lesson 8 the chemistry of natural waters
TRANSCRIPT
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Lesson 8 The Chemistry of Natural Waters Chapter 13 is probably the hardest chapter in the Baird book. It represents an extension, rather than an application of the principles learned in general chemistry. For the serious student of the chemistry of the environment, it is a must. For the dilettante, it would probably be better to skip this chapter. Before beginning to read this chapter, I would advise carefully rereading the sections of your general chemistry book dealing with redox and acid-base chemistry. The development of this subject material is, of necessity, mathematical in nature. The concepts are not advanced but the algebra is detailed and challenging. Most advanced treatments of environmental chemistry, assume one is familiar with this material. While many of the calculations for real world systems are done by computer models, it is very important to understand the underlying basic principles. The trick is to become familiar enough with the math to see beyond it, to develop an intuition about the effect of certain changes upon a system. I append a more rigorous approach to the subject material of this chapter that we have used in the past for this course. Fundamentals of Aquatic Chemistry Focus on Acid/Base Reactions Concept pH vs acidity pH α [H+] acidity: capacity of water to donate protons (for potable H2O, CA(eq/L) = 2H2CO3+HCO3
- + H+-OH- CO2 in H2O !"! !" + !!!⟶ !!!"!∗
!!" =!!!"!∗
!"!= 2.6!10!! !"#$ !"! !"# !!!"!
!!"! =!!!"!∗
!"#!= 10!!.!"
can be written as !"! + !!! ⇄ !"#!! + !!
!"!! = 6.35 !!! =!"#!! !!
!"!= 4.45!10!! = 10!!.!
!"#!! ⇄ !"!! + !!
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!"!! = 10.33 !!! =!! !"!!
!"#!!= 4.68!10!!! = 10!!".!
Can solve these equations:
can solve these for H+
!! =!!"!!!!!"!!"#!!
Define total carbonate
!! = !!!"! + !"#!! + !"!!
!"!! =!!!!
!"#!! =!! !!
!!!!
!!!"! =!! !! !
!!!!!!
!ℎ!"! !! =!! !
!!!!+!!
!!+ 1
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TABLE 5.2 Values of !! from pH to 12 at 25°C pH log !! pH log !! 2 12.68 8 2.34 3 10.68 9 1.35 4 8.68 10 0.497 5 6.70 11 0.0841 6 4.84 12 0.00919 7 3.42 If we define Alkalinity = !! − !! , !! = !!!"! + !"#!! + !"!! ≡”total carbonate”≡total dissolved inorganic C For this system, alk = !"! − !! + !"#!! + 2 !"!! !"# !" < 7.
Suppose Alk = 6!10!! !" ! !" = 7.5 !! =? (6.4!10!!) If !! = 3.2!10!! , !ℎ!" !" = 10.2
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For basic solution: alk = !"#!! + 2 !"!! + !"!
Alkalinity can be measured (by titration) ↗ !"#ℎ!" !"#$%& !" = 4↘ !ℎ!"!"#ℎ!ℎ!"#$% !" = 10
alk = !"!! Alkalinity / Solubility relations Define solubility = !"! + !"#!! If alk = 0 If atm = 350 ppm !"! , !"! = 1.146!10!!
!!! =!! !"#!!
!"!=
!! !
1.146!10!! = 4.45!10!!
!! = !"#!! = 1.146 10!! 4.45 10!! !
! = 2.25!10!! Solubility = 1.146!10!! + 2.25!10!! = 1.371!10!! Now, if alk = 10!! !" ! 10!!! !"!
!"! !" + !"! ⇄ !"#!!
! =!"#!!
!"! !"!=!!!!!
=4.45!10!!
10!!" = 4.45!10!
If !"! = 10!! ⟹ !"#!! = 10!! Solubility = 1.146!10!! + 10!! = 1.01!10!!! Metals in !!! Cations exist as hexaquo complexes.
!!(!!!)!!!! ⇄ !!!" !!! !!! + !!
!!! = 8.9!10!!
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Solutions of metal ions are acid. !"!#! ,+!"#$%&'! !"! (a) !"!"! ⇄ !"!! + !"!! !!" = !" ++ !"!! = 4.47!10!! If only this reaction, solubility of CaCO3=[Ca++]=[CO2-
3] S2=4.47x10-4 S=6.8x10-5 (b) !"!"! + !"! !" + !!! ⇄ !"!! + 2!"!!!
! = !!!! !"#!! !
!"! !"= !!"!!!
!!!= 4.24!10!!
If !"! !" = 1.146!10!!! , !"# !"#!. !"#!! = 9.98!10!! !"!! = 8.96!10!! [!"!!] = 4.99!10!!! !! = 5.17!10!!! pH = 8.29
! =!"!! !"#!! !
!"!= 4.24!10!!
!"!! !"#!! ! = 4.24!10!! 1.146!10!! = Rxn says !!!"! + !"! + !!! → !"!! + 2!"#!! If !"!! = ! !(2!)! = ! = 4.99!10!! ≡ !"!! !! ≡ !"#!! = 9.98!10!!
!! = !"!!"#!!
∙ 4.45!10!! = 5.17!10!!
!"!! =!.!"!!"!!
!!!!= !.!"!!"!!
!.!!!!"!!= 8.96!10!!
TABLE 5.3 Some important processes and reactions that control the !"! content of surface- and groundwaters and, therefore, their pH
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Note: !"!! represents organic matter. Other reactions that lead to carbon fixation may involve species of S and N (cf. Morel & Hering 1993; Stumm and Morgan 1996). Humic and Fulvic Acids Most organic metal in soils + water are "humic substances." No specific cpd. !" = 10! − 10!. ground water 0.03 - 0.1 mg C/L seawater 0.06 - 0.6 mg C/L rivers + lakes 0.5 - 4.0 mg C/L fulvic acid (acid/base sol) 12-60% DOC humic acid (base sol) pH of natural waters
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pH controls 1. A/B eq., hydrolysis, polymerization 2. Adsorption: protons compete for sites 3. Metal - liquid complex formation: " 4. Redox rxns 5. Solubility of minerals Activity Coefficients of Dissolved Species In various eq. expressions, we really should use activities instead of concentrations. Activities can be thought of as "effective concentrations."
!! = γ!!! ai=activity γi=activity coefficient mi=concentration
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γ is a function of the ionic strength of solution, I
! =12 (!!!!!)
can be calculated from a number of prescriptions, depending on I. Complex: cation/anion or neutral association Importance of complexes 1. Increase solubility of minerals in water 2. Some species mostly complexed !"!!,!"!!,!"!!,!"!!!,!!! 3. Complexing affects adsorption properties U carbonate 4. Toxicity depends on complexation Hg Outer sphere + inner sphere complexes Complexes are classified as outer or inner sphere depending on water associated with cation. Outer sphere: cation surrounded by tightly held water anion forms transient association (via long range forces) with hydrated cation +1, +2 cations + simple anions !"!, !"!!,!"!!, !"# !!"#$%&'"( < 10! Inner sphere direct cation/znion contact [covalent bonding] ex. aquo complexes
! !!! ! + ! ⟶ !" !!! !!! + !!! Math of Complexation metal mass balance ! = ! +!" +!"! +⋯!"! = ! + !"!!
!!! ligand mass balance ! = ! +!" + 2!"! +⋯! !"! = ! + !"#!!
!!! average ligand number ! ! = !!!
!
Have stepwise formation constants, K
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!! =!"! !
!! =!"!!" [!]
!! =!"!
!"!!! [!]
Have cumulative formation constants, β !! = !! =
!"! !
!! = !!!! =!"!! [!]!
!! =!"!! ! ! = Π!!
can rewrite mass balance ! = [!] !! [!]! ! = ! + ! !! [!]! Chelation + Complexation A/B behavior in terms of Lewis acids / bases. electron acceptor + electron donor ⇄ complex electron donor liquids
chelates ≡ multi dintate liquids Chelates of interest EDTA
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NTA
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Figure 3.8. Binding of a metal ion, !!!, by humic substances (a) by chelation between carboxyl and phenolic hydroxyl, (b) by chelation between two carboxyl groups, and (c) by complexation with a carboxyl group. Polyprotic Acids NTA is a polyprotic acid with 3 exchangeable hydrogens Have dissociation eq.
!!! ⇄ !! + !!!! !! = 2.18!10!! !!!! ⇄ !! + !!!! !! = 1.12!10!! !!! ⇄ !! + !≡ !! = 5.25!10!!!
with result
Figure 3.6. Plot of fraction of species !! as a function of pH for NTA species in water. Consider the dissolution of Pb from pipe by this strong chelating agent at pH = 8. At pH8, dominant species is !"!.
!"(!")! ! + !"! → !"#! + !"! + !!!
! =!"#! !"!
!"! =!!"!!!!!!
= 2.1!10!!
What is the lead concentration?
!"#!
!"! =!!"! =
2.07!10!!
10!! = 20.7
So !"#! ≈ !"# If NTA = 9.7!10!!! !"#! ≈ 9.7!10!!!
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= 9.7!10!! 200 10! !" ! = 19.4 !" ! = 19.4 !!" Suppose you now make this problem tougher by introducing carbonate into the system. Get NTA equilibria + carbonate equilibria together. The relevant equilibria is
!"#$! + !"! ⟶ !"#! + !"#!! Calculation (book) shows Pb cone ≃ same [at !"#!! ≃ 10!!]. Further calculation (book) shows that throwing !"!! into solution reduces !!"! because !"!! competes with !"!! for !≡. Redox Chemistry Introduction Redox rxns involve !! transfer (gain or loss) Concept of half rxns
!"!! + !" ⇄ !"!! + !" !"!! + 2!! ⟶ !" !"#$ !" !!, !"#$%&'() !" ⇄ !"!! + 2!! !"## !" !!, !"#$%&#!'
Half Rxn not artificial. Can run rxn in two separate beakers
Significance of Redox Chemistry Oxidation of organic material affects available !! !"!! + !! ⟶ !"! + !!! What is being oxidized? Reduced? Dissolution of metals
!" !" ! ! + 3!! + !! ⟶ !"!! + 3!!! Discussion based upon analogy with A/B rxns. ( lewis definition)
!"⟺ !" !" ≈ − log!" !!
low pE, high !! , reducing ⇒ consumes protons high pE, low !! , oxidizing ⇒ releases protons
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Natural example: stratified lake
Figure 4.1. Predominance of various chemical species in a stratified body of water that has a high oxygen concentration (oxidizing, high pE) near the surface and a low oxygen concentration (reducing, low pE) near the bottom. Importance of kinetics conc. of species may not be equilibrium. concs. many redux rxns are slow. dynamics are important. Importance of biology many redox rxns depend on biota + biological activity. Review of Basics Oxidation state (Number) reduction ⇒ reduce oxid. number oxidation ⇒ increase " " Table 8.1. Oxidation State Rules for Assigning Oxidation States: (1) The oxidation state of a monoatomic substance is equal to its electronic charge. (2) In a covalent compound, the oxidation state of each atom is the charge remaining on the atom when each shared pair of electrons is assigned completely to the more electronegative of the twon atoms sharing them. An electron pair shared by two atoms of the same electronegativity is split between them. (3) The sum of oxidation states is equal to zero for molecules, and for ions is equal to the formal charge of the ions. Examples:
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Practice: Determine the oxidation shifts of (a) nitrogen in nitrate (b) sulfur in !!! (c) carbon in chloroform !"!#! Using Half-rxns to write/balance a complete reaction. (a) Need to know pdts/reactants beforehand. (b) balance !! on both sides (c) Table of half rxns (notes, gen-chem. book) Practice: (a) write balanced equation for
!!!! + !"#! ⟶ !"#!! + !"!! (b) !! + !!!!! + !! ⟶ !!!!! + !!! Half cells written as SRP. !"#!! + 8!! + 5!! ⟶ !"!! + 4!!! !"#!(!)+ 4!! + 2!! ⟶ !"!! + 2!!! X2 !"!! + 4!!!⟶ !"#!! + 8!! + 5!! X5 !"#! ! + 4!! + 2!! ⟶ !"!! + 2!!! 2!"!! + 8!!!⟶ 2!"#!! + 16!! + 10!! 5!"#! ! + 20!! + 10!! ⟶ 5!"!! + 10!!! 2!"!! + 8!!! + 5!"#! + 20!! + 10!! ⟶ 2!"#!! + 16!! + 10!! + 5!"!! +10!!! 2!"!! + 4!! + 5!"#! ⟶ 2!!! + 5!"!! + 2!"#!! !!!!! + 2!! ⟶ 2!!!!! !! + 4!! + 4!! ⟶ 2!!!
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X2 2!!!!! ⟶ !!!!! + 2!! !! + 4!! + 4!! ⟶ 2!!! 4!!!!! ⟶ 2!!!!! + 4!! !! + 4!! + 4!!!!! ⟶ 2!!!!! + 2!!! TABLE 11.1 Oxidation states of some important elements as they occur in natural waters and mineral systems.
Element Symbol Number of protons (atomic number) Oxidation states
Aluminum Al 13 3+ Antimony Sb 51 3+, 5+ Arsenic As 33 3+, 5+, (0) Barium Ba 56 2+
Beryllium Be 4 2+ Bismuth Bi 83 3+, (0) Boron B 5 3+
Bromine Br 35 1-, 0 Cadmium Cd 48 2+ Calcium Ca 20 2+ Carbon C 6 4+, (0), 4-, 2-
Chlorine Cl 17 1- Chromium Cr 24 6+, 3+
Cobalt Co 27 2+, (3+) Copper Cu 29 2+, 1+, (0) Fluorine F 9 1-, 0
Gold Au 79 3+, 1+, (0) Hydrogen H 1 1+, 0
Iron Fe 26 3+, 2+ Iodine I 53 5+, 0, 1- Lead Pb 82 2+, (4+), (0)
Lithium Li 3 1+ Magnesium Mg 12 2+ Manganese Mn 25 2+, (3+), (4+)
Mercury Hg 80 2+, 1+, (0) Nickel Ni 28 2+, (3+)
Nitrogen N 7 5+, 3+, 0, 3- Oxygen O 8 2-, 0
Phosphorus P 15 5+ Platinum Pt 78 4+, 2+
Potassium K 19 1+ Radium Ra 88 2+
Selenium Se 34 6+, 4+, (0), 2- Silicon Si 14 4+
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Silver Ag 47 1+, (0) Sodium Na 11 1+
Strontium Sr 38 2+ Sulfur S 16 6+, 4+, 0, (1-), 2-
Thorium Th 90 4+ Tin Sn 50 4+
Titanium Ti 22 4+ Tungsten W 74 6+ Uranium U 92 6+, 4+
Vanadium V 23 5+, 4+, 3+ Zinc Zn 30 2+
Note: Values in parentheses are found in mineral systems only. Standard Reduction Potentials at 25°C
Half-Reaction E° (volts) !! ! + 2!! ⟶ 2!! 2.87 !!!! + 2!!!! + 2!! ⟶ 4!!! 1.776 !"#! ! + !"!!! + 4!!!! ⟶ !"#$! ! + 6!!! 1.685 !"! + !! ⟶ !"(!) 1.68 !"#!! + 4!!!! + 3!! ⟶ !"#! ! + 6!!! 1.679 !"#$! + 2!!!! + 2!! ⟶ !"#$ + 3!!! 1.64
!"#$ + !!!! + !! ⟶12!"! ! + 2!!! 1.63
!"!! + !! ⟶ !"!!(1 ! !"#! !"#$%&"') 1.61 2 !" ! + 2 !!!! + 2!! ⟶ !!! ! + 3!!! 1.59
!"#!! + 6!!!! + 5!! ⟶12!"! ! + 9!!! 1.52
!"!! + !! ⟶ !"!! 1.51 !"#!! + 8!!!! + 2!! ⟶ !"!! + 6!!! 1.491
!"#!! + 6!!!! + 5!! ⟶12!"! ! + 9!!! 1.47
!"#! ! + 4!!!! + 2!! ⟶ !"!! + 6!!! 1.46 !"!! + 3!! ⟶ !"(!) 1.42 !"! ! + 2!! ⟶ 2!"! 1.3583 !"!!!!! + 14!!!! + 6!! ⟶ 2!"!! + 21!!! 1.33 !! ! + !!! + 2!! ⟶ !! + 2!"! 1.24 !! ! + 4!!!! + 4!! ⟶ 6!!! 1.229 !"#! ! + 4!!!! + 2!! ⟶ !"!! + 6!!! 1.208 !"#!! + 2!!!! + 2!! ⟶ !"#! + 3!!! 1.19 !"! ! + 2!! ⟶ 2!"! 1.065 !"!! + 4!!!! + 3!! ⟶ !" ! + 6!!! 0.96
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2!"!! + 2!! ⟶ !"!!! 0.905 !"! + !! ⟶ !"(!) 0.7996 !"!!! + 2!! ⟶ 2!"(!) 0.7961 !"!! + !! ⟶ !"!! 0.770 !! ! + 2!!!! + 2!! ⟶ !!!! + 2!!! 0.682 !"#!! + 3!!! + 6!! ⟶ !"! + 6!"! 0.61 !"#!! + 2!!! + 3!! ⟶ !"#! ! + 4!"! 0.588 !! ! + 2!! ⟶ 2!! 0.535 !"! + !! ⟶ !"(!) 0.522 !! ! + 2!!! + 4!! ⟶ 4!"! 0.401 !"!! + 2!! ⟶ !"(!) 0.3402 !"#! ! + !!! + 2!! ⟶ !"# ! + 2!"! 0.28 !"!!"! ! + 2!! ⟶ 2!" ! + 2!"! 0.2682 !"#$ ! + !! ⟶ !" ! + 2!"! 0.2223 !"!!! + 4!!!! + 2!! ⟶ !!!"! + 5!!! 0.20 !"!! + !! ⟶ !"! 0.158 !!!!!! + 2!! ⟶ 2!!!!!! 0.0895 !"!! + !!! + 2!! ⟶ !"!! + 2!"! 0.01 2!!!! + 2!! ⟶ !! ! + 2!!!(!) 0.000 exactly !"!! + 2!! ⟶ !"(!) -0.1263 !"!! + 2!! ⟶ !"(!) -0.1364 !"!! + 2!! ⟶ !"(!) -0.23 !"!! + 2!! ⟶ !"(!) -0.28 !"#$! ! + 2!! ⟶ !" ! + !"!!! -0.356 !"(!")! ! + !! ⟶ !"(!")! ! + !"! -0.40 !"!! + 2!! ⟶ !"(!) -0.4026 !"!! + 2!! ⟶ !"(!) -0.409 !"!! + !! ⟶ !"!! -0.41 !"!! + 2!! ⟶ !"(!) -0.557 !"(!")! ! + !! ⟶ !" !" !(!)+ !"! -0.56 !"# ! + !!! + 2!! ⟶ !" ! + 2!"! -0.576 2!"!!! + 3!!! + 4!! ⟶ !!!!!! + 2!"! -0.58 !"(!")! ! + 2!! ⟶ !" ! + 2!"! -0.66 !"(!")! ! + 2!! ⟶ !" ! + 2!"! -0.73 !"!! + 3!! ⟶ !"(!) -0.74 !"!! + 2!! ⟶ !"(!) -0.7628 2!!! + 2!! ⟶ !! ! + 2!"! -0.8277 !"!!! + !!! + 2!! ⟶ !"!!! + 2!"! -0.92 !"!! + 2!! ⟶ !"(!) -1.029 !"(!")! ! + 2!! ⟶ !" ! + 2!"! -1.47 !"!! + 3!! ⟶ !"(!) -1.706 !"!! + 3!! ⟶ !"(!) -2.08 !"!! + 3!! ⟶ !"(!) -2.335 !"!! + 3!! ⟶ !"(!) -2.37
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!"!! + 2!! ⟶ !"(!) -2.375 !"(!")! ! + 2!! ⟶ !" ! + 2!"! -2.69 !"! + !! ⟶ !"(!) -2.7109 !"!! + 2!! ⟶ !"(!) -2.76 !"!! + 2!! ⟶ !"(!) -2.90 !! + !! ⟶ !(!) -2.925 !"! + !! ⟶ !"(!) -3.045 All voltages are standard reduction potentials (relative to the standard hydrogen electrode) at 25°C and 1 atm pressure. All species are in aqueous solution unless otherwise indicated. Concept of E° Can run half rxns in separate beakers. If [ ] = 1M, T = std = P measure E° as voltage vs SHE. SHE 2!! + 2!! ⇄ !! E° = 0.00 In Table of SRP, strong oxidizing agents at top, strong reducing agents at bottom. Electron Activity and pE In A/B chemistry, we use pH where
!" = − log!" !! = − log!" !!! In redox chemistry, we use pE where
!" = − log!" !! = − log!" !!! But how do we measure/define !!!? Consider a rxn: !"!!! + !! ! ⇄ !"!! + 2!! !! can write half rxns !"!!! + !! ⟶ !"!! !! !! ! ⟶ 2!! + !! !! Assign !! = 1 (equivalent to saying E°=0.0)
!! = !!!! =!"!!!
!"!!! !!
!" = − log !!
log !! = log !"!!
!"!!!− log !!
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!" = log !! + log !"!!!
!"!!
Define !"° = log!!
!" = !"°+ log !"!!!
!"!!
Can generalize this to a reaction involving n electrons as:
!" = !"°+ !!log !![!"]!!
!![!"#]!!
for !"!! + 3!!! + 6!! ⟶ !! + 6!"!
!" = !"°+ !!log !"!!
!! !"! !
So ---- we have reduced problem of pE to one of determining pE°. Define !"° = !°
!.!"!!"#= !°
!.!"#(!" 25℃)
Thus if we further note that E = Eh !" = !
!.!"!!"#= !
!.!"#
then we just have Nernst equation restated N.E.
!! = ! = !°+2.303!"!" log!" ! = !°+
0.059! log!" !
re-write as
!" = !"°+0.059! log!" !
Tables of SRP's become pE° tables as well. Table 8.3. Equilibrium Constants and Standard Electrode Potentials for Some Reduction Half-Reactions Reaction Log K at 25°C Standard Electrode
Potential (V) at 25°C pE°
!!! + !! = !"(!) -46 -2.71 -46
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!"!! + 2!! = !"(!) -79.7 -2.35 -39.7 !"!! + 2!! = !"(!) -26 -0.76 -13 !"!! + 2!! = !"(!) -14.9 -0.44 -2.45 !"!! + 2!! = !"(!) -9.5 -0.28 -4.75 !!! + !! = !!! -4.3 -0.26 -4.30 2!! + 2!! = !!(!) 0.0 0.00 0 ! ! + 2!! + 2!! = !!! +4.8 +0.14 2.4 !"!! + !! = !"! +2.7 +0.16 2.7 !"#$ ! + !! = !" ! + !"! +3.7 +0.22 3.7 !"!! + 2!! = !"(!) +11.4 +0.34 5.7 !"! + !! = !"(!) +8.8 +0.52 8.8 !"!! + !! = !"!! +13.0 +0.77 13.0 !"! + !! = !"(!) +13.5 +0.80 13.5 !"(!")! ! + 3!! + !! = !"!! + 3!!! +17.1 +1.01 17.1
!"!! + 6!! + 2!! =12 !! ! + 3!!!
+104 +1.23 20.8
!"#! ! + 4!! + 2!! = !"!! + 2!!! +43.6 +1.29 21.8 !"! ! + 2!! = 2!"! +46 +1.36 23 !"!! + !! = !"!! +31 +1.82 31 So ---- let's be sure we can calculate pE values ( calculations first, understanding 2nd? ) Calculate pE for a) acid solution 10!!! = !"!!! , !"!! = 10!!! b) natural water, pH = 7.5 in equilibrium with O2 (PO2=0.21 atm) c) natural water, pH = 8, !"#! ! !" !". with !"!! = 10!!! !"!!! ⟶ !"!! + !!
!" = !"°+ log !"!"#
= 13+ log !"!!
!"!!= 11.
!! ! + 4!! + 4!! ⟶ 2!!! E°=1.229
!" = !"°+ !!log !"
!"#= !.!!"
!.!"#+ !
!log !
!! !!"!
20.83 - 7.67 = 13.2 !"#! + 4!! + 2!! ⟶ !"!! + 2!!! !° = 1.208
!" = !"°+ !!log !"
!"#= !.!"#
!.!"#+ !
!log !! !
!"!!
= 20.5 - 13.5 = 7.0
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E, pE, pH in natural waters What are the limits on pH, E in water? Upper limit ( water + !!) 4!! + !! ! + 4!! = 2!!! !! = !°+ !.!"#
!log!!! !! !
from table E° = 1.23 !!!= 1 bar !! = 1.23− 0.0592!" Lower limit ( water + !!) !! = −0.059!" SHE
Figure 11.2 The stability field of water as a function of Eh and pH at 25°C and 1 bar pressure. Contours showing partial pressures of hydrogen and oxygen at intermediate Eh values have been computed with Eqs. (11.17) and (11.23). The crosshatched area is the locus of Eh values computed assuming the reaction 4!! + !! ! + 4!! = 2!!! is at thermodynamic equilibrium and dissolved oxygen is at or above a detection limit of 5 !"
!.
Natural systems show the following loci on this diagram.
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Figure 11.3 Locus of measured Eh values. After L.G.M. Baas-Becking at al., Limits of the natural environment in terms of pH and oxidation-reduction potentials, J. Geol. 68:243-84. Copy-right © 1960 by The University of Chicago Press. Used by permission.
Figure 11.4 Approximate position of some natural environments in terms of Eh and pH. the dashed line represents the limits of measurements in natural environments, as reported by Baas-Becking et al, (1960) and shown in Fig. 11.3. The crosshatched area defines theoretical conditions under which waters are calculated to contain dissolved oxygen at or above a detection
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limit of 5 !g/L. Modified after R.M. Garrels and C.L. Christ (1965). Solutions, minerals and equilibria. Copyright © (1965) by Freeman, Cooper and Company. used by permission. So what? What the hell do we care about pE, pE°? The answer comes in out connection to Nernst equation We said NE = !" = !"°+ !
!log !"
!"#
Consider the reaction !"!! + !" ⇄ !" + !"!! !"° = 7.84 Eq. const.
! = !"!!
!"!!
Can relate K to pE° !" = !"°+ !
!log !"
!"#
!" = !"°+ !!log !
!
But previously (gen. chem) we showed that ! = !!!
!"⟹ !" = !!!
!.!"!!"#
At eq ΔG = 0 ⟹ pE= 0 !"° = !"#!
!
Relation of pE to real world environment (Caveat: remember pE refers to equilibrium situation.)
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FIGURE 2-19 The ecological redox sequence. In an organic-rich environment that becomes isolated from the atmosphere, bacteria, after first consuming any available oxygen, utilize alternative oxidants in the sequence shown from left to right. As each oxidant is being utilized, the pE (and Eh) of the system lies in the approximate range shown on the vertical axis. The broad and indefinite range of pE and Eh associated with each oxidant is intended to reflect both variation in the oxidant and reductant concentrations and the fact that while pE and Eh are calculated on the basis of equilibrium, natural redox systems are usually not at equilibrium. The same chart viewed "chemically"
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Figure 3.23 Sequence of redox reactions in aqueous environment. O2 in natural waters at 20°C is sufficient to oxidize about 3.4mg of organic carbon (shown here as CH2O) per liter of water. When the rate of replenishment of O2 from the atmosphere is slower than the rate of oxidation of Ch2O, oxygen is depleted and microbes will select the next most energetic oxidant in the sequence shown. For simplicity, only major products and their valence states are shown. See Table 3.7 for balanced equations. Source: W.M. Stigliani (1988). Changes in valued capacities of soils and sediments as indicators of nonlinear and time-delayed environmental effects. Environmental Monitoring and Assessment 10: 245-307. Copyright © 1988 by Kluwer, Academic Publishers. Reprinted with permission of Kluwer. Saying the same thing in another way.
Figure 11.10 The theoretical Eh (mV) of some important oxidation-reduction couples at equal molar ion concentrations except as indicated below, at pH = 7 and 25°C. Cross-hatched area gives Eh's for !!(!") !!!, where !!(!") ranges from 8.25 to 0.01 mg/L. Other conditions are: !"!! !!(!") at !!(!") = 14 mg/L (atmospheric !! = 0.80 bar), !"!! = 62 mg/L; !"#!(!"#$%&'()* !"!! at !"!! = 1 mg/L; !"(!")! !"!! at !"!! = 1 mg/L assuming !!" for !"(!")! = 10!!".!; !"!!! !"#!(!"#$%&) at !"!! = 1 mg/L and !"!!! = 96 mg/L; and !°(!"#$%& !"#$%&) !!!(!") at !!!(!") = 108 mg/L 10!!.! !"# ! . After D. Langmuir,
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Physical and chemical characteristics of carbpnate water. In Guide to the hydrology of carbonate rocks, ed. P. E. Lamoreaux, B. M. Wilson, and B. A. memeon. Copyright 1984 by UNESCO. Used by permission. What are the general controls on the redox state of natural waters? atmospheric !! is the major oxidant organic matter is the major reductant Comments: !! rich environment (high pE) oxidize organic matter
!"!! + !! ⟶ !"! ↑ +!!! oxidation capability of water limited Solubility of !! in water = 9 mg/L (20°C) (~0.3x10!! moles) To oxidize 1 mg organic carbon, need 2.7 mg !! ∴ , at 20°C, 3.4 mg !"!! can be oxidized by !! dissolved in a liter of water. Industrial waste has a carbon content that greatly exceeds this number! TABLE 3.6 TYPICAL BODS FOR VARIOUS PROCESSES
Type of discharge BOD (mg !!/liter wastewater) Domestic sewage 165 All manufacturing 200 Chemicals and allied products 314 Paper 372 Food 747 Metals 13 Other oxidants can operate when !! concentration falls so that aerobic bacteria cannot survive. 5 molecules control this regime. !"!!,!"#!,!"(!")!, !"!!,!"! This gives rise to the following processes: Denitrification 2!"!! + 12!! + 10!! ⟶ !! + 6!!! !"#! Reduction !"#! + 4!! + 2!! ⟶ !"!! + 2!!! Iron Reduction !"(!")! + 3!! + !! ⟶ !"!! + 3!!!
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Sulfate Reduction !"!! + 9!! + 8!! ⟶ !"! + 4!!! !"! ⟶ methane !"! + 8!! + 8!! ⟶ !"! + 2!!! pE can be thought of as a "chemical selector" that determines how oxidation is carried out by micro-organisms. The following table summarizes the situation. TABLE 3.7 REDOX REACTIONS, PRODUCTS, AND CONSEQUENCES
Redox Reaction Reaction Products/Consequences 1. !! + !"!!⟶ !"! + !!! The aerobic condition, characterized by the highest redox
potential, occurs when there is an abundance of !!, and the relative absence of organic matter owing to oxic decomposition by aerobic micro-organisms. Two examples are the aerobic digestion of sewage wastes, and the decomposition of organic matter near the surface of well-aerated soils. The end products, !"! and water, are nontoxic.
2. 4 5 !"!! + !"!! +4 5 !! ⟶ !"! +2 5 !! + 7 5 !!!
When molecular oxygen is depleted from the soil or water column, as would be the case, for example, in waterlogged soils and wetlands, available nitrate is the most efficient oxidant. Denitrifying bacteria consume nitrate and release !!. !!!, a greenhouse gas, is also released as a side-product. In agricultural soils, denitrification can lead to losses of nitrogen fertilizer amounting to as much as 20% of inputs. Denitrifying bacteria are also very active in heavily polluted rivers, or in stratified estuaries where organic matter accumulates. In some estuary systems, denitrification may significantly affect the transfer of nitrogen to the adjacent coastal waters and to the atmosphere.
3a. 2!"#! + !"!! +4!! ⟶ 2!"!! + 3!!! +!"!
In anaerobic environments where nitrates are in low concentration and manganese and ferric oxides are abundant, the metal oxides are a source of oxidant for microbial oxidation. This may be the case in natural soils, and in the sediments of lakes and rivers. The environmental significance of these metals , deleterious organic compounds, phosphates, and gases. When the metal oxides are reduced, they become water-soluble and lose their binding ability. This loss may result in the release of toxic materials.
3b. 4!"(!")! + !"!! +8!! ⟶ 4!"!! + 11!!! +!"!
' ' ' '
4a. 1 2 !"!!! + !"!! +!! ⟶ 1 2 !!! + !!! +!"!
Sulfidic conditions are brought about almost entirely by the bacterial reduction of sulfate to !!! and !"! accompanying organic matter decomposition. Sulfate reduction is very common in marine sediments because of the ubiquity of organic
28
matter and the abundance of dissolved sulfate in seawater. In fresh water, such reactions are important in areas affected by acidic deposition in the form of sulfuric acid. !!! is an extremely toxic gas. Sulfides are also important in scavenging heavy metals in bottom sediments.
4b. !"! + 7 2 !! +!!!⟶ !!! + 2!"!!! +2!!
Conversion of a heavy-metal sulfide (!"!) to sulfate may also occur when anaerobic sediments are exposed to the atmosphere, as in the case of the raising of dredge spoils. It may also occur when wetlands contianing pyrites (!"#!) are drained for agriculture, or in coal mining areas as acid-mining drainage. One consequence may be an increase in acidification from the generation of sulfuric acid; another might be the release of toxic metals.
5. !"!! + !"!!⟶ !"! +!"!
Under anaerobic conditions at a redox potential of about -200 mV and in the presence of methogenic bacteria as may be found in swamps, flooded areas, rice paddies, and the sediments of enclosed bays and lakes, partially reduced carbon compounds can disproportionate to produce methane as well as !"!. This reaction is more typical in freshwater systems because sulfate concentrations are much lower than in marine environments, averaging about one one-hundredth the concentration in seawater. Methane is a critical gas in the determination of global climate. Since the early 1970s, global atmospheric methane levels have been increasing at a rate of 1% per year. Although the reasons for this increase are still under investigation, the expansion of rice paddy cultivation in southeast Asia has been cited as a contributing cause. See discussion, PArt II, pp, 123-125.
Source: W.M. Stigliani(1988). Changes in valued capacites of soils and sediments as indicators of nonlinear and time-delayed environmental efects. Environmental Monitoring and Assessment 10: 245-307 Recap Before going further into the use of pE, pE°, etc to discuss the environment, we need to rewind ourselves that there are 4 quantities that really define redox couples K, ΔG°, pE(pE°), EH°
!"° = !°!.!"#
25℃ = !!log! = −!
!∆!°!.!!"
∆!° = −!" ln!
On the next pages, I append an "environmental redox table" that shows redox couples for several things not found (easily) in standard tables. Before beginning the use of this table, please note the similarities (once again) between A/B and redox rxns.
29
!" ⇄ !! + !! !"!! ⇄ !! + !"!!!
Caveat: "!!" exists, "!!" does not, A/B fast, redox slow, Kredox very large, KA/B small What is pE of an environmental system? Answer: pE of dominant redox couple TABLE 7.1 Half Redox Reasctions
pE°=logK Hydrogen
!! + !! = !!!!(!) 0.0
Oxygen !!!! ! + !! + !! = !
!!! ! + !
!!!! +35.1
!!!! ! + !! + !! = !
!!!! +20.75
!!!!!! + !! + !! = !!! +30.0
(Note also !"!! + !! = !!!; log! = 11.6) Nitrogen
!"!! + 2!! + !! = !!!!!! ! + !!! +13.6
(Note also !!!! ! = 2!"! ! ; log! = −0.47) !!!"!! + !! + !! = !
!!"!! +
!!!!! +14.15
(Note also !"!! + !! = !"#!; log! = 3.35) !!!"!! +
!!!! + !! = !
!!"(!)+ !
!!!! +16.15
!!!"!! +
!!!! + !! = !
!!!! ! + !
!!!! +18.9
!!!"!! +
!!!! + !! = !
!"!! ! + !
!!!! +21.05
!!!"!! +
!!!! + !! = !
!!"!! +
!!!!! +14.9
Sulfur !!!"!!! + !! + !! = !
!!"!!! +
!!!!! -1.65
(Note also !"!!! + !! = !"#!!!; log! ≃ 7 !!!"!!! +
!!!! + !! = !
!!!!!!! +
!!!!! +4.85
!!!"!!! +
!!!! + !! = !
!"!!!(!. !"#. )+
!!!!! +6.03
(Note also !!! !. !"#. = !!! !. !"#. ; log! = −0.6) !!"!"!!! +
!"!"!! + !! = !
!"!!!! +
!"!"!!! +5.40
!!"!"!!! +
!!!! + !! = !
!"!!!! +
!!!!! +5.88
(Note also !!!! + !! = !"!!; log! = 6.1 and !"!! + !! = !!!!; log! = 3.5)
!!"!"!!! +
!"!"!! + !! = !
!"!!!! +
!!"!!! +5.12
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(Note also !!!! + !! = !"!!; log! = 7.0 and !"!! + !! = !!!!; log! = 3.8)
!!!"!!! +
!!!! + !! = !
!!!! !" + !
!!!! +5.13
(Note also !!! ! = !!! !" ; log!! = −1.0, and other acid-base, coordination, and precipitation reactions)
Carbon Inorganic Carbon monoxide !!!"! ! + !! + !! = !
!!" ! + !
!!!! -1.74
Graphite !!!"! ! + !! + !! = !
!! ! + !
!!!! +3.50
Organic-C.1 Formate- !!!"! ! + !
!!! + !! = !
!!"##! -5.22
Formaldehyde !!!"! ! + !! + !! = !
!!"!# !" + !
!!!! -1.20
Methanol !!!"! ! + !! + !! = !
!!"!!" !" + !
!!!! +0.50
Methane !!!"! ! + !! + !! = !
!!"! ! + !
!!!! +2.86
Organic-C.2 Oxalate2- !"! ! + !! = !
!!""! ! -10.7
Acetate !!!"! ! + !
!!! + !! = !
!!"!!""! +
!!!!! +1.27
Acetaldehyde !!!"! ! + !! + !! = !
!"!"!!"# ! + !
!"!!! +0.99
Ethanol !!!"! ! + !! + !! = !
!"!"!!"!!" !" + !
!!!! +1.52
Ethane !!!"! ! + !! + !! = !
!"!!!! ! + !
!!!! +2.41
Ethylene !!!"! ! + !! + !! = !
!"!!!! ! + !
!!!! +1.34
Acetylene !!!"! ! + !! + !! = !
!"!!!!(!)+
!!!!! -0.86
Organic-C.3 Pyruvate- !!"!"!(!)+
!!"!! + !! = !
!"!"!!"!""! +
!!"!!! +0.05
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Lactate- !!!"! ! + !!
!"!! + !!
= !!"!"!!"#"!##! +
!!!!!
+0.68
Glycerol !!"!"! ! + !! + !!
= !!"!"!!"#"!"#"!!" +
!!"!!!
+0.21
Alanine !!!"! ! + !
!"!"!! +
!!!"!! + !!
= !!"!"!!"##!!"!! +
!!!!!
+0.84
Organic-C.4 Succinate2- !!!"! ! + !
!!! + !! = !
!"!"!!""! ! +
!!!!! +0.77
Organic-C.6 Glucose !!!"! ! + !! + !! = !
!"!!!!"!! +
!!!!! -0.20
Halogens !!!"! ! + !! = !"! +23.0 !!!"#$ + !
!!! + !! = !
!!"! + !
!!!! +25.3
(Note also !"#$ = !! + !"#!; log! = 7.50 !!!"!! +
!!!! + !! = !
!"!! ! + !
!!!! +20.1
!!!! ! + !! = !! +9.05
Trace Metals Cr !!!"#$!! +
!!!! + !! = !
!!"!! + !
!!!! +20.2
(Note also !"#$!! = !!!"!!!
!! + !!!!!, log! =
−1.5; !"#$!! = !! + !"#!!!, log! = −6.5
Mn !!!"#!! +
!!!! + !! = !
!!"!! + !
!!!! +25.5
!!!"#! ! + 2!! + !! = !
!!"!! + !!! +20.8
Fe !"!! + !! = !"!! +13.0 !!!"!! + !! = !
!!"(!) -7.5
!!!"!!! ! + 4!! + !! = !
!!"!! + 2!!! +16.6
Co !"(!")! ! + 3!! + !! = !"!! + 3!!! +29.5 !!!"!!! ! + 4!! + !! = !
!!"!! + 2!!! +31.4
Cu !"!! + !! = !"! +2.6
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!!!"!! + !! = !
!!"(!) +5.7
Se !!!"#!!! + 2!! + !! = !
!!!!"#! +
!!!!! +19.4
!!!!!"#! + !! + !! = !
!!" ! + !
!!!! +12.5
!!!" ! + !! + !! = !
!!!!" -6.7
(Note also !!!" = !! + !"#!, log! = −3.9; !!!"#! =!! + !"#$!!, log! = −2.4; !"#$!! = !! +!"#!!!, log! = −7.9; !"#!!! + !! =!"#$!!, log! = +1.7)
Ag !"#$ ! + !! = !" ! + !"! +3.76 !"! + !! = !"(!) +13.5 Hg !!!"!! + !! = !
!!"(!) +14.4
!"!! + !! = !!!"!!! +15.4
Pb !!!"#! + 2!! + !! = !
!!"!! + !!! +24.6
(Note many other reactions for Mn, Fe, Co, Cu, Se, Ag, Hg, and Pb)
pE vs pH (Pourbaix diagrams) Consider two limiting reactions of H2O oxidation a) 2!!! ⇄ !! + 4!! + 4!! reduction b) 2!! + 2!!! ⇄ !! + 20!! Applying NE
!" = !"°+ !!log !"
!"#
a) !" = !!.!!"
!.!"#+ !
!log !!! !
! !
!" = 20.83+ log!!!!! !! = 20.83− !"
b) !" = !"°+ log !! = !" = −!" Boxed:
33
Figure 4.4. Simplified pE-pH diagram for iron in water. The water maximum soluble iron concentration is 1.00x10!!M.
Other Pourbaix diagrams of interest Anoxic waters (!"!! !! system)
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Other diagrams can be very complicated. Let us follow the text book example of how these diagrams are calculated, using the iron system as an example. Rxns: !"!!! + !! ⟶ !"!! !"° = +13.2 !"(!")! ! + 2!! ⇄ !"!! + 2!!!
"Ksp" = !"!!
!! ! = 8.0!10!"
!"(!")! ! + 3!! ⇄ !"!!! + 3!!!
"Ksp" = !"!!!
!! ! = 9.1!10!
Have "water boundaries" for diagram pE = 20.25-pH pE = -pH
very acidic conditions (pH<3) !"!! = !"!! !"#$
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!" = 13.2+ log!"!!!
!"!! = 13.2
For pE > 13.2 , as pH increases (OH- increases), get pptn of !"!!! as !"(!")!
!! ! =!"!!!
!!"!=
10!!
9.1!10!!
pH = 2.99
Can establish !"!!, !"(!")! boundary
!! ! =!"!!
!!"=
10!!
8!10!"
pH=8.95 What about !"!! !"(!")! Earlier we said
pE = 13.2 + log !"!!!
!"!!
!"!!! = !!"! !! !
pE = 13.2 + log !!"! !! !
!"!!
pE = 13.2 - 3pH
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!"(!")! !"(!")! boundary
!" = 13.2+ log!!"! !! !
!"!! = 13.2+ log!"!!"! !! !
!!" !! !
pE = 4.3 - pH Result
Figure 4.4. Simplified pE-pH diagram for iron in water. The water maximum soluble iron concentration is 1.00x10!!M.