Ksp

Example Calcium Carbonate

sources Smith amp Martell SampM table 71 (pg362-364)

David Reckhow CEE 680 34 7

Solid Cation Anion

Kso and Q Reaction Quotient (Q)

computed value from actual measurements may not be at thermodynamic equilibrium

comparison with Ksp will tell you about tendency toward dissolution or precipitation QgtKso then water will precipitate solid phase QltKso then water will dissolve solid phase

Example Calcium Carbonate solubility Ca+2 = 40 mgL and CO3

-2 = 100 mgL as CaCO3 what is Q if Kso is 10-834 what does this tell us

David Reckhow CEE 680 34 8

Presenter
Presentation Notes
Note GFW for Ca is 40 so Q = 10-6 and system is over saturated and will precipitate CaCO3

Solubility of some simple salts Barium sulfate

BaSO4 = Ba+2 + SO4-2

Kso = 10-996 = [Ba+2][SO4-2]

How much will dissolve and what will the barium and sulfate concentrations be

How much will dissolve in a 1mM solution of Na2SO4

David Reckhow CEE 680 34 9

984

2969

1010

minus

minus

=

=

xx

( )

9667

96963

32

3969

101009712

1041010

101010

minusminus

minusminusminus

minus

minusminus

==

minusplusmnminus=

+=

+=

x

xx

xxxx

Presenter
Presentation Notes
Simplify last equation by neglecting the second ldquoxrdquo in right hand term

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
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-11 -3 0 11 -516 -558 0 0 0 0 0 00000069183 00000026303 0 0 0 0 0 0 0
-1105 -295 0 1105 -526 -563 0 0 0 0 0 00000054954 00000023442 0 0 0 0 0 0 0
-111 -29 0 111 -536 -568 0 0 0 0 0 00000043652 00000020893 0 0 0 0 0 0 0
-1115 -285 0 1115 -546 -573 0 0 0 0 0 00000034674 00000018621 0 0 0 0 0 0 0
-112 -28 0 112 -556 -578 0 0 0 0 0 00000027542 00000016596 0 0 0 0 0 0 0
-1125 -275 0 1125 -566 -583 0 0 0 0 0 00000021878 00000014791 0 0 0 0 0 0 0
-113 -27 0 113 -576 -588 0 0 0 0 0 00000017378 00000013183 0 0 0 0 0 0 0
-1135 -265 0 1135 -586 -593 0 0 0 0 0 00000013804 00000011749 0 0 0 0 0 0 0
-114 -26 0 114 -596 -598 0 0 0 0 0 00000010965 00000010471 0 0 0 0 0 0 0
-1145 -255 0 1145 -606 -603 0 0 0 0 0 0000000871 00000009333 0 0 0 0 0 0 0
-115 -25 0 115 -616 -608 0 0 0 0 0 00000006918 00000008318 0 0 0 0 0 0 0
-1155 -245 0 1155 -626 -613 0 0 0 0 0 00000005495 00000007413 0 0 0 0 0 0 0
-116 -24 0 116 -636 -618 0 0 0 0 0 00000004365 00000006607 0 0 0 0 0 0 0
-1165 -235 0 1165 -646 -623 0 0 0 0 0 00000003467 00000005888 0 0 0 0 0 0 0
-117 -23 0 117 -656 -628 0 0 0 0 0 00000002754 00000005248 0 0 0 0 0 0 0
-1175 -225 0 1175 -666 -633 0 0 0 0 0 00000002188 00000004677 0 0 0 0 0 0 0
-118 -22 0 118 -676 -638 0 0 0 0 0 00000001738 00000004169 0 0 0 0 0 0 0
-1185 -215 0 1185 -686 -643 0 0 0 0 0 0000000138 00000003715 0 0 0 0 0 0 0
-119 -21 0 119 -696 -648 0 0 0 0 0 00000001096 00000003311 0 0 0 0 0 0 0
-1195 -205 0 1195 -706 -653 0 0 0 0 0 00000000871 00000002951 0 0 0 0 0 0 0
-12 -2 0 12 -716 -658 0 0 0 0 0 00000000692 0000000263 0 0 0 0 0 0 0
-1205 -195 0 1205 -726 -663 0 0 0 0 0 0000000055 00000002344 0 0 0 0 0 0 0
-121 -19 0 121 -736 -668 0 0 0 0 0 00000000437 00000002089 0 0 0 0 0 0 0
-1215 -185 0 1215 -746 -673 0 0 0 0 0 00000000347 00000001862 0 0 0 0 0 0 0
-122 -18 0 122 -756 -678 0 0 0 0 0 00000000275 0000000166 0 0 0 0 0 0 0
-1225 -175 0 1225 -766 -683 0 0 0 0 0 00000000219 00000001479 0 0 0 0 0 0 0
-123 -17 0 123 -776 -688 0 0 0 0 0 00000000174 00000001318 0 0 0 0 0 0 0
-1235 -165 0 1235 -786 -693 0 0 0 0 0 00000000138 00000001175 0 0 0 0 0 0 0
-124 -16 0 124 -796 -698 0 0 0 0 0 0000000011 00000001047 0 0 0 0 0 0 0
-1245 -155 0 1245 -806 -703 0 0 0 0 0 00000000087 00000000933 0 0 0 0 0 0 0
-125 -15 0 125 -816 -708 0 0 0 0 0 00000000069 00000000832 0 0 0 0 0 0 0
-1255 -145 0 1255 -826 -713 0 0 0 0 0 00000000055 00000000741 0 0 0 0 0 0 0
-126 -14 0 126 -836 -718 0 0 0 0 0 00000000044 00000000661 0 0 0 0 0 0 0
-1265 -135 0 1265 -846 -723 0 0 0 0 0 00000000035 00000000589 0 0 0 0 0 0 0
-127 -13 0 127 -856 -728 0 0 0 0 0 00000000028 00000000525 0 0 0 0 0 0 0
-1275 -125 0 1275 -866 -733 0 0 0 0 0 00000000022 00000000468 0 0 0 0 0 0 0
-128 -12 0 128 -876 -738 0 0 0 0 0 00000000017 00000000417 0 0 0 0 0 0 0
-1285 -115 0 1285 -886 -743 0 0 0 0 0 00000000014 00000000372 0 0 0 0 0 0 0
-129 -11 0 129 -896 -748 0 0 0 0 0 00000000011 00000000331 0 0 0 0 0 0 0
-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
-13 -1 0 13 -916 -758 0 0 0 0 0 00000000007 00000000263 0 0 0 0 0 0 0
-1305 -095 0 1305 -926 -763 0 0 0 0 0 00000000005 00000000234 0 0 0 0 0 0 0
-131 -09 0 131 -936 -768 0 0 0 0 0 00000000004 00000000209 0 0 0 0 0 0 0
-1315 -085 0 1315 -946 -773 0 0 0 0 0 00000000003 00000000186 0 0 0 0 0 0 0
-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
-1325 -075 0 1325 -966 -783 0 0 0 0 0 00000000002 00000000148 0 0 0 0 0 0 0
-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
-1395 -005 0 1395 -1106 -853 0 0 0 0 0 0 0000000003 0 0 0 0 0 0 0
-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 7: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Solubility Products General Equilibrium

AmBn(s) harr mA+n + nB-m

Solubility Product Equation Kso = [A+n]m[B-m]n

also sometimes written Ksp

Example Calcium Carbonate

sources Smith amp Martell SampM table 71 (pg362-364)

David Reckhow CEE 680 34 7

Solid Cation Anion

Kso and Q Reaction Quotient (Q)

computed value from actual measurements may not be at thermodynamic equilibrium

comparison with Ksp will tell you about tendency toward dissolution or precipitation QgtKso then water will precipitate solid phase QltKso then water will dissolve solid phase

Example Calcium Carbonate solubility Ca+2 = 40 mgL and CO3

-2 = 100 mgL as CaCO3 what is Q if Kso is 10-834 what does this tell us

David Reckhow CEE 680 34 8

Presenter
Presentation Notes
Note GFW for Ca is 40 so Q = 10-6 and system is over saturated and will precipitate CaCO3

Solubility of some simple salts Barium sulfate

BaSO4 = Ba+2 + SO4-2

Kso = 10-996 = [Ba+2][SO4-2]

How much will dissolve and what will the barium and sulfate concentrations be

How much will dissolve in a 1mM solution of Na2SO4

David Reckhow CEE 680 34 9

984

2969

1010

minus

minus

=

=

xx

( )

9667

96963

32

3969

101009712

1041010

101010

minusminus

minusminusminus

minus

minusminus

==

minusplusmnminus=

+=

+=

x

xx

xxxx

Presenter
Presentation Notes
Simplify last equation by neglecting the second ldquoxrdquo in right hand term

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-28 -112 00015848932 28 1124 262 0 0 0 0 0 173780082874938 4168693834703 0 0 0 0 0 0 0
-285 -1115 00014125375 285 1114 257 0 0 0 0 0 138038426460289 3715352290972 0 0 0 0 0 0 0
-29 -111 00012589254 29 1104 252 0 0 0 0 0 109647819614319 3311311214826 0 0 0 0 0 0 0
-295 -1105 00011220185 295 1094 247 0 0 0 0 0 870963589956082 2951209226666 0 0 0 0 0 0 0
-3 -11 0001 3 1084 242 0 0 0 0 0 691830970918939 2630267991895 0 0 0 0 0 0 0
-305 -1095 00008912509 305 1074 237 0 0 0 0 0 549540873857627 234422881532 0 0 0 0 0 0 0
-31 -109 00007943282 31 1064 232 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-315 -1085 00007079458 315 1054 227 0 0 0 0 0 346736850452531 1862087136663 0 0 0 0 0 0 0
-32 -108 00006309573 32 1044 222 0 0 0 0 0 275422870333817 1659586907438 0 0 0 0 0 0 0
-325 -1075 00005623413 325 1034 217 0 0 0 0 0 218776162394955 1479108388168 0 0 0 0 0 0 0
-33 -107 00005011872 33 1024 212 0 0 0 0 0 173780082874938 1318256738556 0 0 0 0 0 0 0
-335 -1065 00004466836 335 1014 207 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-34 -106 00003981072 34 1004 202 0 0 0 0 0 109647819614319 1047128548051 0 0 0 0 0 0 0
-345 -1055 00003548134 345 994 197 0 0 0 0 0 870963589956081 933254300797 0 0 0 0 0 0 0
-35 -105 00003162278 35 984 192 0 0 0 0 0 691830970918938 831763771103 0 0 0 0 0 0 0
-355 -1045 00002818383 355 974 187 0 0 0 0 0 549540873857626 741310241301 0 0 0 0 0 0 0
-36 -104 00002511886 36 964 182 0 0 0 0 0 436515832240168 660693448008 0 0 0 0 0 0 0
-365 -1035 00002238721 365 954 177 0 0 0 0 0 346736850452532 588843655356 0 0 0 0 0 0 0
-37 -103 00001995262 37 944 172 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-375 -1025 00001778279 375 934 167 0 0 0 0 0 218776162394956 467735141287 0 0 0 0 0 0 0
-38 -102 00001584893 38 924 162 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-385 -1015 00001412538 385 914 157 0 0 0 0 0 138038426460289 371535229097 0 0 0 0 0 0 0
-39 -101 00001258925 39 904 152 0 0 0 0 0 109647819614318 331131121483 0 0 0 0 0 0 0
-395 -1005 00001122018 395 894 147 0 0 0 0 0 870963589956081 295120922667 0 0 0 0 0 0 0
-4 -10 00001 4 884 142 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-405 -995 00000891251 405 874 137 0 0 0 0 0 549540873857625 234422881532 0 0 0 0 0 0 0
-41 -99 00000794328 41 864 132 0 0 0 0 0 436515832240167 208929613085 0 0 0 0 0 0 0
-415 -985 00000707946 415 854 127 0 0 0 0 0 346736850452532 186208713666 0 0 0 0 0 0 0
-42 -98 00000630957 42 844 122 0 0 0 0 0 275422870333817 165958690744 0 0 0 0 0 0 0
-425 -975 00000562341 425 834 117 0 0 0 0 0 218776162394956 147910838817 0 0 0 0 0 0 0
-43 -97 00000501187 43 824 112 0 0 0 0 0 173780082874938 131825673856 0 0 0 0 0 0 0
-435 -965 00000446684 435 814 107 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-44 -96 00000398107 44 804 102 0 0 0 0 0 109647819614319 104712854805 0 0 0 0 0 0 0
-445 -955 00000354813 445 794 097 0 0 0 0 0 870963589956083 9332543008 0 0 0 0 0 0 0
-45 -95 00000316228 45 784 092 0 0 0 0 0 691830970918936 8317637711 0 0 0 0 0 0 0
-455 -945 00000281838 455 774 087 0 0 0 0 0 549540873857625 7413102413 0 0 0 0 0 0 0
-46 -94 00000251189 46 764 082 0 0 0 0 0 436515832240167 66069344801 0 0 0 0 0 0 0
-465 -935 00000223872 465 754 077 0 0 0 0 0 346736850452531 58884365536 0 0 0 0 0 0 0
-47 -93 00000199526 47 744 072 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-475 -925 00000177828 475 734 067 0 0 0 0 0 218776162394955 46773514129 0 0 0 0 0 0 0
-48 -92 00000158489 48 724 062 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-485 -915 00000141254 485 714 057 0 0 0 0 0 138038426460289 3715352291 0 0 0 0 0 0 0
-49 -91 00000125893 49 704 052 0 0 0 0 0 109647819614319 33113112148 0 0 0 0 0 0 0
-495 -905 00000112202 495 694 047 0 0 0 0 0 870963589956082 29512092267 0 0 0 0 0 0 0
-5 -9 000001 5 684 042 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-505 -895 00000089125 505 674 037 0 0 0 0 0 549540873857625 23442288153 0 0 0 0 0 0 0
-51 -89 00000079433 51 664 032 0 0 0 0 0 436515832240167 20892961309 0 0 0 0 0 0 0
-515 -885 00000070795 515 654 027 0 0 0 0 0 346736850452532 18620871367 0 0 0 0 0 0 0
-52 -88 00000063096 52 644 022 0 0 0 0 0 275422870333817 16595869074 0 0 0 0 0 0 0
-525 -875 00000056234 525 634 017 0 0 0 0 0 218776162394956 14791083882 0 0 0 0 0 0 0
-53 -87 00000050119 53 624 012 0 0 0 0 0 173780082874938 13182567386 0 0 0 0 0 0 0
-535 -865 00000044668 535 614 007 0 0 0 0 0 138038426460289 11748975549 0 0 0 0 0 0 0
-54 -86 00000039811 54 604 002 0 0 0 0 0 109647819614318 10471285481 0 0 0 0 0 0 0
-545 -855 00000035481 545 594 -003 0 0 0 0 0 870963589956081 09332543008 0 0 0 0 0 0 0
-55 -85 00000031623 55 584 -008 0 0 0 0 0 691830970918937 08317637711 0 0 0 0 0 0 0
-555 -845 00000028184 555 574 -013 0 0 0 0 0 549540873857626 07413102413 0 0 0 0 0 0 0
-56 -84 00000025119 56 564 -018 0 0 0 0 0 436515832240167 0660693448 0 0 0 0 0 0 0
-565 -835 00000022387 565 554 -023 0 0 0 0 0 346736850452531 05888436554 0 0 0 0 0 0 0
-57 -83 00000019953 57 544 -028 0 0 0 0 0 275422870333817 05248074602 0 0 0 0 0 0 0
-575 -825 00000017783 575 534 -033 0 0 0 0 0 218776162394955 04677351413 0 0 0 0 0 0 0
-58 -82 00000015849 58 524 -038 0 0 0 0 0 173780082874938 04168693835 0 0 0 0 0 0 0
-585 -815 00000014125 585 514 -043 0 0 0 0 0 138038426460289 03715352291 0 0 0 0 0 0 0
-59 -81 00000012589 59 504 -048 0 0 0 0 0 109647819614318 03311311215 0 0 0 0 0 0 0
-595 -805 0000001122 595 494 -053 0 0 0 0 0 870963589956081 02951209227 0 0 0 0 0 0 0
-6 -8 0000001 6 484 -058 0 0 0 0 0 691830970918937 02630267992 0 0 0 0 0 0 0
-605 -795 00000008913 605 474 -063 0 0 0 0 0 549540873857625 02344228815 0 0 0 0 0 0 0
-61 -79 00000007943 61 464 -068 0 0 0 0 0 436515832240167 02089296131 0 0 0 0 0 0 0
-615 -785 00000007079 615 454 -073 0 0 0 0 0 346736850452531 01862087137 0 0 0 0 0 0 0
-62 -78 0000000631 62 444 -078 0 0 0 0 0 275422870333817 01659586907 0 0 0 0 0 0 0
-625 -775 00000005623 625 434 -083 0 0 0 0 0 218776162394955 01479108388 0 0 0 0 0 0 0
-63 -77 00000005012 63 424 -088 0 0 0 0 0 173780082874938 01318256739 0 0 0 0 0 0 0
-635 -765 00000004467 635 414 -093 0 0 0 0 0 138038426460289 01174897555 0 0 0 0 0 0 0
-64 -76 00000003981 64 404 -098 0 0 0 0 0 109647819614318 01047128548 0 0 0 0 0 0 0
-645 -755 00000003548 645 394 -103 0 0 0 0 0 87096358995608 00933254301 0 0 0 0 0 0 0
-65 -75 00000003162 65 384 -108 0 0 0 0 0 69183097091894 00831763771 0 0 0 0 0 0 0
-655 -745 00000002818 655 374 -113 0 0 0 0 0 54954087385762 00741310241 0 0 0 0 0 0 0
-66 -74 00000002512 66 364 -118 0 0 0 0 0 43651583224017 00660693448 0 0 0 0 0 0 0
-665 -735 00000002239 665 354 -123 0 0 0 0 0 34673685045253 00588843655 0 0 0 0 0 0 0
-67 -73 00000001995 67 344 -128 0 0 0 0 0 27542287033382 0052480746 0 0 0 0 0 0 0
-675 -725 00000001778 675 334 -133 0 0 0 0 0 21877616239496 00467735141 0 0 0 0 0 0 0
-68 -72 00000001585 68 324 -138 0 0 0 0 0 17378008287494 00416869383 0 0 0 0 0 0 0
-685 -715 00000001413 685 314 -143 0 0 0 0 0 13803842646029 00371535229 0 0 0 0 0 0 0
-69 -71 00000001259 69 304 -148 0 0 0 0 0 10964781961432 00331131121 0 0 0 0 0 0 0
-695 -705 00000001122 695 294 -153 0 0 0 0 0 8709635899561 00295120923 0 0 0 0 0 0 0
-7 -7 00000001 7 284 -158 0 0 0 0 0 6918309709189 00263026799 0 0 0 0 0 0 0
-705 -695 00000000891 705 274 -163 0 0 0 0 0 5495408738576 00234422882 0 0 0 0 0 0 0
-71 -69 00000000794 71 264 -168 0 0 0 0 0 4365158322402 00208929613 0 0 0 0 0 0 0
-715 -685 00000000708 715 254 -173 0 0 0 0 0 3467368504525 00186208714 0 0 0 0 0 0 0
-72 -68 00000000631 72 244 -178 0 0 0 0 0 2754228703338 00165958691 0 0 0 0 0 0 0
-725 -675 00000000562 725 234 -183 0 0 0 0 0 218776162395 00147910839 0 0 0 0 0 0 0
-73 -67 00000000501 73 224 -188 0 0 0 0 0 1737800828749 00131825674 0 0 0 0 0 0 0
-735 -665 00000000447 735 214 -193 0 0 0 0 0 1380384264603 00117489755 0 0 0 0 0 0 0
-74 -66 00000000398 74 204 -198 0 0 0 0 0 1096478196143 00104712855 0 0 0 0 0 0 0
-745 -655 00000000355 745 194 -203 0 0 0 0 0 870963589956 0009332543 0 0 0 0 0 0 0
-75 -65 00000000316 75 184 -208 0 0 0 0 0 691830970919 00083176377 0 0 0 0 0 0 0
-755 -645 00000000282 755 174 -213 0 0 0 0 0 549540873858 00074131024 0 0 0 0 0 0 0
-76 -64 00000000251 76 164 -218 0 0 0 0 0 43651583224 00066069345 0 0 0 0 0 0 0
-765 -635 00000000224 765 154 -223 0 0 0 0 0 346736850453 00058884366 0 0 0 0 0 0 0
-77 -63 000000002 77 144 -228 0 0 0 0 0 275422870334 00052480746 0 0 0 0 0 0 0
-775 -625 00000000178 775 134 -233 0 0 0 0 0 218776162395 00046773514 0 0 0 0 0 0 0
-78 -62 00000000158 78 124 -238 0 0 0 0 0 173780082875 00041686938 0 0 0 0 0 0 0
-785 -615 00000000141 785 114 -243 0 0 0 0 0 13803842646 00037153523 0 0 0 0 0 0 0
-79 -61 00000000126 79 104 -248 0 0 0 0 0 109647819614 00033113112 0 0 0 0 0 0 0
-795 -605 00000000112 795 094 -253 0 0 0 0 0 87096358996 00029512092 0 0 0 0 0 0 0
-8 -6 000000001 8 084 -258 0 0 0 0 0 69183097092 0002630268 0 0 0 0 0 0 0
-805 -595 00000000089 805 074 -263 0 0 0 0 0 54954087386 00023442288 0 0 0 0 0 0 0
-81 -59 00000000079 81 064 -268 0 0 0 0 0 43651583224 00020892961 0 0 0 0 0 0 0
-815 -585 00000000071 815 054 -273 0 0 0 0 0 34673685045 00018620871 0 0 0 0 0 0 0
-82 -58 00000000063 82 044 -278 0 0 0 0 0 27542287033 00016595869 0 0 0 0 0 0 0
-825 -575 00000000056 825 034 -283 0 0 0 0 0 21877616239 00014791084 0 0 0 0 0 0 0
-83 -57 0000000005 83 024 -288 0 0 0 0 0 17378008287 00013182567 0 0 0 0 0 0 0
-835 -565 00000000045 835 014 -293 0 0 0 0 0 13803842646 00011748976 0 0 0 0 0 0 0
-84 -56 0000000004 84 004 -298 0 0 0 0 0 10964781961 00010471285 0 0 0 0 0 0 0
-845 -555 00000000035 845 -006 -303 0 0 0 0 0 087096359 00009332543 0 0 0 0 0 0 0
-85 -55 00000000032 85 -016 -308 0 0 0 0 0 06918309709 00008317638 0 0 0 0 0 0 0
-855 -545 00000000028 855 -026 -313 0 0 0 0 0 05495408739 00007413102 0 0 0 0 0 0 0
-86 -54 00000000025 86 -036 -318 0 0 0 0 0 04365158322 00006606934 0 0 0 0 0 0 0
-865 -535 00000000022 865 -046 -323 0 0 0 0 0 03467368505 00005888437 0 0 0 0 0 0 0
-87 -53 0000000002 87 -056 -328 0 0 0 0 0 02754228703 00005248075 0 0 0 0 0 0 0
-875 -525 00000000018 875 -066 -333 0 0 0 0 0 02187761624 00004677351 0 0 0 0 0 0 0
-88 -52 00000000016 88 -076 -338 0 0 0 0 0 01737800829 00004168694 0 0 0 0 0 0 0
-885 -515 00000000014 885 -086 -343 0 0 0 0 0 01380384265 00003715352 0 0 0 0 0 0 0
-89 -51 00000000013 89 -096 -348 0 0 0 0 0 01096478196 00003311311 0 0 0 0 0 0 0
-895 -505 00000000011 895 -106 -353 0 0 0 0 0 0087096359 00002951209 0 0 0 0 0 0 0
-9 -5 0000000001 9 -116 -358 0 0 0 0 0 00691830971 00002630268 0 0 0 0 0 0 0
-905 -495 00000000009 905 -126 -363 0 0 0 0 0 00549540874 00002344229 0 0 0 0 0 0 0
-91 -49 00000000008 91 -136 -368 0 0 0 0 0 00436515832 00002089296 0 0 0 0 0 0 0
-915 -485 00000000007 915 -146 -373 0 0 0 0 0 0034673685 00001862087 0 0 0 0 0 0 0
-92 -48 00000000006 92 -156 -378 0 0 0 0 0 0027542287 00001659587 0 0 0 0 0 0 0
-925 -475 00000000006 925 -166 -383 0 0 0 0 0 00218776162 00001479108 0 0 0 0 0 0 0
-93 -47 00000000005 93 -176 -388 0 0 0 0 0 00173780083 00001318257 0 0 0 0 0 0 0
-935 -465 00000000004 935 -186 -393 0 0 0 0 0 00138038426 00001174898 0 0 0 0 0 0 0
-94 -46 00000000004 94 -196 -398 0 0 0 0 0 0010964782 00001047129 0 0 0 0 0 0 0
-945 -455 00000000004 945 -206 -403 0 0 0 0 0 00087096359 00000933254 0 0 0 0 0 0 0
-95 -45 00000000003 95 -216 -408 0 0 0 0 0 00069183097 00000831764 0 0 0 0 0 0 0
-955 -445 00000000003 955 -226 -413 0 0 0 0 0 00054954087 0000074131 0 0 0 0 0 0 0
-96 -44 00000000003 96 -236 -418 0 0 0 0 0 00043651583 00000660693 0 0 0 0 0 0 0
-965 -435 00000000002 965 -246 -423 0 0 0 0 0 00034673685 00000588844 0 0 0 0 0 0 0
-97 -43 00000000002 97 -256 -428 0 0 0 0 0 00027542287 00000524807 0 0 0 0 0 0 0
-975 -425 00000000002 975 -266 -433 0 0 0 0 0 00021877616 00000467735 0 0 0 0 0 0 0
-98 -42 00000000002 98 -276 -438 0 0 0 0 0 00017378008 00000416869 0 0 0 0 0 0 0
-985 -415 00000000001 985 -286 -443 0 0 0 0 0 00013803843 00000371535 0 0 0 0 0 0 0
-99 -41 00000000001 99 -296 -448 0 0 0 0 0 00010964782 00000331131 0 0 0 0 0 0 0
-995 -405 00000000001 995 -306 -453 0 0 0 0 0 00008709636 00000295121 0 0 0 0 0 0 0
-10 -4 00000000001 10 -316 -458 0 0 0 0 0 0000691831 00000263027 0 0 0 0 0 0 0
-1005 -395 00000000001 1005 -326 -463 0 0 0 0 0 00005495409 00000234423 0 0 0 0 0 0 0
-101 -39 00000000001 101 -336 -468 0 0 0 0 0 00004365158 0000020893 0 0 0 0 0 0 0
-1015 -385 00000000001 1015 -346 -473 0 0 0 0 0 00003467369 00000186209 0 0 0 0 0 0 0
-102 -38 00000000001 102 -356 -478 0 0 0 0 0 00002754229 00000165959 0 0 0 0 0 0 0
-1025 -375 00000000001 1025 -366 -483 0 0 0 0 0 00002187762 00000147911 0 0 0 0 0 0 0
-103 -37 00000000001 103 -376 -488 0 0 0 0 0 00001737801 00000131826 0 0 0 0 0 0 0
-1035 -365 0 1035 -386 -493 0 0 0 0 0 00001380384 0000011749 0 0 0 0 0 0 0
-104 -36 0 104 -396 -498 0 0 0 0 0 00001096478 00000104713 0 0 0 0 0 0 0
-1045 -355 0 1045 -406 -503 0 0 0 0 0 00000870964 00000093325 0 0 0 0 0 0 0
-105 -35 0 105 -416 -508 0 0 0 0 0 00000691831 00000083176 0 0 0 0 0 0 0
-1055 -345 0 1055 -426 -513 0 0 0 0 0 00000549541 00000074131 0 0 0 0 0 0 0
-106 -34 0 106 -436 -518 0 0 0 0 0 00000436516 00000066069 0 0 0 0 0 0 0
-1065 -335 0 1065 -446 -523 0 0 0 0 0 00000346737 00000058884 0 0 0 0 0 0 0
-107 -33 0 107 -456 -528 0 0 0 0 0 00000275423 00000052481 0 0 0 0 0 0 0
-1075 -325 0 1075 -466 -533 0 0 0 0 0 00000218776 00000046774 0 0 0 0 0 0 0
-108 -32 0 108 -476 -538 0 0 0 0 0 0000017378 00000041687 0 0 0 0 0 0 0
-1085 -315 0 1085 -486 -543 0 0 0 0 0 00000138038 00000037154 0 0 0 0 0 0 0
-109 -31 0 109 -496 -548 0 0 0 0 0 00000109648 00000033113 0 0 0 0 0 0 0
-1095 -305 0 1095 -506 -553 0 0 0 0 0 00000087096 00000029512 0 0 0 0 0 0 0
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-111 -29 0 111 -536 -568 0 0 0 0 0 00000043652 00000020893 0 0 0 0 0 0 0
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-112 -28 0 112 -556 -578 0 0 0 0 0 00000027542 00000016596 0 0 0 0 0 0 0
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-1135 -265 0 1135 -586 -593 0 0 0 0 0 00000013804 00000011749 0 0 0 0 0 0 0
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-1185 -215 0 1185 -686 -643 0 0 0 0 0 0000000138 00000003715 0 0 0 0 0 0 0
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-1235 -165 0 1235 -786 -693 0 0 0 0 0 00000000138 00000001175 0 0 0 0 0 0 0
-124 -16 0 124 -796 -698 0 0 0 0 0 0000000011 00000001047 0 0 0 0 0 0 0
-1245 -155 0 1245 -806 -703 0 0 0 0 0 00000000087 00000000933 0 0 0 0 0 0 0
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-1255 -145 0 1255 -826 -713 0 0 0 0 0 00000000055 00000000741 0 0 0 0 0 0 0
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-1265 -135 0 1265 -846 -723 0 0 0 0 0 00000000035 00000000589 0 0 0 0 0 0 0
-127 -13 0 127 -856 -728 0 0 0 0 0 00000000028 00000000525 0 0 0 0 0 0 0
-1275 -125 0 1275 -866 -733 0 0 0 0 0 00000000022 00000000468 0 0 0 0 0 0 0
-128 -12 0 128 -876 -738 0 0 0 0 0 00000000017 00000000417 0 0 0 0 0 0 0
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-129 -11 0 129 -896 -748 0 0 0 0 0 00000000011 00000000331 0 0 0 0 0 0 0
-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
-13 -1 0 13 -916 -758 0 0 0 0 0 00000000007 00000000263 0 0 0 0 0 0 0
-1305 -095 0 1305 -926 -763 0 0 0 0 0 00000000005 00000000234 0 0 0 0 0 0 0
-131 -09 0 131 -936 -768 0 0 0 0 0 00000000004 00000000209 0 0 0 0 0 0 0
-1315 -085 0 1315 -946 -773 0 0 0 0 0 00000000003 00000000186 0 0 0 0 0 0 0
-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
-1325 -075 0 1325 -966 -783 0 0 0 0 0 00000000002 00000000148 0 0 0 0 0 0 0
-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
-1395 -005 0 1395 -1106 -853 0 0 0 0 0 0 0000000003 0 0 0 0 0 0 0
-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 8: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Kso and Q Reaction Quotient (Q)

computed value from actual measurements may not be at thermodynamic equilibrium

comparison with Ksp will tell you about tendency toward dissolution or precipitation QgtKso then water will precipitate solid phase QltKso then water will dissolve solid phase

Example Calcium Carbonate solubility Ca+2 = 40 mgL and CO3

-2 = 100 mgL as CaCO3 what is Q if Kso is 10-834 what does this tell us

David Reckhow CEE 680 34 8

Presenter
Presentation Notes
Note GFW for Ca is 40 so Q = 10-6 and system is over saturated and will precipitate CaCO3

Solubility of some simple salts Barium sulfate

BaSO4 = Ba+2 + SO4-2

Kso = 10-996 = [Ba+2][SO4-2]

How much will dissolve and what will the barium and sulfate concentrations be

How much will dissolve in a 1mM solution of Na2SO4

David Reckhow CEE 680 34 9

984

2969

1010

minus

minus

=

=

xx

( )

9667

96963

32

3969

101009712

1041010

101010

minusminus

minusminusminus

minus

minusminus

==

minusplusmnminus=

+=

+=

x

xx

xxxx

Presenter
Presentation Notes
Simplify last equation by neglecting the second ldquoxrdquo in right hand term

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
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-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
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-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
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-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
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-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
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-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
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-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
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-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
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-107 -33 0 107 -456 -528 0 0 0 0 0 00000275423 00000052481 0 0 0 0 0 0 0
-1075 -325 0 1075 -466 -533 0 0 0 0 0 00000218776 00000046774 0 0 0 0 0 0 0
-108 -32 0 108 -476 -538 0 0 0 0 0 0000017378 00000041687 0 0 0 0 0 0 0
-1085 -315 0 1085 -486 -543 0 0 0 0 0 00000138038 00000037154 0 0 0 0 0 0 0
-109 -31 0 109 -496 -548 0 0 0 0 0 00000109648 00000033113 0 0 0 0 0 0 0
-1095 -305 0 1095 -506 -553 0 0 0 0 0 00000087096 00000029512 0 0 0 0 0 0 0
-11 -3 0 11 -516 -558 0 0 0 0 0 00000069183 00000026303 0 0 0 0 0 0 0
-1105 -295 0 1105 -526 -563 0 0 0 0 0 00000054954 00000023442 0 0 0 0 0 0 0
-111 -29 0 111 -536 -568 0 0 0 0 0 00000043652 00000020893 0 0 0 0 0 0 0
-1115 -285 0 1115 -546 -573 0 0 0 0 0 00000034674 00000018621 0 0 0 0 0 0 0
-112 -28 0 112 -556 -578 0 0 0 0 0 00000027542 00000016596 0 0 0 0 0 0 0
-1125 -275 0 1125 -566 -583 0 0 0 0 0 00000021878 00000014791 0 0 0 0 0 0 0
-113 -27 0 113 -576 -588 0 0 0 0 0 00000017378 00000013183 0 0 0 0 0 0 0
-1135 -265 0 1135 -586 -593 0 0 0 0 0 00000013804 00000011749 0 0 0 0 0 0 0
-114 -26 0 114 -596 -598 0 0 0 0 0 00000010965 00000010471 0 0 0 0 0 0 0
-1145 -255 0 1145 -606 -603 0 0 0 0 0 0000000871 00000009333 0 0 0 0 0 0 0
-115 -25 0 115 -616 -608 0 0 0 0 0 00000006918 00000008318 0 0 0 0 0 0 0
-1155 -245 0 1155 -626 -613 0 0 0 0 0 00000005495 00000007413 0 0 0 0 0 0 0
-116 -24 0 116 -636 -618 0 0 0 0 0 00000004365 00000006607 0 0 0 0 0 0 0
-1165 -235 0 1165 -646 -623 0 0 0 0 0 00000003467 00000005888 0 0 0 0 0 0 0
-117 -23 0 117 -656 -628 0 0 0 0 0 00000002754 00000005248 0 0 0 0 0 0 0
-1175 -225 0 1175 -666 -633 0 0 0 0 0 00000002188 00000004677 0 0 0 0 0 0 0
-118 -22 0 118 -676 -638 0 0 0 0 0 00000001738 00000004169 0 0 0 0 0 0 0
-1185 -215 0 1185 -686 -643 0 0 0 0 0 0000000138 00000003715 0 0 0 0 0 0 0
-119 -21 0 119 -696 -648 0 0 0 0 0 00000001096 00000003311 0 0 0 0 0 0 0
-1195 -205 0 1195 -706 -653 0 0 0 0 0 00000000871 00000002951 0 0 0 0 0 0 0
-12 -2 0 12 -716 -658 0 0 0 0 0 00000000692 0000000263 0 0 0 0 0 0 0
-1205 -195 0 1205 -726 -663 0 0 0 0 0 0000000055 00000002344 0 0 0 0 0 0 0
-121 -19 0 121 -736 -668 0 0 0 0 0 00000000437 00000002089 0 0 0 0 0 0 0
-1215 -185 0 1215 -746 -673 0 0 0 0 0 00000000347 00000001862 0 0 0 0 0 0 0
-122 -18 0 122 -756 -678 0 0 0 0 0 00000000275 0000000166 0 0 0 0 0 0 0
-1225 -175 0 1225 -766 -683 0 0 0 0 0 00000000219 00000001479 0 0 0 0 0 0 0
-123 -17 0 123 -776 -688 0 0 0 0 0 00000000174 00000001318 0 0 0 0 0 0 0
-1235 -165 0 1235 -786 -693 0 0 0 0 0 00000000138 00000001175 0 0 0 0 0 0 0
-124 -16 0 124 -796 -698 0 0 0 0 0 0000000011 00000001047 0 0 0 0 0 0 0
-1245 -155 0 1245 -806 -703 0 0 0 0 0 00000000087 00000000933 0 0 0 0 0 0 0
-125 -15 0 125 -816 -708 0 0 0 0 0 00000000069 00000000832 0 0 0 0 0 0 0
-1255 -145 0 1255 -826 -713 0 0 0 0 0 00000000055 00000000741 0 0 0 0 0 0 0
-126 -14 0 126 -836 -718 0 0 0 0 0 00000000044 00000000661 0 0 0 0 0 0 0
-1265 -135 0 1265 -846 -723 0 0 0 0 0 00000000035 00000000589 0 0 0 0 0 0 0
-127 -13 0 127 -856 -728 0 0 0 0 0 00000000028 00000000525 0 0 0 0 0 0 0
-1275 -125 0 1275 -866 -733 0 0 0 0 0 00000000022 00000000468 0 0 0 0 0 0 0
-128 -12 0 128 -876 -738 0 0 0 0 0 00000000017 00000000417 0 0 0 0 0 0 0
-1285 -115 0 1285 -886 -743 0 0 0 0 0 00000000014 00000000372 0 0 0 0 0 0 0
-129 -11 0 129 -896 -748 0 0 0 0 0 00000000011 00000000331 0 0 0 0 0 0 0
-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
-13 -1 0 13 -916 -758 0 0 0 0 0 00000000007 00000000263 0 0 0 0 0 0 0
-1305 -095 0 1305 -926 -763 0 0 0 0 0 00000000005 00000000234 0 0 0 0 0 0 0
-131 -09 0 131 -936 -768 0 0 0 0 0 00000000004 00000000209 0 0 0 0 0 0 0
-1315 -085 0 1315 -946 -773 0 0 0 0 0 00000000003 00000000186 0 0 0 0 0 0 0
-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
-1325 -075 0 1325 -966 -783 0 0 0 0 0 00000000002 00000000148 0 0 0 0 0 0 0
-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
-1395 -005 0 1395 -1106 -853 0 0 0 0 0 0 0000000003 0 0 0 0 0 0 0
-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 9: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Solubility of some simple salts Barium sulfate

BaSO4 = Ba+2 + SO4-2

Kso = 10-996 = [Ba+2][SO4-2]

How much will dissolve and what will the barium and sulfate concentrations be

How much will dissolve in a 1mM solution of Na2SO4

David Reckhow CEE 680 34 9

984

2969

1010

minus

minus

=

=

xx

( )

9667

96963

32

3969

101009712

1041010

101010

minusminus

minusminusminus

minus

minusminus

==

minusplusmnminus=

+=

+=

x

xx

xxxx

Presenter
Presentation Notes
Simplify last equation by neglecting the second ldquoxrdquo in right hand term

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-28 -112 00015848932 28 1124 262 0 0 0 0 0 173780082874938 4168693834703 0 0 0 0 0 0 0
-285 -1115 00014125375 285 1114 257 0 0 0 0 0 138038426460289 3715352290972 0 0 0 0 0 0 0
-29 -111 00012589254 29 1104 252 0 0 0 0 0 109647819614319 3311311214826 0 0 0 0 0 0 0
-295 -1105 00011220185 295 1094 247 0 0 0 0 0 870963589956082 2951209226666 0 0 0 0 0 0 0
-3 -11 0001 3 1084 242 0 0 0 0 0 691830970918939 2630267991895 0 0 0 0 0 0 0
-305 -1095 00008912509 305 1074 237 0 0 0 0 0 549540873857627 234422881532 0 0 0 0 0 0 0
-31 -109 00007943282 31 1064 232 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-315 -1085 00007079458 315 1054 227 0 0 0 0 0 346736850452531 1862087136663 0 0 0 0 0 0 0
-32 -108 00006309573 32 1044 222 0 0 0 0 0 275422870333817 1659586907438 0 0 0 0 0 0 0
-325 -1075 00005623413 325 1034 217 0 0 0 0 0 218776162394955 1479108388168 0 0 0 0 0 0 0
-33 -107 00005011872 33 1024 212 0 0 0 0 0 173780082874938 1318256738556 0 0 0 0 0 0 0
-335 -1065 00004466836 335 1014 207 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-34 -106 00003981072 34 1004 202 0 0 0 0 0 109647819614319 1047128548051 0 0 0 0 0 0 0
-345 -1055 00003548134 345 994 197 0 0 0 0 0 870963589956081 933254300797 0 0 0 0 0 0 0
-35 -105 00003162278 35 984 192 0 0 0 0 0 691830970918938 831763771103 0 0 0 0 0 0 0
-355 -1045 00002818383 355 974 187 0 0 0 0 0 549540873857626 741310241301 0 0 0 0 0 0 0
-36 -104 00002511886 36 964 182 0 0 0 0 0 436515832240168 660693448008 0 0 0 0 0 0 0
-365 -1035 00002238721 365 954 177 0 0 0 0 0 346736850452532 588843655356 0 0 0 0 0 0 0
-37 -103 00001995262 37 944 172 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-375 -1025 00001778279 375 934 167 0 0 0 0 0 218776162394956 467735141287 0 0 0 0 0 0 0
-38 -102 00001584893 38 924 162 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-385 -1015 00001412538 385 914 157 0 0 0 0 0 138038426460289 371535229097 0 0 0 0 0 0 0
-39 -101 00001258925 39 904 152 0 0 0 0 0 109647819614318 331131121483 0 0 0 0 0 0 0
-395 -1005 00001122018 395 894 147 0 0 0 0 0 870963589956081 295120922667 0 0 0 0 0 0 0
-4 -10 00001 4 884 142 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-405 -995 00000891251 405 874 137 0 0 0 0 0 549540873857625 234422881532 0 0 0 0 0 0 0
-41 -99 00000794328 41 864 132 0 0 0 0 0 436515832240167 208929613085 0 0 0 0 0 0 0
-415 -985 00000707946 415 854 127 0 0 0 0 0 346736850452532 186208713666 0 0 0 0 0 0 0
-42 -98 00000630957 42 844 122 0 0 0 0 0 275422870333817 165958690744 0 0 0 0 0 0 0
-425 -975 00000562341 425 834 117 0 0 0 0 0 218776162394956 147910838817 0 0 0 0 0 0 0
-43 -97 00000501187 43 824 112 0 0 0 0 0 173780082874938 131825673856 0 0 0 0 0 0 0
-435 -965 00000446684 435 814 107 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-44 -96 00000398107 44 804 102 0 0 0 0 0 109647819614319 104712854805 0 0 0 0 0 0 0
-445 -955 00000354813 445 794 097 0 0 0 0 0 870963589956083 9332543008 0 0 0 0 0 0 0
-45 -95 00000316228 45 784 092 0 0 0 0 0 691830970918936 8317637711 0 0 0 0 0 0 0
-455 -945 00000281838 455 774 087 0 0 0 0 0 549540873857625 7413102413 0 0 0 0 0 0 0
-46 -94 00000251189 46 764 082 0 0 0 0 0 436515832240167 66069344801 0 0 0 0 0 0 0
-465 -935 00000223872 465 754 077 0 0 0 0 0 346736850452531 58884365536 0 0 0 0 0 0 0
-47 -93 00000199526 47 744 072 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-475 -925 00000177828 475 734 067 0 0 0 0 0 218776162394955 46773514129 0 0 0 0 0 0 0
-48 -92 00000158489 48 724 062 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-485 -915 00000141254 485 714 057 0 0 0 0 0 138038426460289 3715352291 0 0 0 0 0 0 0
-49 -91 00000125893 49 704 052 0 0 0 0 0 109647819614319 33113112148 0 0 0 0 0 0 0
-495 -905 00000112202 495 694 047 0 0 0 0 0 870963589956082 29512092267 0 0 0 0 0 0 0
-5 -9 000001 5 684 042 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-505 -895 00000089125 505 674 037 0 0 0 0 0 549540873857625 23442288153 0 0 0 0 0 0 0
-51 -89 00000079433 51 664 032 0 0 0 0 0 436515832240167 20892961309 0 0 0 0 0 0 0
-515 -885 00000070795 515 654 027 0 0 0 0 0 346736850452532 18620871367 0 0 0 0 0 0 0
-52 -88 00000063096 52 644 022 0 0 0 0 0 275422870333817 16595869074 0 0 0 0 0 0 0
-525 -875 00000056234 525 634 017 0 0 0 0 0 218776162394956 14791083882 0 0 0 0 0 0 0
-53 -87 00000050119 53 624 012 0 0 0 0 0 173780082874938 13182567386 0 0 0 0 0 0 0
-535 -865 00000044668 535 614 007 0 0 0 0 0 138038426460289 11748975549 0 0 0 0 0 0 0
-54 -86 00000039811 54 604 002 0 0 0 0 0 109647819614318 10471285481 0 0 0 0 0 0 0
-545 -855 00000035481 545 594 -003 0 0 0 0 0 870963589956081 09332543008 0 0 0 0 0 0 0
-55 -85 00000031623 55 584 -008 0 0 0 0 0 691830970918937 08317637711 0 0 0 0 0 0 0
-555 -845 00000028184 555 574 -013 0 0 0 0 0 549540873857626 07413102413 0 0 0 0 0 0 0
-56 -84 00000025119 56 564 -018 0 0 0 0 0 436515832240167 0660693448 0 0 0 0 0 0 0
-565 -835 00000022387 565 554 -023 0 0 0 0 0 346736850452531 05888436554 0 0 0 0 0 0 0
-57 -83 00000019953 57 544 -028 0 0 0 0 0 275422870333817 05248074602 0 0 0 0 0 0 0
-575 -825 00000017783 575 534 -033 0 0 0 0 0 218776162394955 04677351413 0 0 0 0 0 0 0
-58 -82 00000015849 58 524 -038 0 0 0 0 0 173780082874938 04168693835 0 0 0 0 0 0 0
-585 -815 00000014125 585 514 -043 0 0 0 0 0 138038426460289 03715352291 0 0 0 0 0 0 0
-59 -81 00000012589 59 504 -048 0 0 0 0 0 109647819614318 03311311215 0 0 0 0 0 0 0
-595 -805 0000001122 595 494 -053 0 0 0 0 0 870963589956081 02951209227 0 0 0 0 0 0 0
-6 -8 0000001 6 484 -058 0 0 0 0 0 691830970918937 02630267992 0 0 0 0 0 0 0
-605 -795 00000008913 605 474 -063 0 0 0 0 0 549540873857625 02344228815 0 0 0 0 0 0 0
-61 -79 00000007943 61 464 -068 0 0 0 0 0 436515832240167 02089296131 0 0 0 0 0 0 0
-615 -785 00000007079 615 454 -073 0 0 0 0 0 346736850452531 01862087137 0 0 0 0 0 0 0
-62 -78 0000000631 62 444 -078 0 0 0 0 0 275422870333817 01659586907 0 0 0 0 0 0 0
-625 -775 00000005623 625 434 -083 0 0 0 0 0 218776162394955 01479108388 0 0 0 0 0 0 0
-63 -77 00000005012 63 424 -088 0 0 0 0 0 173780082874938 01318256739 0 0 0 0 0 0 0
-635 -765 00000004467 635 414 -093 0 0 0 0 0 138038426460289 01174897555 0 0 0 0 0 0 0
-64 -76 00000003981 64 404 -098 0 0 0 0 0 109647819614318 01047128548 0 0 0 0 0 0 0
-645 -755 00000003548 645 394 -103 0 0 0 0 0 87096358995608 00933254301 0 0 0 0 0 0 0
-65 -75 00000003162 65 384 -108 0 0 0 0 0 69183097091894 00831763771 0 0 0 0 0 0 0
-655 -745 00000002818 655 374 -113 0 0 0 0 0 54954087385762 00741310241 0 0 0 0 0 0 0
-66 -74 00000002512 66 364 -118 0 0 0 0 0 43651583224017 00660693448 0 0 0 0 0 0 0
-665 -735 00000002239 665 354 -123 0 0 0 0 0 34673685045253 00588843655 0 0 0 0 0 0 0
-67 -73 00000001995 67 344 -128 0 0 0 0 0 27542287033382 0052480746 0 0 0 0 0 0 0
-675 -725 00000001778 675 334 -133 0 0 0 0 0 21877616239496 00467735141 0 0 0 0 0 0 0
-68 -72 00000001585 68 324 -138 0 0 0 0 0 17378008287494 00416869383 0 0 0 0 0 0 0
-685 -715 00000001413 685 314 -143 0 0 0 0 0 13803842646029 00371535229 0 0 0 0 0 0 0
-69 -71 00000001259 69 304 -148 0 0 0 0 0 10964781961432 00331131121 0 0 0 0 0 0 0
-695 -705 00000001122 695 294 -153 0 0 0 0 0 8709635899561 00295120923 0 0 0 0 0 0 0
-7 -7 00000001 7 284 -158 0 0 0 0 0 6918309709189 00263026799 0 0 0 0 0 0 0
-705 -695 00000000891 705 274 -163 0 0 0 0 0 5495408738576 00234422882 0 0 0 0 0 0 0
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-715 -685 00000000708 715 254 -173 0 0 0 0 0 3467368504525 00186208714 0 0 0 0 0 0 0
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-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 10: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Solubility of ldquosimplerdquo salts

David Reckhow CEE 680 34 10

Stumm amp Morgan 1996 Figure 71 pg 354

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
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-114 -26 0 114 -596 -598 0 0 0 0 0 00000010965 00000010471 0 0 0 0 0 0 0
-1145 -255 0 1145 -606 -603 0 0 0 0 0 0000000871 00000009333 0 0 0 0 0 0 0
-115 -25 0 115 -616 -608 0 0 0 0 0 00000006918 00000008318 0 0 0 0 0 0 0
-1155 -245 0 1155 -626 -613 0 0 0 0 0 00000005495 00000007413 0 0 0 0 0 0 0
-116 -24 0 116 -636 -618 0 0 0 0 0 00000004365 00000006607 0 0 0 0 0 0 0
-1165 -235 0 1165 -646 -623 0 0 0 0 0 00000003467 00000005888 0 0 0 0 0 0 0
-117 -23 0 117 -656 -628 0 0 0 0 0 00000002754 00000005248 0 0 0 0 0 0 0
-1175 -225 0 1175 -666 -633 0 0 0 0 0 00000002188 00000004677 0 0 0 0 0 0 0
-118 -22 0 118 -676 -638 0 0 0 0 0 00000001738 00000004169 0 0 0 0 0 0 0
-1185 -215 0 1185 -686 -643 0 0 0 0 0 0000000138 00000003715 0 0 0 0 0 0 0
-119 -21 0 119 -696 -648 0 0 0 0 0 00000001096 00000003311 0 0 0 0 0 0 0
-1195 -205 0 1195 -706 -653 0 0 0 0 0 00000000871 00000002951 0 0 0 0 0 0 0
-12 -2 0 12 -716 -658 0 0 0 0 0 00000000692 0000000263 0 0 0 0 0 0 0
-1205 -195 0 1205 -726 -663 0 0 0 0 0 0000000055 00000002344 0 0 0 0 0 0 0
-121 -19 0 121 -736 -668 0 0 0 0 0 00000000437 00000002089 0 0 0 0 0 0 0
-1215 -185 0 1215 -746 -673 0 0 0 0 0 00000000347 00000001862 0 0 0 0 0 0 0
-122 -18 0 122 -756 -678 0 0 0 0 0 00000000275 0000000166 0 0 0 0 0 0 0
-1225 -175 0 1225 -766 -683 0 0 0 0 0 00000000219 00000001479 0 0 0 0 0 0 0
-123 -17 0 123 -776 -688 0 0 0 0 0 00000000174 00000001318 0 0 0 0 0 0 0
-1235 -165 0 1235 -786 -693 0 0 0 0 0 00000000138 00000001175 0 0 0 0 0 0 0
-124 -16 0 124 -796 -698 0 0 0 0 0 0000000011 00000001047 0 0 0 0 0 0 0
-1245 -155 0 1245 -806 -703 0 0 0 0 0 00000000087 00000000933 0 0 0 0 0 0 0
-125 -15 0 125 -816 -708 0 0 0 0 0 00000000069 00000000832 0 0 0 0 0 0 0
-1255 -145 0 1255 -826 -713 0 0 0 0 0 00000000055 00000000741 0 0 0 0 0 0 0
-126 -14 0 126 -836 -718 0 0 0 0 0 00000000044 00000000661 0 0 0 0 0 0 0
-1265 -135 0 1265 -846 -723 0 0 0 0 0 00000000035 00000000589 0 0 0 0 0 0 0
-127 -13 0 127 -856 -728 0 0 0 0 0 00000000028 00000000525 0 0 0 0 0 0 0
-1275 -125 0 1275 -866 -733 0 0 0 0 0 00000000022 00000000468 0 0 0 0 0 0 0
-128 -12 0 128 -876 -738 0 0 0 0 0 00000000017 00000000417 0 0 0 0 0 0 0
-1285 -115 0 1285 -886 -743 0 0 0 0 0 00000000014 00000000372 0 0 0 0 0 0 0
-129 -11 0 129 -896 -748 0 0 0 0 0 00000000011 00000000331 0 0 0 0 0 0 0
-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
-13 -1 0 13 -916 -758 0 0 0 0 0 00000000007 00000000263 0 0 0 0 0 0 0
-1305 -095 0 1305 -926 -763 0 0 0 0 0 00000000005 00000000234 0 0 0 0 0 0 0
-131 -09 0 131 -936 -768 0 0 0 0 0 00000000004 00000000209 0 0 0 0 0 0 0
-1315 -085 0 1315 -946 -773 0 0 0 0 0 00000000003 00000000186 0 0 0 0 0 0 0
-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
-1325 -075 0 1325 -966 -783 0 0 0 0 0 00000000002 00000000148 0 0 0 0 0 0 0
-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
-1395 -005 0 1395 -1106 -853 0 0 0 0 0 0 0000000003 0 0 0 0 0 0 0
-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 11: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Solubility of oxides amp hydroxides Does not consider the hydroxometal complexes

David Reckhow CEE 680 34 11

Stumm amp Morgan 1996 Figure 73 pg 365

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-28 -112 00015848932 28 1124 262 0 0 0 0 0 173780082874938 4168693834703 0 0 0 0 0 0 0
-285 -1115 00014125375 285 1114 257 0 0 0 0 0 138038426460289 3715352290972 0 0 0 0 0 0 0
-29 -111 00012589254 29 1104 252 0 0 0 0 0 109647819614319 3311311214826 0 0 0 0 0 0 0
-295 -1105 00011220185 295 1094 247 0 0 0 0 0 870963589956082 2951209226666 0 0 0 0 0 0 0
-3 -11 0001 3 1084 242 0 0 0 0 0 691830970918939 2630267991895 0 0 0 0 0 0 0
-305 -1095 00008912509 305 1074 237 0 0 0 0 0 549540873857627 234422881532 0 0 0 0 0 0 0
-31 -109 00007943282 31 1064 232 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-315 -1085 00007079458 315 1054 227 0 0 0 0 0 346736850452531 1862087136663 0 0 0 0 0 0 0
-32 -108 00006309573 32 1044 222 0 0 0 0 0 275422870333817 1659586907438 0 0 0 0 0 0 0
-325 -1075 00005623413 325 1034 217 0 0 0 0 0 218776162394955 1479108388168 0 0 0 0 0 0 0
-33 -107 00005011872 33 1024 212 0 0 0 0 0 173780082874938 1318256738556 0 0 0 0 0 0 0
-335 -1065 00004466836 335 1014 207 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-34 -106 00003981072 34 1004 202 0 0 0 0 0 109647819614319 1047128548051 0 0 0 0 0 0 0
-345 -1055 00003548134 345 994 197 0 0 0 0 0 870963589956081 933254300797 0 0 0 0 0 0 0
-35 -105 00003162278 35 984 192 0 0 0 0 0 691830970918938 831763771103 0 0 0 0 0 0 0
-355 -1045 00002818383 355 974 187 0 0 0 0 0 549540873857626 741310241301 0 0 0 0 0 0 0
-36 -104 00002511886 36 964 182 0 0 0 0 0 436515832240168 660693448008 0 0 0 0 0 0 0
-365 -1035 00002238721 365 954 177 0 0 0 0 0 346736850452532 588843655356 0 0 0 0 0 0 0
-37 -103 00001995262 37 944 172 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-375 -1025 00001778279 375 934 167 0 0 0 0 0 218776162394956 467735141287 0 0 0 0 0 0 0
-38 -102 00001584893 38 924 162 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-385 -1015 00001412538 385 914 157 0 0 0 0 0 138038426460289 371535229097 0 0 0 0 0 0 0
-39 -101 00001258925 39 904 152 0 0 0 0 0 109647819614318 331131121483 0 0 0 0 0 0 0
-395 -1005 00001122018 395 894 147 0 0 0 0 0 870963589956081 295120922667 0 0 0 0 0 0 0
-4 -10 00001 4 884 142 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-405 -995 00000891251 405 874 137 0 0 0 0 0 549540873857625 234422881532 0 0 0 0 0 0 0
-41 -99 00000794328 41 864 132 0 0 0 0 0 436515832240167 208929613085 0 0 0 0 0 0 0
-415 -985 00000707946 415 854 127 0 0 0 0 0 346736850452532 186208713666 0 0 0 0 0 0 0
-42 -98 00000630957 42 844 122 0 0 0 0 0 275422870333817 165958690744 0 0 0 0 0 0 0
-425 -975 00000562341 425 834 117 0 0 0 0 0 218776162394956 147910838817 0 0 0 0 0 0 0
-43 -97 00000501187 43 824 112 0 0 0 0 0 173780082874938 131825673856 0 0 0 0 0 0 0
-435 -965 00000446684 435 814 107 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-44 -96 00000398107 44 804 102 0 0 0 0 0 109647819614319 104712854805 0 0 0 0 0 0 0
-445 -955 00000354813 445 794 097 0 0 0 0 0 870963589956083 9332543008 0 0 0 0 0 0 0
-45 -95 00000316228 45 784 092 0 0 0 0 0 691830970918936 8317637711 0 0 0 0 0 0 0
-455 -945 00000281838 455 774 087 0 0 0 0 0 549540873857625 7413102413 0 0 0 0 0 0 0
-46 -94 00000251189 46 764 082 0 0 0 0 0 436515832240167 66069344801 0 0 0 0 0 0 0
-465 -935 00000223872 465 754 077 0 0 0 0 0 346736850452531 58884365536 0 0 0 0 0 0 0
-47 -93 00000199526 47 744 072 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-475 -925 00000177828 475 734 067 0 0 0 0 0 218776162394955 46773514129 0 0 0 0 0 0 0
-48 -92 00000158489 48 724 062 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-485 -915 00000141254 485 714 057 0 0 0 0 0 138038426460289 3715352291 0 0 0 0 0 0 0
-49 -91 00000125893 49 704 052 0 0 0 0 0 109647819614319 33113112148 0 0 0 0 0 0 0
-495 -905 00000112202 495 694 047 0 0 0 0 0 870963589956082 29512092267 0 0 0 0 0 0 0
-5 -9 000001 5 684 042 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-505 -895 00000089125 505 674 037 0 0 0 0 0 549540873857625 23442288153 0 0 0 0 0 0 0
-51 -89 00000079433 51 664 032 0 0 0 0 0 436515832240167 20892961309 0 0 0 0 0 0 0
-515 -885 00000070795 515 654 027 0 0 0 0 0 346736850452532 18620871367 0 0 0 0 0 0 0
-52 -88 00000063096 52 644 022 0 0 0 0 0 275422870333817 16595869074 0 0 0 0 0 0 0
-525 -875 00000056234 525 634 017 0 0 0 0 0 218776162394956 14791083882 0 0 0 0 0 0 0
-53 -87 00000050119 53 624 012 0 0 0 0 0 173780082874938 13182567386 0 0 0 0 0 0 0
-535 -865 00000044668 535 614 007 0 0 0 0 0 138038426460289 11748975549 0 0 0 0 0 0 0
-54 -86 00000039811 54 604 002 0 0 0 0 0 109647819614318 10471285481 0 0 0 0 0 0 0
-545 -855 00000035481 545 594 -003 0 0 0 0 0 870963589956081 09332543008 0 0 0 0 0 0 0
-55 -85 00000031623 55 584 -008 0 0 0 0 0 691830970918937 08317637711 0 0 0 0 0 0 0
-555 -845 00000028184 555 574 -013 0 0 0 0 0 549540873857626 07413102413 0 0 0 0 0 0 0
-56 -84 00000025119 56 564 -018 0 0 0 0 0 436515832240167 0660693448 0 0 0 0 0 0 0
-565 -835 00000022387 565 554 -023 0 0 0 0 0 346736850452531 05888436554 0 0 0 0 0 0 0
-57 -83 00000019953 57 544 -028 0 0 0 0 0 275422870333817 05248074602 0 0 0 0 0 0 0
-575 -825 00000017783 575 534 -033 0 0 0 0 0 218776162394955 04677351413 0 0 0 0 0 0 0
-58 -82 00000015849 58 524 -038 0 0 0 0 0 173780082874938 04168693835 0 0 0 0 0 0 0
-585 -815 00000014125 585 514 -043 0 0 0 0 0 138038426460289 03715352291 0 0 0 0 0 0 0
-59 -81 00000012589 59 504 -048 0 0 0 0 0 109647819614318 03311311215 0 0 0 0 0 0 0
-595 -805 0000001122 595 494 -053 0 0 0 0 0 870963589956081 02951209227 0 0 0 0 0 0 0
-6 -8 0000001 6 484 -058 0 0 0 0 0 691830970918937 02630267992 0 0 0 0 0 0 0
-605 -795 00000008913 605 474 -063 0 0 0 0 0 549540873857625 02344228815 0 0 0 0 0 0 0
-61 -79 00000007943 61 464 -068 0 0 0 0 0 436515832240167 02089296131 0 0 0 0 0 0 0
-615 -785 00000007079 615 454 -073 0 0 0 0 0 346736850452531 01862087137 0 0 0 0 0 0 0
-62 -78 0000000631 62 444 -078 0 0 0 0 0 275422870333817 01659586907 0 0 0 0 0 0 0
-625 -775 00000005623 625 434 -083 0 0 0 0 0 218776162394955 01479108388 0 0 0 0 0 0 0
-63 -77 00000005012 63 424 -088 0 0 0 0 0 173780082874938 01318256739 0 0 0 0 0 0 0
-635 -765 00000004467 635 414 -093 0 0 0 0 0 138038426460289 01174897555 0 0 0 0 0 0 0
-64 -76 00000003981 64 404 -098 0 0 0 0 0 109647819614318 01047128548 0 0 0 0 0 0 0
-645 -755 00000003548 645 394 -103 0 0 0 0 0 87096358995608 00933254301 0 0 0 0 0 0 0
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-67 -73 00000001995 67 344 -128 0 0 0 0 0 27542287033382 0052480746 0 0 0 0 0 0 0
-675 -725 00000001778 675 334 -133 0 0 0 0 0 21877616239496 00467735141 0 0 0 0 0 0 0
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-685 -715 00000001413 685 314 -143 0 0 0 0 0 13803842646029 00371535229 0 0 0 0 0 0 0
-69 -71 00000001259 69 304 -148 0 0 0 0 0 10964781961432 00331131121 0 0 0 0 0 0 0
-695 -705 00000001122 695 294 -153 0 0 0 0 0 8709635899561 00295120923 0 0 0 0 0 0 0
-7 -7 00000001 7 284 -158 0 0 0 0 0 6918309709189 00263026799 0 0 0 0 0 0 0
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Page 12: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Solubility of metal hydroxides Adds complexity

hydroxide concentration is controlled by pH and therefore affected by buffering

many ldquohydrolyzingrdquo metals have soluble hydroxide species too

Example Magnesium Hydroxide Weakly hydrolyzes Only one soluble hydroxide species Practical we remove Mg by precipitative softening

David Reckhow CEE 680 34 12

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
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-126 -14 0 126 -836 -718 0 0 0 0 0 00000000044 00000000661 0 0 0 0 0 0 0
-1265 -135 0 1265 -846 -723 0 0 0 0 0 00000000035 00000000589 0 0 0 0 0 0 0
-127 -13 0 127 -856 -728 0 0 0 0 0 00000000028 00000000525 0 0 0 0 0 0 0
-1275 -125 0 1275 -866 -733 0 0 0 0 0 00000000022 00000000468 0 0 0 0 0 0 0
-128 -12 0 128 -876 -738 0 0 0 0 0 00000000017 00000000417 0 0 0 0 0 0 0
-1285 -115 0 1285 -886 -743 0 0 0 0 0 00000000014 00000000372 0 0 0 0 0 0 0
-129 -11 0 129 -896 -748 0 0 0 0 0 00000000011 00000000331 0 0 0 0 0 0 0
-1295 -105 0 1295 -906 -753 0 0 0 0 0 00000000009 00000000295 0 0 0 0 0 0 0
-13 -1 0 13 -916 -758 0 0 0 0 0 00000000007 00000000263 0 0 0 0 0 0 0
-1305 -095 0 1305 -926 -763 0 0 0 0 0 00000000005 00000000234 0 0 0 0 0 0 0
-131 -09 0 131 -936 -768 0 0 0 0 0 00000000004 00000000209 0 0 0 0 0 0 0
-1315 -085 0 1315 -946 -773 0 0 0 0 0 00000000003 00000000186 0 0 0 0 0 0 0
-132 -08 0 132 -956 -778 0 0 0 0 0 00000000003 00000000166 0 0 0 0 0 0 0
-1325 -075 0 1325 -966 -783 0 0 0 0 0 00000000002 00000000148 0 0 0 0 0 0 0
-133 -07 0 133 -976 -788 0 0 0 0 0 00000000002 00000000132 0 0 0 0 0 0 0
-1335 -065 0 1335 -986 -793 0 0 0 0 0 00000000001 00000000117 0 0 0 0 0 0 0
-134 -06 0 134 -996 -798 0 0 0 0 0 00000000001 00000000105 0 0 0 0 0 0 0
-1345 -055 0 1345 -1006 -803 0 0 0 0 0 00000000001 00000000093 0 0 0 0 0 0 0
-135 -05 0 135 -1016 -808 0 0 0 0 0 00000000001 00000000083 0 0 0 0 0 0 0
-1355 -045 0 1355 -1026 -813 0 0 0 0 0 00000000001 00000000074 0 0 0 0 0 0 0
-136 -04 0 136 -1036 -818 0 0 0 0 0 0 00000000066 0 0 0 0 0 0 0
-1365 -035 0 1365 -1046 -823 0 0 0 0 0 0 00000000059 0 0 0 0 0 0 0
-137 -03 0 137 -1056 -828 0 0 0 0 0 0 00000000052 0 0 0 0 0 0 0
-1375 -025 0 1375 -1066 -833 0 0 0 0 0 0 00000000047 0 0 0 0 0 0 0
-138 -02 0 138 -1076 -838 0 0 0 0 0 0 00000000042 0 0 0 0 0 0 0
-1385 -015 0 1385 -1086 -843 0 0 0 0 0 0 00000000037 0 0 0 0 0 0 0
-139 -01 0 139 -1096 -848 0 0 0 0 0 0 00000000033 0 0 0 0 0 0 0
-1395 -005 0 1395 -1106 -853 0 0 0 0 0 0 0000000003 0 0 0 0 0 0 0
-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 13: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Magnesium Hydroxide Thermodynamics Mg(OH)2 (s) = Mg+2 + 2OH- Kso = 10-1116

Mg+2 + OH- = MgOH+ K1 = 1026

Mass Balance MgT = [Mg+2] + [MgOH+]

David Reckhow CEE 680 34 13

Total dissolved concentration does not include precipitated Mg

256 Stumm212 Benjamin26 Morel258 Smith

-1179 Benjamin-111 Morel-1074 Butler-129 SMampP-1116 Brezonik-1115 Smith

Mg(OH)2 (s) is crystalline Brucite

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-28 -112 00015848932 28 1124 262 0 0 0 0 0 173780082874938 4168693834703 0 0 0 0 0 0 0
-285 -1115 00014125375 285 1114 257 0 0 0 0 0 138038426460289 3715352290972 0 0 0 0 0 0 0
-29 -111 00012589254 29 1104 252 0 0 0 0 0 109647819614319 3311311214826 0 0 0 0 0 0 0
-295 -1105 00011220185 295 1094 247 0 0 0 0 0 870963589956082 2951209226666 0 0 0 0 0 0 0
-3 -11 0001 3 1084 242 0 0 0 0 0 691830970918939 2630267991895 0 0 0 0 0 0 0
-305 -1095 00008912509 305 1074 237 0 0 0 0 0 549540873857627 234422881532 0 0 0 0 0 0 0
-31 -109 00007943282 31 1064 232 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-315 -1085 00007079458 315 1054 227 0 0 0 0 0 346736850452531 1862087136663 0 0 0 0 0 0 0
-32 -108 00006309573 32 1044 222 0 0 0 0 0 275422870333817 1659586907438 0 0 0 0 0 0 0
-325 -1075 00005623413 325 1034 217 0 0 0 0 0 218776162394955 1479108388168 0 0 0 0 0 0 0
-33 -107 00005011872 33 1024 212 0 0 0 0 0 173780082874938 1318256738556 0 0 0 0 0 0 0
-335 -1065 00004466836 335 1014 207 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-34 -106 00003981072 34 1004 202 0 0 0 0 0 109647819614319 1047128548051 0 0 0 0 0 0 0
-345 -1055 00003548134 345 994 197 0 0 0 0 0 870963589956081 933254300797 0 0 0 0 0 0 0
-35 -105 00003162278 35 984 192 0 0 0 0 0 691830970918938 831763771103 0 0 0 0 0 0 0
-355 -1045 00002818383 355 974 187 0 0 0 0 0 549540873857626 741310241301 0 0 0 0 0 0 0
-36 -104 00002511886 36 964 182 0 0 0 0 0 436515832240168 660693448008 0 0 0 0 0 0 0
-365 -1035 00002238721 365 954 177 0 0 0 0 0 346736850452532 588843655356 0 0 0 0 0 0 0
-37 -103 00001995262 37 944 172 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-375 -1025 00001778279 375 934 167 0 0 0 0 0 218776162394956 467735141287 0 0 0 0 0 0 0
-38 -102 00001584893 38 924 162 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-385 -1015 00001412538 385 914 157 0 0 0 0 0 138038426460289 371535229097 0 0 0 0 0 0 0
-39 -101 00001258925 39 904 152 0 0 0 0 0 109647819614318 331131121483 0 0 0 0 0 0 0
-395 -1005 00001122018 395 894 147 0 0 0 0 0 870963589956081 295120922667 0 0 0 0 0 0 0
-4 -10 00001 4 884 142 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-405 -995 00000891251 405 874 137 0 0 0 0 0 549540873857625 234422881532 0 0 0 0 0 0 0
-41 -99 00000794328 41 864 132 0 0 0 0 0 436515832240167 208929613085 0 0 0 0 0 0 0
-415 -985 00000707946 415 854 127 0 0 0 0 0 346736850452532 186208713666 0 0 0 0 0 0 0
-42 -98 00000630957 42 844 122 0 0 0 0 0 275422870333817 165958690744 0 0 0 0 0 0 0
-425 -975 00000562341 425 834 117 0 0 0 0 0 218776162394956 147910838817 0 0 0 0 0 0 0
-43 -97 00000501187 43 824 112 0 0 0 0 0 173780082874938 131825673856 0 0 0 0 0 0 0
-435 -965 00000446684 435 814 107 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-44 -96 00000398107 44 804 102 0 0 0 0 0 109647819614319 104712854805 0 0 0 0 0 0 0
-445 -955 00000354813 445 794 097 0 0 0 0 0 870963589956083 9332543008 0 0 0 0 0 0 0
-45 -95 00000316228 45 784 092 0 0 0 0 0 691830970918936 8317637711 0 0 0 0 0 0 0
-455 -945 00000281838 455 774 087 0 0 0 0 0 549540873857625 7413102413 0 0 0 0 0 0 0
-46 -94 00000251189 46 764 082 0 0 0 0 0 436515832240167 66069344801 0 0 0 0 0 0 0
-465 -935 00000223872 465 754 077 0 0 0 0 0 346736850452531 58884365536 0 0 0 0 0 0 0
-47 -93 00000199526 47 744 072 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-475 -925 00000177828 475 734 067 0 0 0 0 0 218776162394955 46773514129 0 0 0 0 0 0 0
-48 -92 00000158489 48 724 062 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-485 -915 00000141254 485 714 057 0 0 0 0 0 138038426460289 3715352291 0 0 0 0 0 0 0
-49 -91 00000125893 49 704 052 0 0 0 0 0 109647819614319 33113112148 0 0 0 0 0 0 0
-495 -905 00000112202 495 694 047 0 0 0 0 0 870963589956082 29512092267 0 0 0 0 0 0 0
-5 -9 000001 5 684 042 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-505 -895 00000089125 505 674 037 0 0 0 0 0 549540873857625 23442288153 0 0 0 0 0 0 0
-51 -89 00000079433 51 664 032 0 0 0 0 0 436515832240167 20892961309 0 0 0 0 0 0 0
-515 -885 00000070795 515 654 027 0 0 0 0 0 346736850452532 18620871367 0 0 0 0 0 0 0
-52 -88 00000063096 52 644 022 0 0 0 0 0 275422870333817 16595869074 0 0 0 0 0 0 0
-525 -875 00000056234 525 634 017 0 0 0 0 0 218776162394956 14791083882 0 0 0 0 0 0 0
-53 -87 00000050119 53 624 012 0 0 0 0 0 173780082874938 13182567386 0 0 0 0 0 0 0
-535 -865 00000044668 535 614 007 0 0 0 0 0 138038426460289 11748975549 0 0 0 0 0 0 0
-54 -86 00000039811 54 604 002 0 0 0 0 0 109647819614318 10471285481 0 0 0 0 0 0 0
-545 -855 00000035481 545 594 -003 0 0 0 0 0 870963589956081 09332543008 0 0 0 0 0 0 0
-55 -85 00000031623 55 584 -008 0 0 0 0 0 691830970918937 08317637711 0 0 0 0 0 0 0
-555 -845 00000028184 555 574 -013 0 0 0 0 0 549540873857626 07413102413 0 0 0 0 0 0 0
-56 -84 00000025119 56 564 -018 0 0 0 0 0 436515832240167 0660693448 0 0 0 0 0 0 0
-565 -835 00000022387 565 554 -023 0 0 0 0 0 346736850452531 05888436554 0 0 0 0 0 0 0
-57 -83 00000019953 57 544 -028 0 0 0 0 0 275422870333817 05248074602 0 0 0 0 0 0 0
-575 -825 00000017783 575 534 -033 0 0 0 0 0 218776162394955 04677351413 0 0 0 0 0 0 0
-58 -82 00000015849 58 524 -038 0 0 0 0 0 173780082874938 04168693835 0 0 0 0 0 0 0
-585 -815 00000014125 585 514 -043 0 0 0 0 0 138038426460289 03715352291 0 0 0 0 0 0 0
-59 -81 00000012589 59 504 -048 0 0 0 0 0 109647819614318 03311311215 0 0 0 0 0 0 0
-595 -805 0000001122 595 494 -053 0 0 0 0 0 870963589956081 02951209227 0 0 0 0 0 0 0
-6 -8 0000001 6 484 -058 0 0 0 0 0 691830970918937 02630267992 0 0 0 0 0 0 0
-605 -795 00000008913 605 474 -063 0 0 0 0 0 549540873857625 02344228815 0 0 0 0 0 0 0
-61 -79 00000007943 61 464 -068 0 0 0 0 0 436515832240167 02089296131 0 0 0 0 0 0 0
-615 -785 00000007079 615 454 -073 0 0 0 0 0 346736850452531 01862087137 0 0 0 0 0 0 0
-62 -78 0000000631 62 444 -078 0 0 0 0 0 275422870333817 01659586907 0 0 0 0 0 0 0
-625 -775 00000005623 625 434 -083 0 0 0 0 0 218776162394955 01479108388 0 0 0 0 0 0 0
-63 -77 00000005012 63 424 -088 0 0 0 0 0 173780082874938 01318256739 0 0 0 0 0 0 0
-635 -765 00000004467 635 414 -093 0 0 0 0 0 138038426460289 01174897555 0 0 0 0 0 0 0
-64 -76 00000003981 64 404 -098 0 0 0 0 0 109647819614318 01047128548 0 0 0 0 0 0 0
-645 -755 00000003548 645 394 -103 0 0 0 0 0 87096358995608 00933254301 0 0 0 0 0 0 0
-65 -75 00000003162 65 384 -108 0 0 0 0 0 69183097091894 00831763771 0 0 0 0 0 0 0
-655 -745 00000002818 655 374 -113 0 0 0 0 0 54954087385762 00741310241 0 0 0 0 0 0 0
-66 -74 00000002512 66 364 -118 0 0 0 0 0 43651583224017 00660693448 0 0 0 0 0 0 0
-665 -735 00000002239 665 354 -123 0 0 0 0 0 34673685045253 00588843655 0 0 0 0 0 0 0
-67 -73 00000001995 67 344 -128 0 0 0 0 0 27542287033382 0052480746 0 0 0 0 0 0 0
-675 -725 00000001778 675 334 -133 0 0 0 0 0 21877616239496 00467735141 0 0 0 0 0 0 0
-68 -72 00000001585 68 324 -138 0 0 0 0 0 17378008287494 00416869383 0 0 0 0 0 0 0
-685 -715 00000001413 685 314 -143 0 0 0 0 0 13803842646029 00371535229 0 0 0 0 0 0 0
-69 -71 00000001259 69 304 -148 0 0 0 0 0 10964781961432 00331131121 0 0 0 0 0 0 0
-695 -705 00000001122 695 294 -153 0 0 0 0 0 8709635899561 00295120923 0 0 0 0 0 0 0
-7 -7 00000001 7 284 -158 0 0 0 0 0 6918309709189 00263026799 0 0 0 0 0 0 0
-705 -695 00000000891 705 274 -163 0 0 0 0 0 5495408738576 00234422882 0 0 0 0 0 0 0
-71 -69 00000000794 71 264 -168 0 0 0 0 0 4365158322402 00208929613 0 0 0 0 0 0 0
-715 -685 00000000708 715 254 -173 0 0 0 0 0 3467368504525 00186208714 0 0 0 0 0 0 0
-72 -68 00000000631 72 244 -178 0 0 0 0 0 2754228703338 00165958691 0 0 0 0 0 0 0
-725 -675 00000000562 725 234 -183 0 0 0 0 0 218776162395 00147910839 0 0 0 0 0 0 0
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Page 14: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

David Reckhow CEE 680 34 14

Smith amp Martell

Mg(OH)2 solid

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

Sheet1

ampA
Page ampP

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
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Page 15: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Magnesium Hydroxide Tableau

[Mg+2] = 101684[H+]2

same as [Mg+2] = 10-1116[OH+]2

David Reckhow CEE 680 34 15

Components MgOH2 (Brucite H+Mg+2 1 2 1684MgOH+ 1 1 542H+ 0 1 0

ReactantsLog K

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Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
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Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-28 -112 00015848932 28 1124 262 0 0 0 0 0 173780082874938 4168693834703 0 0 0 0 0 0 0
-285 -1115 00014125375 285 1114 257 0 0 0 0 0 138038426460289 3715352290972 0 0 0 0 0 0 0
-29 -111 00012589254 29 1104 252 0 0 0 0 0 109647819614319 3311311214826 0 0 0 0 0 0 0
-295 -1105 00011220185 295 1094 247 0 0 0 0 0 870963589956082 2951209226666 0 0 0 0 0 0 0
-3 -11 0001 3 1084 242 0 0 0 0 0 691830970918939 2630267991895 0 0 0 0 0 0 0
-305 -1095 00008912509 305 1074 237 0 0 0 0 0 549540873857627 234422881532 0 0 0 0 0 0 0
-31 -109 00007943282 31 1064 232 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-315 -1085 00007079458 315 1054 227 0 0 0 0 0 346736850452531 1862087136663 0 0 0 0 0 0 0
-32 -108 00006309573 32 1044 222 0 0 0 0 0 275422870333817 1659586907438 0 0 0 0 0 0 0
-325 -1075 00005623413 325 1034 217 0 0 0 0 0 218776162394955 1479108388168 0 0 0 0 0 0 0
-33 -107 00005011872 33 1024 212 0 0 0 0 0 173780082874938 1318256738556 0 0 0 0 0 0 0
-335 -1065 00004466836 335 1014 207 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-34 -106 00003981072 34 1004 202 0 0 0 0 0 109647819614319 1047128548051 0 0 0 0 0 0 0
-345 -1055 00003548134 345 994 197 0 0 0 0 0 870963589956081 933254300797 0 0 0 0 0 0 0
-35 -105 00003162278 35 984 192 0 0 0 0 0 691830970918938 831763771103 0 0 0 0 0 0 0
-355 -1045 00002818383 355 974 187 0 0 0 0 0 549540873857626 741310241301 0 0 0 0 0 0 0
-36 -104 00002511886 36 964 182 0 0 0 0 0 436515832240168 660693448008 0 0 0 0 0 0 0
-365 -1035 00002238721 365 954 177 0 0 0 0 0 346736850452532 588843655356 0 0 0 0 0 0 0
-37 -103 00001995262 37 944 172 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-375 -1025 00001778279 375 934 167 0 0 0 0 0 218776162394956 467735141287 0 0 0 0 0 0 0
-38 -102 00001584893 38 924 162 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-385 -1015 00001412538 385 914 157 0 0 0 0 0 138038426460289 371535229097 0 0 0 0 0 0 0
-39 -101 00001258925 39 904 152 0 0 0 0 0 109647819614318 331131121483 0 0 0 0 0 0 0
-395 -1005 00001122018 395 894 147 0 0 0 0 0 870963589956081 295120922667 0 0 0 0 0 0 0
-4 -10 00001 4 884 142 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-405 -995 00000891251 405 874 137 0 0 0 0 0 549540873857625 234422881532 0 0 0 0 0 0 0
-41 -99 00000794328 41 864 132 0 0 0 0 0 436515832240167 208929613085 0 0 0 0 0 0 0
-415 -985 00000707946 415 854 127 0 0 0 0 0 346736850452532 186208713666 0 0 0 0 0 0 0
-42 -98 00000630957 42 844 122 0 0 0 0 0 275422870333817 165958690744 0 0 0 0 0 0 0
-425 -975 00000562341 425 834 117 0 0 0 0 0 218776162394956 147910838817 0 0 0 0 0 0 0
-43 -97 00000501187 43 824 112 0 0 0 0 0 173780082874938 131825673856 0 0 0 0 0 0 0
-435 -965 00000446684 435 814 107 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-44 -96 00000398107 44 804 102 0 0 0 0 0 109647819614319 104712854805 0 0 0 0 0 0 0
-445 -955 00000354813 445 794 097 0 0 0 0 0 870963589956083 9332543008 0 0 0 0 0 0 0
-45 -95 00000316228 45 784 092 0 0 0 0 0 691830970918936 8317637711 0 0 0 0 0 0 0
-455 -945 00000281838 455 774 087 0 0 0 0 0 549540873857625 7413102413 0 0 0 0 0 0 0
-46 -94 00000251189 46 764 082 0 0 0 0 0 436515832240167 66069344801 0 0 0 0 0 0 0
-465 -935 00000223872 465 754 077 0 0 0 0 0 346736850452531 58884365536 0 0 0 0 0 0 0
-47 -93 00000199526 47 744 072 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-475 -925 00000177828 475 734 067 0 0 0 0 0 218776162394955 46773514129 0 0 0 0 0 0 0
-48 -92 00000158489 48 724 062 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-485 -915 00000141254 485 714 057 0 0 0 0 0 138038426460289 3715352291 0 0 0 0 0 0 0
-49 -91 00000125893 49 704 052 0 0 0 0 0 109647819614319 33113112148 0 0 0 0 0 0 0
-495 -905 00000112202 495 694 047 0 0 0 0 0 870963589956082 29512092267 0 0 0 0 0 0 0
-5 -9 000001 5 684 042 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-505 -895 00000089125 505 674 037 0 0 0 0 0 549540873857625 23442288153 0 0 0 0 0 0 0
-51 -89 00000079433 51 664 032 0 0 0 0 0 436515832240167 20892961309 0 0 0 0 0 0 0
-515 -885 00000070795 515 654 027 0 0 0 0 0 346736850452532 18620871367 0 0 0 0 0 0 0
-52 -88 00000063096 52 644 022 0 0 0 0 0 275422870333817 16595869074 0 0 0 0 0 0 0
-525 -875 00000056234 525 634 017 0 0 0 0 0 218776162394956 14791083882 0 0 0 0 0 0 0
-53 -87 00000050119 53 624 012 0 0 0 0 0 173780082874938 13182567386 0 0 0 0 0 0 0
-535 -865 00000044668 535 614 007 0 0 0 0 0 138038426460289 11748975549 0 0 0 0 0 0 0
-54 -86 00000039811 54 604 002 0 0 0 0 0 109647819614318 10471285481 0 0 0 0 0 0 0
-545 -855 00000035481 545 594 -003 0 0 0 0 0 870963589956081 09332543008 0 0 0 0 0 0 0
-55 -85 00000031623 55 584 -008 0 0 0 0 0 691830970918937 08317637711 0 0 0 0 0 0 0
-555 -845 00000028184 555 574 -013 0 0 0 0 0 549540873857626 07413102413 0 0 0 0 0 0 0
-56 -84 00000025119 56 564 -018 0 0 0 0 0 436515832240167 0660693448 0 0 0 0 0 0 0
-565 -835 00000022387 565 554 -023 0 0 0 0 0 346736850452531 05888436554 0 0 0 0 0 0 0
-57 -83 00000019953 57 544 -028 0 0 0 0 0 275422870333817 05248074602 0 0 0 0 0 0 0
-575 -825 00000017783 575 534 -033 0 0 0 0 0 218776162394955 04677351413 0 0 0 0 0 0 0
-58 -82 00000015849 58 524 -038 0 0 0 0 0 173780082874938 04168693835 0 0 0 0 0 0 0
-585 -815 00000014125 585 514 -043 0 0 0 0 0 138038426460289 03715352291 0 0 0 0 0 0 0
-59 -81 00000012589 59 504 -048 0 0 0 0 0 109647819614318 03311311215 0 0 0 0 0 0 0
-595 -805 0000001122 595 494 -053 0 0 0 0 0 870963589956081 02951209227 0 0 0 0 0 0 0
-6 -8 0000001 6 484 -058 0 0 0 0 0 691830970918937 02630267992 0 0 0 0 0 0 0
-605 -795 00000008913 605 474 -063 0 0 0 0 0 549540873857625 02344228815 0 0 0 0 0 0 0
-61 -79 00000007943 61 464 -068 0 0 0 0 0 436515832240167 02089296131 0 0 0 0 0 0 0
-615 -785 00000007079 615 454 -073 0 0 0 0 0 346736850452531 01862087137 0 0 0 0 0 0 0
-62 -78 0000000631 62 444 -078 0 0 0 0 0 275422870333817 01659586907 0 0 0 0 0 0 0
-625 -775 00000005623 625 434 -083 0 0 0 0 0 218776162394955 01479108388 0 0 0 0 0 0 0
-63 -77 00000005012 63 424 -088 0 0 0 0 0 173780082874938 01318256739 0 0 0 0 0 0 0
-635 -765 00000004467 635 414 -093 0 0 0 0 0 138038426460289 01174897555 0 0 0 0 0 0 0
-64 -76 00000003981 64 404 -098 0 0 0 0 0 109647819614318 01047128548 0 0 0 0 0 0 0
-645 -755 00000003548 645 394 -103 0 0 0 0 0 87096358995608 00933254301 0 0 0 0 0 0 0
-65 -75 00000003162 65 384 -108 0 0 0 0 0 69183097091894 00831763771 0 0 0 0 0 0 0
-655 -745 00000002818 655 374 -113 0 0 0 0 0 54954087385762 00741310241 0 0 0 0 0 0 0
-66 -74 00000002512 66 364 -118 0 0 0 0 0 43651583224017 00660693448 0 0 0 0 0 0 0
-665 -735 00000002239 665 354 -123 0 0 0 0 0 34673685045253 00588843655 0 0 0 0 0 0 0
-67 -73 00000001995 67 344 -128 0 0 0 0 0 27542287033382 0052480746 0 0 0 0 0 0 0
-675 -725 00000001778 675 334 -133 0 0 0 0 0 21877616239496 00467735141 0 0 0 0 0 0 0
-68 -72 00000001585 68 324 -138 0 0 0 0 0 17378008287494 00416869383 0 0 0 0 0 0 0
-685 -715 00000001413 685 314 -143 0 0 0 0 0 13803842646029 00371535229 0 0 0 0 0 0 0
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-695 -705 00000001122 695 294 -153 0 0 0 0 0 8709635899561 00295120923 0 0 0 0 0 0 0
-7 -7 00000001 7 284 -158 0 0 0 0 0 6918309709189 00263026799 0 0 0 0 0 0 0
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-785 -615 00000000141 785 114 -243 0 0 0 0 0 13803842646 00037153523 0 0 0 0 0 0 0
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-8 -6 000000001 8 084 -258 0 0 0 0 0 69183097092 0002630268 0 0 0 0 0 0 0
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-835 -565 00000000045 835 014 -293 0 0 0 0 0 13803842646 00011748976 0 0 0 0 0 0 0
-84 -56 0000000004 84 004 -298 0 0 0 0 0 10964781961 00010471285 0 0 0 0 0 0 0
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Page 16: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet1

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Sheet2

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Sheet5

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Sheet6

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Sheet7

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Sheet8

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Sheet9

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Sheet10

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Sheet11

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Sheet12

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Sheet13

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Sheet14

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Sheet15

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Sheet16

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Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
pK w = 14
Tableau Reactants Log K
Components MgOH2 (Brucite) H+
Mg+2 1 2 1684 Log[ Mg+2 ] = 1684 -2 pH
MgOH+ 1 1 542 Log[ MgOH+ ] = 542 -1 pH
H+ 0 1 0 Log[ H+ ] = 0 -1 pH
K = [components][reactants]
Log (Concentration) Concentration (M)
[Me][OH]z log Kso = -1116 Log[H+] Log[OH] H+ pH Mg+2 MgOH+ 0 0 0 0 0 Mg+2 MgOH+ 0 0 0 0 0 Total Metal Log[Mtot]
log K1 = 258 0 -14 1 0 1684 542 0 0 0 0 0 691830970918938E+16 263026799189539 0 0 0 0 0 0 0
-005 -1395 08912509381 005 1674 537 0 0 0 0 0 549540873857626E+16 234422881531993 0 0 0 0 0 0 0
-01 -139 07943282347 01 1664 532 0 0 0 0 0 436515832240168E+16 208929613085404 0 0 0 0 0 0 0
-015 -1385 07079457844 015 1654 527 0 0 0 0 0 346736850452531E+16 186208713666287 0 0 0 0 0 0 0
-02 -138 06309573445 02 1644 522 0 0 0 0 0 275422870333818E+16 165958690743756 0 0 0 0 0 0 0
-025 -1375 05623413252 025 1634 517 0 0 0 0 0 218776162394955E+16 147910838816821 0 0 0 0 0 0 0
-03 -137 05011872336 03 1624 512 0 0 0 0 0 173780082874938E+16 131825673855641 0 0 0 0 0 0 0
-035 -1365 04466835922 035 1614 507 0 0 0 0 0 138038426460289E+16 117489755493953 0 0 0 0 0 0 0
-04 -136 03981071706 04 1604 502 0 0 0 0 0 109647819614319E+16 10471285480509 0 0 0 0 0 0 0
-045 -1355 03548133892 045 1594 497 0 0 0 0 0 870963589956084E+15 933254300796991 0 0 0 0 0 0 0
-05 -135 0316227766 05 1584 492 0 0 0 0 0 69183097091894E+15 831763771102672 0 0 0 0 0 0 0
-055 -1345 02818382931 055 1574 487 0 0 0 0 0 549540873857628E+15 741310241300919 0 0 0 0 0 0 0
-06 -134 02511886432 06 1564 482 0 0 0 0 0 436515832240169E+15 660693448007597 0 0 0 0 0 0 0
-065 -1335 02238721139 065 1554 477 0 0 0 0 0 346736850452532E+15 588843655355589 0 0 0 0 0 0 0
-07 -133 01995262315 07 1544 472 0 0 0 0 0 275422870333817E+15 524807460249773 0 0 0 0 0 0 0
-075 -1325 0177827941 075 1534 467 0 0 0 0 0 218776162394956E+15 467735141287199 0 0 0 0 0 0 0
-08 -132 01584893192 08 1524 462 0 0 0 0 0 173780082874938E+15 416869383470336 0 0 0 0 0 0 0
-085 -1315 01412537545 085 1514 457 0 0 0 0 0 138038426460289E+15 371535229097174 0 0 0 0 0 0 0
-09 -131 01258925412 09 1504 452 0 0 0 0 0 109647819614318E+15 331131121482591 0 0 0 0 0 0 0
-095 -1305 01122018454 095 1494 447 0 0 0 0 0 870963589956080 295120922666639 0 0 0 0 0 0 0
-1 -13 01 1 1484 442 0 0 0 0 0 691830970918937 263026799189538 0 0 0 0 0 0 0
-105 -1295 00891250938 105 1474 437 0 0 0 0 0 549540873857625 234422881531992 0 0 0 0 0 0 0
-11 -129 00794328235 11 1464 432 0 0 0 0 0 436515832240167 208929613085404 0 0 0 0 0 0 0
-115 -1285 00707945784 115 1454 427 0 0 0 0 0 346736850452533 186208713666287 0 0 0 0 0 0 0
-12 -128 00630957344 12 1444 422 0 0 0 0 0 275422870333818 165958690743756 0 0 0 0 0 0 0
-125 -1275 00562341325 125 1434 417 0 0 0 0 0 218776162394956 147910838816821 0 0 0 0 0 0 0
-13 -127 00501187234 13 1424 412 0 0 0 0 0 173780082874939 131825673855641 0 0 0 0 0 0 0
-135 -1265 00446683592 135 1414 407 0 0 0 0 0 138038426460289 117489755493953 0 0 0 0 0 0 0
-14 -126 00398107171 14 1404 402 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-145 -1255 00354813389 145 1394 397 0 0 0 0 0 870963589956082 93325430079699 0 0 0 0 0 0 0
-15 -125 00316227766 15 1384 392 0 0 0 0 0 691830970918938 83176377110267 0 0 0 0 0 0 0
-155 -1245 00281838293 155 1374 387 0 0 0 0 0 549540873857627 74131024130092 0 0 0 0 0 0 0
-16 -124 00251188643 16 1364 382 0 0 0 0 0 436515832240168 6606934480076 0 0 0 0 0 0 0
-165 -1235 00223872114 165 1354 377 0 0 0 0 0 346736850452532 58884365535559 0 0 0 0 0 0 0
-17 -123 00199526231 17 1344 372 0 0 0 0 0 275422870333818 52480746024977 0 0 0 0 0 0 0
-175 -1225 00177827941 175 1334 367 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-18 -122 00158489319 18 1324 362 0 0 0 0 0 173780082874938 41686938347034 0 0 0 0 0 0 0
-185 -1215 00141253754 185 1314 357 0 0 0 0 0 138038426460289 37153522909717 0 0 0 0 0 0 0
-19 -121 00125892541 19 1304 352 0 0 0 0 0 109647819614318 33113112148259 0 0 0 0 0 0 0
-195 -1205 00112201845 195 1294 347 0 0 0 0 0 870963589956081 29512092266664 0 0 0 0 0 0 0
-2 -12 001 2 1284 342 0 0 0 0 0 691830970918938 26302679918954 0 0 0 0 0 0 0
-205 -1195 00089125094 205 1274 337 0 0 0 0 0 549540873857626 23442288153199 0 0 0 0 0 0 0
-21 -119 00079432823 21 1264 332 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-215 -1185 00070794578 215 1254 327 0 0 0 0 0 346736850452532 18620871366629 0 0 0 0 0 0 0
-22 -118 00063095734 22 1244 322 0 0 0 0 0 275422870333817 16595869074376 0 0 0 0 0 0 0
-225 -1175 00056234133 225 1234 317 0 0 0 0 0 218776162394956 14791083881682 0 0 0 0 0 0 0
-23 -117 00050118723 23 1224 312 0 0 0 0 0 173780082874938 13182567385564 0 0 0 0 0 0 0
-235 -1165 00044668359 235 1214 307 0 0 0 0 0 138038426460289 11748975549395 0 0 0 0 0 0 0
-24 -116 00039810717 24 1204 302 0 0 0 0 0 109647819614319 10471285480509 0 0 0 0 0 0 0
-245 -1155 00035481339 245 1194 297 0 0 0 0 0 870963589956083 933254300797 0 0 0 0 0 0 0
-25 -115 00031622777 25 1184 292 0 0 0 0 0 691830970918937 8317637711027 0 0 0 0 0 0 0
-255 -1145 00028183829 255 1174 287 0 0 0 0 0 549540873857625 7413102413009 0 0 0 0 0 0 0
-26 -114 00025118864 26 1164 282 0 0 0 0 0 436515832240167 6606934480076 0 0 0 0 0 0 0
-265 -1135 00022387211 265 1154 277 0 0 0 0 0 346736850452532 5888436553556 0 0 0 0 0 0 0
-27 -113 00019952623 27 1144 272 0 0 0 0 0 275422870333817 5248074602498 0 0 0 0 0 0 0
-275 -1125 00017782794 275 1134 267 0 0 0 0 0 218776162394956 4677351412872 0 0 0 0 0 0 0
-28 -112 00015848932 28 1124 262 0 0 0 0 0 173780082874938 4168693834703 0 0 0 0 0 0 0
-285 -1115 00014125375 285 1114 257 0 0 0 0 0 138038426460289 3715352290972 0 0 0 0 0 0 0
-29 -111 00012589254 29 1104 252 0 0 0 0 0 109647819614319 3311311214826 0 0 0 0 0 0 0
-295 -1105 00011220185 295 1094 247 0 0 0 0 0 870963589956082 2951209226666 0 0 0 0 0 0 0
-3 -11 0001 3 1084 242 0 0 0 0 0 691830970918939 2630267991895 0 0 0 0 0 0 0
-305 -1095 00008912509 305 1074 237 0 0 0 0 0 549540873857627 234422881532 0 0 0 0 0 0 0
-31 -109 00007943282 31 1064 232 0 0 0 0 0 436515832240168 2089296130854 0 0 0 0 0 0 0
-315 -1085 00007079458 315 1054 227 0 0 0 0 0 346736850452531 1862087136663 0 0 0 0 0 0 0
-32 -108 00006309573 32 1044 222 0 0 0 0 0 275422870333817 1659586907438 0 0 0 0 0 0 0
-325 -1075 00005623413 325 1034 217 0 0 0 0 0 218776162394955 1479108388168 0 0 0 0 0 0 0
-33 -107 00005011872 33 1024 212 0 0 0 0 0 173780082874938 1318256738556 0 0 0 0 0 0 0
-335 -1065 00004466836 335 1014 207 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-34 -106 00003981072 34 1004 202 0 0 0 0 0 109647819614319 1047128548051 0 0 0 0 0 0 0
-345 -1055 00003548134 345 994 197 0 0 0 0 0 870963589956081 933254300797 0 0 0 0 0 0 0
-35 -105 00003162278 35 984 192 0 0 0 0 0 691830970918938 831763771103 0 0 0 0 0 0 0
-355 -1045 00002818383 355 974 187 0 0 0 0 0 549540873857626 741310241301 0 0 0 0 0 0 0
-36 -104 00002511886 36 964 182 0 0 0 0 0 436515832240168 660693448008 0 0 0 0 0 0 0
-365 -1035 00002238721 365 954 177 0 0 0 0 0 346736850452532 588843655356 0 0 0 0 0 0 0
-37 -103 00001995262 37 944 172 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-375 -1025 00001778279 375 934 167 0 0 0 0 0 218776162394956 467735141287 0 0 0 0 0 0 0
-38 -102 00001584893 38 924 162 0 0 0 0 0 173780082874938 41686938347 0 0 0 0 0 0 0
-385 -1015 00001412538 385 914 157 0 0 0 0 0 138038426460289 371535229097 0 0 0 0 0 0 0
-39 -101 00001258925 39 904 152 0 0 0 0 0 109647819614318 331131121483 0 0 0 0 0 0 0
-395 -1005 00001122018 395 894 147 0 0 0 0 0 870963589956081 295120922667 0 0 0 0 0 0 0
-4 -10 00001 4 884 142 0 0 0 0 0 691830970918937 26302679919 0 0 0 0 0 0 0
-405 -995 00000891251 405 874 137 0 0 0 0 0 549540873857625 234422881532 0 0 0 0 0 0 0
-41 -99 00000794328 41 864 132 0 0 0 0 0 436515832240167 208929613085 0 0 0 0 0 0 0
-415 -985 00000707946 415 854 127 0 0 0 0 0 346736850452532 186208713666 0 0 0 0 0 0 0
-42 -98 00000630957 42 844 122 0 0 0 0 0 275422870333817 165958690744 0 0 0 0 0 0 0
-425 -975 00000562341 425 834 117 0 0 0 0 0 218776162394956 147910838817 0 0 0 0 0 0 0
-43 -97 00000501187 43 824 112 0 0 0 0 0 173780082874938 131825673856 0 0 0 0 0 0 0
-435 -965 00000446684 435 814 107 0 0 0 0 0 138038426460289 117489755494 0 0 0 0 0 0 0
-44 -96 00000398107 44 804 102 0 0 0 0 0 109647819614319 104712854805 0 0 0 0 0 0 0
-445 -955 00000354813 445 794 097 0 0 0 0 0 870963589956083 9332543008 0 0 0 0 0 0 0
-45 -95 00000316228 45 784 092 0 0 0 0 0 691830970918936 8317637711 0 0 0 0 0 0 0
-455 -945 00000281838 455 774 087 0 0 0 0 0 549540873857625 7413102413 0 0 0 0 0 0 0
-46 -94 00000251189 46 764 082 0 0 0 0 0 436515832240167 66069344801 0 0 0 0 0 0 0
-465 -935 00000223872 465 754 077 0 0 0 0 0 346736850452531 58884365536 0 0 0 0 0 0 0
-47 -93 00000199526 47 744 072 0 0 0 0 0 275422870333817 52480746025 0 0 0 0 0 0 0
-475 -925 00000177828 475 734 067 0 0 0 0 0 218776162394955 46773514129 0 0 0 0 0 0 0
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-14 0 0 14 -1116 -858 0 0 0 0 0 0 00000000026 0 0 0 0 0 0 0
Page 17: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet2

ampA
Page ampP

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 18: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet3

ampA
Page ampP

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 19: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet4

ampA
Page ampP

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 20: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet5

ampA
Page ampP

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 21: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet6

ampA
Page ampP

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 22: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet7

ampA
Page ampP

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 23: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet8

ampA
Page ampP

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 24: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet9

ampA
Page ampP

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 25: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet10

ampA
Page ampP

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 26: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet11

ampA
Page ampP

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 27: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet12

ampA
Page ampP

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 28: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet13

ampA
Page ampP

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 29: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet14

ampA
Page ampP

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 30: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet15

ampA
Page ampP

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 31: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Sheet16

ampA
Page ampP

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 32: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Magnesium Hydroxide II From the Kso and Kw

develop an equation for the free metal in terms of H+

Then use the K1 to get an equation for the soluble hydroxide species

David Reckhow CEE 680 34 16

pHMgLogHMg

HKKMg

OHKMg

OHMgK

W

so

so

so

28416][][10][

][][

][][

]][[

2

284162

22

2

22

22

minus=

=

=

=

=

+

++

++

minus+

minus+

pHMgOHLogH

H

MgKOHMgKMgOH

OHMgMgOHK

H

HKW

minus=

=

=

=

=

=

+

+

+

+

minus++

minus+

+

+minus

+

445][][10

][1010

][]][[][

]][[][

445

][102841662

][2

1

21

21

14

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 33: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Magnesium Hydroxide III Total Magnesium

MgT= [Mg+2] + [MgOH+]

Follows upper line where lines are well separated

Falls 03 log units above intersection of any two major species

Applications Mg is a hardness cation Solubility is controlled

by hydroxide precipitate Easily removed by

softening at high pH

David Reckhow CEE 680 34 17

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 34: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

David Reckhow CEE 680 34 18pH0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log

C

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

H+

OH-

Mg(OH)-

Mg+2

MgTotal

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 35: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

To next lecture

David Reckhow CEE 680 34 19

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate
Page 36: Updated: 26 March 2020 Print version · Print version. Topics Hydrolysis Aquo metal ion gives rise to hydroxocomplexes Magnesium and Iron Hydroxide solubility. David Reckhow CEE 680

Calcium Phosphate Providence RI example

See Edwards amp Giammar manuscripts

David Reckhow CEE 680 34 20

  • CEE 680 Water Chemistry
  • Topics
  • Precipitation and Dissolution
  • Elemental Abundance in Crust
  • Slide Number 5
  • Abundance of inorganics in fresh water and in earthrsquos crust
  • Solubility Products
  • Kso and Q
  • Solubility of some simple salts
  • Solubility of ldquosimplerdquo salts
  • Solubility of oxides amp hydroxides
  • Solubility of metal hydroxides
  • Magnesium Hydroxide
  • Slide Number 14
  • Magnesium Hydroxide
  • Magnesium Hydroxide II
  • Magnesium Hydroxide III
  • Slide Number 18
  • Slide Number 19
  • Calcium Phosphate

Leaf Leaching Experiment - UMass Amherst Leaching Experiment.pdf · Leaf Leaching Experiment Monday PM David A. Reckhow University of Massachusetts. Introduction • Water treatment

Lecture #19 MINEQL: Intro & Tutorial Benjamin; … Intro & Tutorial Benjamin; Chapter 6 David Reckhow CEE 680 #19 1 Updated: 6 October 2013 Print version MINEQL today

High Performance Liquid Chromatography - UMass … · High Performance Liquid Chromatography Print version Updated: 3 November 2014 David Reckhow CEE 772 #18 1

PRINT 1 PRINT 2 - biteradio.me · print 1 print 2 print 3 print 4. print 5 print 6 print 7 print 8. print 9 print 10 print 11 print 12. print 13 print 14 print 15 print 16. print

T AVUS BREDBERG - DiVA portal1189631/...fccredebet exemplr,qtire ad imirandum antiqufras pro-pofuerit,.aquo haec retentiorasta5, Eauca qnoque ejus-naodiexempla, eaqiie illuftria,intet.monumentaPopuli

CEE 370 Environmental Engineering Principles · Reading: Mihelcic& Zimmerman, Chapter 5 Davis & Masten, Chapter 3 Updated: 4 October 2019 Print version David Reckhow CEE 370 L#14

Lecture #51 RedoxChemistry: Lead II › cee › reckhow › courses › 680 › slides › 680l51.… · From: Aquatic Chemistry Concepts, by Pankow, 1991. David Reckhow CEE 680 #51

CEE 370 Environmental Engineering PrinciplesCEE 370 Lecture #2 9/6/2019 Lecture #2 Dave Reckhow 4 acv David Reckhow CEE 370 L#1 7 On June 22, 1969 the Cuyahoga River Caught fire, and

CEE 370 Environmental Engineering Principles · CEE 370 Lecture #33 12/6/2019 Lecture #36 Dave Reckhow 8 David Reckhow CEE 370 L#33 15 Functional Elements of a SW Management System

Wisconsin Lakes PreConvention Workshop Lake · PDF fileLake Eutrophication Modeling and WiLMS ... Wisconsin Lakes PreConvention Workshop. ... check out Reckhow and Chapra Book pages

Water Quality in Catchments and its Impact on Human and Ecological Health Kenneth H. Reckhow

beaverislandnews.combeaverislandnews.com/2015 BICS Board Minutes Agendas and packet... · 9 TOZ aunf paeoq pearl (spoqos s,Kepm aouetuv10Jvrad uodn-paaaîe Ked aoueu1v10Jd0d aquo

CEE 370 Environmental Engineering Principles · 2019-09-09 · CEE 370 Lecture #3 9/9/2019 Lecture #3 Dave Reckhow 2 David Reckhow CEE 370 L#1 3 CEE 370: Gateway CEE 370 Environmental

Brayden Aquo 11 Smart Electric Kettle

Molecular orbital treatments of the aquo and ammine ...ufdcimages.uflib.ufl.edu/UF/00/09/78/53/00001/molecularorbital00feilrich.pdftableopcontents page acknowledgments ii listoftables

CEE 690K Environmental Reaction KineticsCEE 697K ENVIRONMENTAL REACTION KINETICS . David A. Reckhow . Case Studies . Updated: 25 November 2013 . CEE697K Lecture #20 . 1 . Print version

Water Quality in Catchments and its Impact on Human and Ecological Health Kenneth H. Reckhow Duke University

CEE 370 Environmental Engineering Principles 370 Lecture #36 12/4/2015 Lecture #36 Dave Reckhow 1 David Reckhow CEE 370 L#36 1 CEE 370 Environmental Engineering Principles Lecture

CEE 370 Environmental Engineering PrinciplesCEE 370 Lecture #28 11/15/2019 Lecture #28 Dave Reckhow 1 David Reckhow CEE 370 L#28 1 CEE 370 Environmental Engineering Principles Lecture

Aquo HR Portfolio

CEE 370 Environmental Engineering Principles - UMass … · CEE 370 Environmental Engineering Principles ... combinations (b) David Reckhow: CEE 370 L#20: 12: ... determination of

Using Digital Imaging to Assess Water Quality Presented by Amy Biddle Dave Reckhow

CEE 370 Environmental Engineering Principles · 2019-10-04 · CEE 370 Lecture #15 10/4/2019 Lecture #15 Dave Reckhow 5 David Reckhow CEE 370 L#15 9 Bacteria Unicellular organisms

Aquo Life Magazine Start 5

Updated: 24 March 2020 Print versionBenjamin; Chapter 8.1- 8.6 David Reckhow CEE 680 #32 1 Updated: 24 March 2020 Print version Biotic ligand model of the acute toxicity of metals

David Reckhow CEE 680 #47 1 - UMass AmherstDavid Reckhow CEE 680 #46 21 6.1 0.5 3 0.5 2 0.33 0.33 4 10 { } { } { } { } O MnO H O K A B A B K b red a ox b ox a red 6.1 6 0.5 0.33 7

DAVID A. RECKHOW · 1 DAVID A. RECKHOW EDUCATION Degree Institution Dates Major B.S. Tufts University 1973-1977 Civil Engineering M.S. Stanford University 1977-1978 Civil Engineering

Leaf Leaching Experiment Monday PM David A. Reckhow University of Massachusetts

Lecture #3 Intro: Atoms and Isotopes · Intro: Atoms and Isotopes (Stumm & Morgan, Chapt. 4.9 ) (Pg. 195-202) David Reckhow CEE 680 #3 1. Updated: 24 January 2020. Print version Best

CEE 772: Instrumental Methods - College of Engineering | …€¦ ·  · 2014-09-187 CEE 772 #5 David Reckhow ... 8 CEE 772 #5 David Reckhow ... Structural rigidity

Gas Chromatography - UMass · PDF fileGas Chromatography Rosa Yu, David Reckhow CEE772 Instrumental Methods in Environmental Analysis . Print version. CEE 772 #16 1

CUAHSI Hydrologic Observatories and the Neuse Basin Prototype Kenneth Reckhow UNC Water Resources Research Institute

ENVIRONMENTAL REACTION KINETICS Lecture #18 REACTION KINETICS David A. Reckhow Introduction ... No Degradation Degradation CEE 679 Kinetics Lecture #18 …

CEE 370 Environmental Engineering PrinciplesCEE 370 Lecture #37 12/11/2019 Lecture #37 Dave Reckhow 5 David Reckhow CEE 370 L#37 9 Tropospheric Photochemical Pollutants Photochemical

CEE 772: Instrumental Methods in Environmental Analysis€¦ ·  · 2014-09-187 CEE 772 #5 David Reckhow ... 8 CEE 772 #5 David Reckhow ... information for qualitative or quantitative