d.o. in hyper saline water

7/24/2019 D.O. in Hyper Saline Water

1/16

Limnoi. Oceanogr., 36(2),

1991,235-250

0 1991, by the American

Society of Limnology and Oceanography,

Inc.

Dissolved oxygen concentrations in hypersaline waters

J. E. Sherwood,F. Stagnitti, and M. J. Kokkinn

Faculty of Applied Science and Technology, Warrnambool Institute of Advanced Education,

Warrnambool, Victoria 3280, Australia

W. D. Williams

Department of Zoology, University of Adelaide, G.P.O. Box 498, Adelaide, South Australia 5001

Abstract

Henrys law constants (kO) and equilibrium concentrations (CO*) of dissolved oxygen (DO) at 1

atm were measured in NaCl solutions of concentration (S) up to -260%~ and at temperatures (7)

between 273 and 308K. An equation of the form

In Co* = a, +

$ + a,ln T + a,T + a,T2 + S(a, + a,T + a7P) + asS2

was found to predict DO values to within the experimental uncertainty. An equation of the same

form satisfactorily described the variation of In kO over the same temperature and concentration

ranges. In order to develop these equations it was also necessary to develop ones to describe the

variation of density and vapor pressure of NaCl solutions with T and S. The equations can be

used to generate ables of oxygen solubility values that can be used for hypersaline waters dominated

by NaCl. Theoretically, DO values based on NaCl can be corrected for the presence of other ionic

salts in natural waters. At present this correction is limited by the availability of DO data for these

subdominant electrolytes.

It is a century since L. W. Winkler pub-

lished his pioneering studies on the solu-

bility of oxygen in water. Since then, equi-

librium concentrations of dissolved oxygen

(DO) in marine and estuarine waters have

been measured over a range of salinity and

temperature with his technique or minor

modifications of it. In these saline waters,

as well as in freshwaters, his basic technique

has become the standard to determine the

concentration of DO, and tables are avail-

able that document the relationship be-

tween salinity, temperature, and DO at

equilibrium in such waters (Weiss 1970;

Benson and Krause 1980; Mortimer 198 1).

It is only relatively recently that other meth-

ods of measuring DO have been developed;

they involve diffusion to a reducing elec-

trode. They have not supplanted Winklers

method where simplicity and accuracy are

important.

Acknowledgments

R. Evans prepared the figures. Fred Post provided

literature otherwise inaccessible to us. D. J. J. Kinsman

donated a copy of a paper we found difficult to obtain.

W.D.W. thanks the Australian Water Research Ad-

visory Council for support (Scientific Merit Grant).

Remarks by anonymous referees are also ackuowl-

edged.

Concentrations of DO in hypersaline wa-

ters, that is waters with salt concentrations

>40%, have been much less studied, al-

though it has long been known that DO con-

centrations decline markedly with increas-

ing salinity. Perhaps, at least in part, the

difficulties of measuring DO by the Winkler

method in hypersaline waters, alluded to by

Walker et al. (1970) and Hammer (1986),

explain why so few studies have taken place.

In any event, for limnologists studying sa-

line lakes there are no tab les available of the

sort that freshwater limnologists or marine

and estuarine scientists have. The few stud-

ies that have been made of DO in hyper-

saline waters genera lly involve experimen-

tal techniques that can be criticized on

methodological grounds, measurements at

only one or two temperatures, and (or)

par-

ticular

bodies of salt water (Laguna Ta-

maulipas, marine brines, Great Salt Lake)

(e.g. Macarthur 1916; Copeland 1967; Loe-

flich 1972; Kinsman et al. 1974; Jones et

al. 1976). For the most part, studies of DO

in hypersaline waters have been published

in journals lacking wide circulation among

limnologists.

There is a need to remedy this situation

given the wide distribution and abundance

235


2/16

236

Sherwood et al.

of inland saline waters (Hammer 1986; Wil-

liams 1986a) and the biological significance

Notation

__-

of DO to thkm. This papei attempts to do

so. We report a systematic-study of DO con-

centrations in hypersaline waters between

temperatures ,3f 0 and 35C. NaCl solutions

ranging up to near saturation (- 26OY&$ ere

selected as model solutions because most

natural saline waters are dominated by this

salt. The effect of other salts on DO levels

is also examined.

Theory

Gas solubi/ity and Henrys Iaw-Appli-

cation of Hellrys law to the solubility of

atmospheric gases n natural waters has been

thoroughly outlined in papers by Benson

and Krause (1980), Weiss (1974), and Weiss

and Price (19 80). According to Henrys law

the solubility of a gas, , in a solvent o f fixed

composition .atconstant temperature (T), is

given by

A= kix,

(1)

whereA is the fugacity of the gas n the vapor

phase, Xi is its mole fraction in the liquid

phase, and k, is the Henrys law coefficient

(units given in list of notation).

Following the treatment of Benson and

Krause for o:uygen,

where Znj is lbe sum of the moles of oxygen

(n,J, water, and all other dissolved sub-

stances in some volume, V,, of solution at

the equilibrillm temperature. But

i.e. the solution mass (m3 divided by its

density at the equilibrium temperature (p,).

The concentration of dissolved oxygen

(C,) is commonly measured in molar units,

i.e.

c-&y.

s

Thus from Eq. 2 and 4

Co( mol liter- ) =

fOG%)

k, v, ,

(5)

and by Eq. 3

(6)

B

B

co

CO

G

c

MX

Bunsen coefficient for a dissolved gas

Second virial coefficient for oxygen gas,

atm-

Dissolved oxygen concentration in equilibri-

um with an oxygen-containing atmosphere

of total pressure, Pa,, mg liter-l

Dissolved oxygen concentration in equilibri-

um with an atmosphere of standard com-

position and saturated with water vapor at

a total pressure of 1 atm, mg liter-l

Co* in distilled water, mg liter-

CO* in a solution of the electrolyte MX, mg

liter-l

Co* in a salt mixture, mg liter

Fugacity of the real gas i, atm

Setschenow constant for an ion of fype i, li-

ters mol-*

Henrys law coefficient for disgolved gas i,

atm

Ion-specific Setschenow constant, kg mol-

Temperature-dependent Setschenow constant

for an electrolyte, liters mol-

A modified Henrys law constant defined by

the equation: CO = K&, mol liter- aim-

Number of moles of component i, mol

Gas pressure, atm

Equilibrium vapor pressure of water, atm

Solution density at a known temperature, g

liter-l

Coefficient of determination adjusted for de

it is an approximate unbiased estimate of

the population rz

rms error of a regression analysis

Salinity, measured as grams of salt per kilo-

gram of solution, %

Celsius temperature, C

Absolute or Kelvin temperature, K

Solution volume, liters

Mole fraction of component i in a solution

Valency of an ion of type i

Application to NaCl solutioris-In the salt

solutions used in our experiments the fol-

lowing approximations can be made:

Znj N n, + nsalt

(7)

ms = mw + %an

(8)

where the subscripts w and salt refer to wa-

ter and NaCl.

Neglecting dissolved gases (chiefly oxy-

gen and nitrogen) introduces an error of

~0.01% in Eq. 7 and 8. Thus,

znj_ (n, + n,.d


3/16

Oxygen in hypersaline waters

For NaCl solutions whose concentrations

are measured as salinity (S in ?&)), he fol-

lowing substitutions are possible for Eq. 9:

m, = l,OOOg

m,

= (1,000 - 5) g

m

salt

=sg

M, = 18.015 g mol-l for Hz0

M

N&l

= 58.443 g mol-l for NaCl,

i.e.

$ = (5.5509 x 1O-2 - 3.8399

s

x 10-5s).

(10)

Substituting Eq. 10 into 6 gives

Co(mo1 liter-)

=fp (5.5509 x 1O-2 - 3.8399

0

x 10-5s).

(11)

Fugacity of oxygen-similar expressions

for the fugacity of a real gas have been de-

rived by both Benson and Krause (1980)

and Weiss (1974):

fo = Poexp(PB) (12)

where PO is the partial pressure of oxygen

in the gas mixture (atm), P is the total pres-

sure of the gas mixture (atm), and B is the

second virial coefficient for oxygen at tem-

perature T(atm-I).

For oxygen, Benson and Krause derived

the following expression for B (although they

represented the virial coefficient by the sym-

bol -0) for 0 3, the

SE is given.

Results (Table 1) indicate that iodine loss

was not significant during the pipetting step.

An uncertainty of f 0. 1C in water bath

temperature introduces a maximal uncer-

tainty of 0.04 mg liter- in Co at 0C. This

uncertainty decreases as temperatures and

salinity increase.

With the exception of the value for YC,

all measurements of Co* for distilled water

lie within 0.04 mg liter- of accepted values

(Table 2). The reason for the discrepancy at

5C is not known. Values for other temper-

atures indicate that systematic errors are not

significant when compared to the random

errors of the experiment.

DO determinations reported here are thus

considered reliable to at least +0.05 mg li-

ter-. The experimental technique does ap-

pear to lead to a true solubility equilibrium,

despite reports of a tendency for this meth-

od of aeration to lead to supersaturation

(Carpenter 1966). A similar conclusion was

reached by Khomutov and Konnik (1974).

An equation of state or k0 and Co* values

in NaCl solutions-The data set for Henrys

law constants (ko) and DO concentrations

(Co*), consisting of 102 paired values (Ta-

ble 3), was the basis of our mathematical

models. Multiple regression was used to de-

velop a model of best fit for predicting In

k0 and In Co* given concentration S(?&)and

temperature T(K). Initial attempts to model

our data set were to fit it to an equation

derived for dissolved gases in seawater

(Weiss 1970). This equation has the form:

lnx=aO+a,l + aJn T + a,T

+ a,F T S(a, + a,T + a,F) (24)

where x = k0 or Co*.

These equations proved to be statistically

ineffective and of insufficient accuracy. Their

major problems were an overall lack of fit,

lack of statistical significance of the partial

regression coefficients ai, and a strong cur-

vilinear response in salinity terms. After

considerable analysis and testing of regres-

sion equations consistent with the Weiss

formulation, it became apparent that the fit

could not be improved unless higher order

salinity terms were included. Consistently

better results were obtained by introducing

an P term. In this paper, we shall refer to

equations with an additional s2 term as the

modified Weiss equations. They are of the

form

In x = a, + a, f + aJn T + a,T

+ a,T2 % S(a, + a,T + a7F) +

asp

(25)

where x = k, or Co*.

Both the Weiss and modified Weiss equa-

tions have a considerable degree of multi-

collinearity (Table 4), as is to be expected

with fitting polynomials of this nature.

Therefore, the values of the partial regres-

sion coefficients are highly sensitive to the

inherent accuracy of the experimental data.

In other words, changing the data set may

produce a different set of values. The sta-

bility of the coefficients was checked by

splitting the data set into two (by random

draw) and then running the regressions

through each of the subsets. The changes n

the coefficients were generally ~2% and

comparable accuracy to the original data set

was maintained. These results indicated that

in spite of the multicollinearity, the coeffi-

cients were reasonably stable and reliable.

Another consequenceof multicollinearity

is that extrapolation outside the range of

values for S and T presented here is unre-

liable and should be avoided. Our equations

cannot be expected to perform satisfactorily

for values oft outside the range O-35C and

S > 2607~. Bearing in mind the conditions

stated above, we find the modified Weiss

equations will produce accurate predictions

of our measured dissolved oxygen concen-

trations and are significantly better than the

Weiss equation. Calculation of the absolute


8/16

242

Sherwood et al.

Table 3. Expknental determinations of k. and

Co*. These data kere used in deriving the regression

equations.

Temp.

(C)

COltCll 10 k,

co*

w (atm)

(mg liter-)

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

5

5

5

5

5

5

5.4

5.4

5.4

5.4

5.4

5.4

10.4

10.4

10.4

10.4

10.4

10.4

10.4

10.4

10.4

10.4

10.4

10.4

19.4

19.4

19.4

19.4

19.4

19.4

19.4

19.4

19.4

0

0

0

0

0

0

0

50.37

50.37

57.4

.57.4

f00.25

100.25

141.9

141.9

143.52

$43.52

152.6

152.6

200.43

1 00.43

253.15

:;53.15

154.63

X54.63

0

1Oi.61

102.61

i158.58

2158.58

55.55

55.55

160.92

160.92

: 03.28

: 03.28

0

0

63.05

63.05

106.46

: 06.46

:i47.9

il47.9

:195.19

:195.19

250.79

250.79

0

0

0

0

54.13

54.13

98.44

98.44

103.13

2.508

14.73

2.537

14.56

2.500

14.77

2.516

14.68

2.509 14.72

2.525

14.63

2.545

14.51

3.568 10.38

3.569

10.38

3.78

9.80

3.77

9.83

5.09

7.28

5.09

7.28

7.07 5.23

7.11

5.20

7.12

5.20

7.08 5.23

7.54

4.91

7.53

4.9 1

11.1

3.34

10.9

3.39

17.2

2.13

17.0

2.16

17.5

2.10

17.2

2.13

2.913

12.65

2.920 12.62

5.82 6.35

5.80 6.37

19.1

1.91

18.5 1.97

4.17

8.84

4.20

8.79

8.80

4.18

8.83 4.17

12.1

3.03

12.2

3.01

3.30 11.13

3.283 11.18

4.84

7.60

4.80

7.66

6.51 5.64

6.49

5.66

8.56

4.28

8.52 4.30

11.9 3.06

12.2

3.01

18.7

1.95

18.7 1.94

3.95 9.19

3.92 9.26

3.95 9.18

3.93 9.25

5.38 6.75

5.36

6.78

7.16

5.07

7.06 5.14

7.28

4.98

Table 3. Continued.

Temp.

(0

19.4

103.13

7.24 5.01

19.4 147.96 9.75 3.72

19.4 147.96

9.78 3.70

19.4 195.69

13.5

2.67

19.4

195.69 13.4 2.70

19.4 247.43

19.5

1.84

19.4 247.43

19.3

1.87

19.4

250.59 20.2

1.78

19.4 250.59

19.6

1.83

27.25

0 4.49 7.96

27.25

0 4.51

7.93

27.25

53.76 6.12

5.84

27.25

53.76

6.12 5.84

27.25

104.31 8.10

4.41

27.25

104.31 8.09

4.42

27.25 160.39 11.6 3.08

27.25

160.39 11.6 3.08

27.25

215.14 16.6

2.14

27.25 215.14

16.6

2.14

27.25

258.49 22.2 1.59

27.25

258.49 22.2

1.59

34.1

0 4.98

7.03

34.1

0 4.96 7.06

34.1

158.39 11.8

2.96

34.1 158.39

11.8

2.97

35.2 0 5.06

6.90

35.4 0 5.09 6.85

35.4 0 5.00

6.98

35.4

0

5.07

6.88

35.4 0 5.05

6.9L

35.4 52.78 6.64

5.26

35.4

52.78 6.59 5.29

35.4 102.6

8.74 3.99

35.4 102.6 8.80

3.96

35.4 114.89 9.31

3.75

35.4

114.89

9.31 :

3.75

35.4

159.56 12.2 2.86

35.4 159.56 12.2

2.85

35.4

199.48 15.6

2.23

35.4

199.48 15.3

2.28

35.4

251.73 21.2

1.64

35.4 251.73 21.5

1.62

35.4 256.54

22.4 1.55

35.4

256.54 22.4

1.55

differences between experimental and pre-

dicted values of C,* showed ,that for the

Weiss equation 22 of the 102: data points

differed by ~0.05 mg liter-, 48 by ~0.10

mg liter-, and 87 by 10.20 mg lil.er-l. By

contrast, for the modified Weiss equations,

85 differences were 10.05 mg liter-, 96

were 10.10 mg liter-, and all were within

0.20 mg liter-l.

Modeling errors for the modified Weiss

equations thus compare very favorably to


9/16


243

Salinity (g kg-)

Fig. 1. Variation of Co* with salinity at, in de-

scending order, O, 5, lo, 20, 30, and 40C. Curves

are drawn using Eq. 25; 95% of the experimental data

points lie within 0.10 mg liter-l of the predicted curves.

the experimental precision of the data.

Equation 25 was thus used to construct the

curves of Fig. 1. Note that the relationship

between DO and salinity approaches lin-

earity at higher temperatures. In all cases

DO concentration decreasesas salinity in-

creases, although the effect is reduced at

higher temperature.

Violation of the Setschenow relation-

ship-Equation 25 developed as the best-fit

model for our data violates the Setschenow

equation. This empirical relationship is that

at constant temperature

= K[MX]

CW

where C, = Co*

in distilled water, C,, =

Co* in an electrolyte solution of concentra-

tion [MX], and K = temperature-dependent

Setschenow constant (varies with the nature

of the electrolyte, MX).

Equation 26 indicates that the logarithm

of DO should be a

linear

function of salin-

ity, not a

quadratic

as we have found. The

validity of Eq. 26 has been demonstrated

for a wide range of solutes in various elec-

trolyte solutions (Long and McDevit 1952;

Battino and Clever 1966; Weiss 1970).

We examined the effect of the Sz carefully

using data at each of our constant temper-

atures (see Table 3). For Co* at lower

temperatures (OV, 5C) the rms error of re-

gression (.s) or a quadratic in NaCl concen-

tration was two-thirds that for a linear re-

gression in concentration. At higher

temperatures (10.4-35.2C) s for the qua-

dratic regression was similar in magnitude

-mo

OclO

00 mb-m-

m OOCIN~

m ~000

6 id66

* 4 + I(

* * * *

***xc*+*+

*wP-CINbl-w

000000000

PWb-C-lhlbr-

00000000


10/16

244

Sherwood et al.

Table 5.

Setschenowonstants

K) calculated from published data on the solubility of oxygen in NaCl solutions

and from this inve$tigation.

Temp.

(c)

0

10

25

40

MA paa]

(m(bl liter)

5.37

5.11

2.49

5.35

5.10

5.31

2.0

5.06

1.2

4.0

1.92

,1.53

.5.28

5.03

(W2LP)

0.1600f0.0008

0.174~0.011

0.1699t0.0007

0.1486+0.0006

0.154f0.010

0.1336a0.0003

0.125+0.010

0.136+0.007

0.136

0.1374+-0.0004

0.1416+0.0008

0.145LO.002

0.1210~0.001

0.125+0.004

n

11

3

4

11

4

11

4

4

8

7

3

11

4

--

-

Reference ;

-

This study

Cramer 1980

Eucken and Hertzber@,1950

This study

Cramer 1980

This study

Finn 1967

Cramer 1980

Khomutov and Konnik 1974t

Macarthur 1916 :

Geffcken 1904

Eucken and Hertzberg 1950

This study

Cramer 1980

to, but general\y smaller than, s for the lin-

ear regression*.:This s to be expected since

our analysis qldicates that the Sz term is

always statisti:cally significant. What our

analysis also sljows, however, is that at each

temperature our data fit a linear regression

very well (P = 1 OO,s values 0.003-0.006,

12 I n 5 25).,

The questionsmay be asked whether the

S term resu1t.s rom curvature in the ex-

perimental dai.a set that is caused by some

nonideal behayrior at very high salinities. To

check we performed regressions or both the

Weiss and modified Weiss equations to a

number of da;ta subsets containing values

for salinities i:n the ranges O-100$& inclu-

sive, O-l 507~ nclusive, and 0-2007~ inclu-

sive. In all capes, he term s2 was statisti-

cally significant and the modified Weiss

equations pedormed better than the Weiss

model, althou:+ its influence on the regres-

sion diminishlzd in the data sets containing

lower salinity values, e.g. 0-100~~. One

would expect that the S term would have

little influence on the outcome of the re-

gression in the salinity ranges (< 4Oo/oo)on-

sidered by Weiss (1970).

It is possiblie that the significance of the

P term has been generally overlooked by

previous workers because inear regression

fitted their data sets to within experimental

uncertainty. Also, at lower salinities and

higher tempeTatures the influence of the s2

term on the r,egressiondiminishes.

In order to facilitate comparison of our

data with the available literature we have

calculated Setschenow constants from it.

They are consistent with findings by other

workers (Table 5) and have standard devi-

ations of 0.5% or less.

Comparison with other stud&s-The ef-

fect of electrolyte concentrations on the sol-

ubility of gases n aqueous solutions is an

area of cons iderable theoretical and app lied

interest. Two reviews have summarized the

literature up to 1966 (Long and McDevit

1952; Battino and Clever 1966). This lit-

erature includes several studies on the sol-

ubility of oxygen in solutions of NaCl and

other salts of limnological significance. A

number of single-temperature studies (25C)

have been published (Macarthur 1916; Finn

1967; Kinsman et al. 1974; Khomutov and

Konnik 1974). Studies of NaCl solutions at

several temperatures include those of

Geffcken (1904: 15C, 25(Z), Eucken and

Hertzberg (1950: OC, 15C, 20C 25Q

and Cramer (1980: 0-300C). Only Cra-

mers study, involving distilled water and

three NaCl concentrations (-50, 150, and

2507) covers the entire concentration and

temperature ranges of our work. IJnfortu-

nately, the solubility data of ihese earlier

studies are presented with a number of dif-

ferent concentration units for both DO and

electrolyte.

Comparison of our results with olthersne-

cessitated conversion of all measurements


11/16


245

to a common set of units. The empirical

Setschenow Eq. 26 was selected for this

comparison, Molarity was used rather than

molality because t typically gives linear Set-

schenow plots to higher concentrations

(Long and McDevit 1952). Several inves-

tigators have reported Setschenow con-

stants in these units.

Equation 25 was used to generate C,*

values at 10 salt concentrations (O-250?&)

and four temperatures. Linear regression of

h3ul co*

against NaCl molarity was then

used to determine the Setschenow constants

for our data and those of other workers, after

unit conversion if necessary (Table 5 ). As

previously discussed, small standard errors

(< lo/o) associated with constants found by

us and others indicate a good fit of the data

to Eq. 26 over the entire concentration range

to saturation. A lack of overlap of constants

measured at the same temperature, how-

ever, indicates significant systematic errors

among experiments.

Cramers Setschenow constants a re with-

in 2-3% of ours (except at OC), but have a

larger SE. His measured DO values for dis-

tilled water differ by up to 0.9 mg liter-

from accepted values and are consistently

lower than ours at other salt concentrations

(max difference, 0.9 mg liter-). In contrast,

Macarthurs value for Cc,* in distilled water

is within 0.2% of the currently accepted val-

ue, and at higher salt concentrations his val-

ues and those of Kinsman et al. are in ex-

cellent agreement. There is also good

agreement with our values; over the con-

centration range of 0-2OOY&NaCl, the max-

imal difference between their DO values and

values predicted w ith Eq. 25 is 0.08 mg li-

ter-. Agreement between all three investi-

gations is thus very good. Values of K found

by Geffcken (1904), Eucken and Hertzberg

(1950), and Finn (1967) are up to 8% dif-

ferent from ours.

NaCl solutions as models or natural wa-

ters-In most saline lakes worldwide, so-

dium and chloride ions predominate (see

appendix C, Hammer 1986). In Australia

especially, there are very few exceptions to

this pattern of ionic dominance (Williams

1967, 1986b; Hart and McKelvie 1986). It

was for these reasons that NaCl was chosen

as the principal experimental solution. Nev-

ertheless, numerous exceptions to the gen-

eral pattern of ionic dominance occur, and

it is of interest therefore to consider the na-

ture of differences in DO solubility in salt

solutions other than pure NaCl.

Studies of oxygen solubility in salt

mixtures are rare. A comparison was made

between the data of Weiss (1970) for sea-

water and the predictions of Eq. 25, using

the coefficients of Table 4. Differences be-

tween the two C,* values were calculated

at temperatures of O, 1O,20, 30, and 40C

and salinities of 0, 10,20, 30, and 40%~ In

all 25 cases, he differences were I 0.14 mg

liter-i, with the values of Weiss being less

than ours in 2 1 cases.As later results show,

these lower values are qualitatively consis-

tent w ith the presence of ions such as Mg2+

and SOA2- n seawater solutions. In 9 of the

25 cases he difference was ~0.02 mg liter-,

in 15 it was 10.06 mg liter-, and in only

4 caseswas the difference >O. 10 mg liter-.

All the latter were at 40C (1O-40?&). Equa-

tion 25 appears able to predict C,* in sea-

water or diluted seawater o within 0.15 mg

liter- over the temperature range 0-4OC.

Extrapolation of the seawater equation

(Weiss 1970) above 4Oo/oos of doubtful va-

lidity. At high salinities (-200?7m)solubili-

ties predicted by the equation were lo-20%

higher than those measured for NaCl so-

lutions. Similarly high predictions have been

found for He and Ar in Dead Sea brines

(Weiss and Price 1989).

DO concentrations in MgSO, (Fig. 2A)

and other electrolyte solutions (Fig. 2B) de-

crease less rapidly with increasing concen-

trations of these salts than is the case with

NaCl. Because he concentrations of DO in

pure NaCl and MgSO, solutions differ by

< 1 mg liter- at all but the lowest temper-

atures and highest concentrations (Fig. 2A),

it would seem hat DO solubility in mixtures

of these salts should not differ significantly

from DO solubility in pure solutions of

NaCl.

To test this, we studied mixtures of MgS04

and NaCl, as well as solutions made from

coarse sea salt. The differences of measured

DO concentrations from those predicted

with Eq. 25 for pure NaCl solutions are ~0.3

mg liter- (Table 6). As expected from Fig.

2, the predicted DO value is less than that


12/16

246

Sherwood et al.

I

0

,- I

I

50 : 100 150

200 250 300

Conceidration of Solution (g kg-l)

Fig. 2. Effect pf the nature of electrolytes on the

variation of DO wjth salt concentration. A. This study.

B. Macarthur (1916) at 25C.

measured for e~ach f the salt mixtures. Most

of the differen&esare within 0.12 mg liter-.

It should be iioted that the experimental

uncertainty of each of the single determi-

nations of DC) in Table 6 is -0.05 mg li-

ter-l. Maxim@ differences (0.2-0.3 mg li-

ter-) were foynd for the higher proportions

of MgSO, (7 : 3). It seems, hen, that values

predicted from pure NaCl solutions are like-

ly to provide near but low estimates (within

-0.1 mg liter- in many cases)of DO con-

centrations in Australian salt lakes.

Copeland (1967) carried out a limited

study of DO levels in a Mexican hypersali ne

lagoon, Laguna Tamaulipas. This coastal la-

goon is probably dominated by NaCl, al-

though details of ionic composition are not

given. For salinities < 150?&, Copelands

measured values are within 0.2 mg liter-l

of the predicted values using Eq. 2.5, with

three of the four values being within 0.1 mg

liter- (Table 7). Agreement at 220% is poor

and may be due to peculiarities in the ionic

composition of the lagoon.

;

Predictions of DO for salt mixtures-In

electrolyte solutions there is evidence that

to a good approximation each ion can be

considered to contribute independently to

the salting out effect on DO. As a con-

sequence, tables of ion-specific Setschenow

constants have been produced by Schumpe

et al. (1978) and Pawlikowski and Praus-

nitz (1983, 1984). These tables open the

possibility of predicting DO values in com-

plex salt mixtures in which ion,concentra-

tions are known. In practice, the approach

is presently limited by insufficient data.

Setschenow constants at 25C are available

for most dominant ions in natural waters

(Na+, K+, Mg2+, Ca2+, Cl-, SOd2-, C032-).

Only a few ions have had constants deter-

mined at other temperatures (Na+, K+, Cl-).

Interstudy differences in the magnitude of

Setschenow constants for a particular salt

are up to 200/6 e.g. Table 5; see also Kho-

mutov and Konnik 1974). This disparity

limits the accuracy of ion-specific con-

stants derived from these data. Despite

these restrictions, it has been possible, in

a few cases, to test the potential of this

technique for limnologists.

i

For the artificial salt mixtures given in

Table 6, the assumption of independent

ionic contributions to salting out gives

= KN,,,[NaC1l+ ~M~~,[M~SQI

= oglo + oglo(+--)

07)


13/16


247

Table 6. DO concentrations in artificial lake mixtures compared to those in pure NaCl solutions of the same

concentration.

DO Ima liter-9

Temp.

0

0

23.3

35.2

Concn

6s kg- )

53.4

103.0

140.4

192.6

100.0

250.0

51.8

101.3

143.1

199.6

253.2

Predicted

Fraction NaCl* MWtSUId

Eq. 25

At

Eq. 28

At

0.723 10.30 10.13 0.17 10.42 -0.12

0.717 7.36 7.08 0.28 7.49 -0.13

0.910 5.41 5.34 0.07 5.48 -0.07

0.907 3.64 3.55 0.09 3.68 -0.04

4.81 4.77 0.04

1.86 1.75 0.11

0.699 5.38 5.30 0.08 5.41 -0.03

0.707 4.15 4.05 0.10 4.24 -0.09

0.902 3.21 3.18 0.03 3.27 -0.06

0.905 2.37 2.25 0.12 2.35 +0.02

0.712 1.87 1.58 0.29 1.86 +0.01

* Fraction by mass of NaCl in salt mixtures.

t Difference between measured and predicted values.

I) Solutions prepared from coarse sea salt.

Thus,

crnix =

c

NaCl cMgSOzt

G

(28)

where Cmix s the DO concentration in the

salt mixture, C,,,, that in a pure NaCl so-

lution of concentration [NaCl], and C,,,,

that in a pure MgS04 solution of concen-

tration [MgSO,].

From the data of Fig. 2A, Setschenow

constants were determined for pure MgSO,

at 35.2Y (0.228, s = 0.004 kg mol-I,

n =

6) and 5.2% (0.279, s = 0.008 kg mol-l, n

= 6). They were used to estimate a value

for MgSO, at 0C (0.288 kg mol-I), assum-

ing K is a linear function of temperature.

We have found this assumption to be true

for NaCl at these temperatures

(see Table

5) as have other workers (Pawlikowski and

Prausnitz 1983, 1984). Values of the Set-

schenow constants at 0C and 35.2C were

used to predict CMgsoq or each of the

mixtures in Table 6. Values for C,,, were

determined with Eq. 25. Substituting them

into Eq. 28 allowed prediction of the CmiX

values given in Table 6. The differences be-

tween measured and predicted values are

generally smaller than those found with pre-

dicted DO values for NaCl solutions of the

same total salinity (i.e. based on Eq. 25).

This improvement is particularly noticeable

at higher salinities.

Schumpe et al. (1978) have determined

Setschenow constants at 25C for individual

ions. Their equation for predicting DO in

salt mixtures is

where Hi is the Setschenow constant for an

ion of type i, [Ml, the concentration (mol

liter-) of ions of type

i,

and zi the valency

of ions of type i. Since they list values of Hi

for all major ions in seawater, t was possible

to predict DO for seawater and Laguna Ta-

maulipas at 25C (Table 7). For the latter-

a coastal lagoon- we assumed a relative

ionic composition the same as seawater and,

since I& values are given in liters mol-l, a

density for lagoon water equal to a NaCl

solution of the same salinity. The salting out

effects of C0,2- and HCO,- were also ne-

glected. Although agreement between mea-

sured and predicted DO values is better than

that given by Eq. 25 for seawater and 957~

lagoon water, it is -0.15 mg liter- worse

at 150 and 22OY& Given the assumption

outlined above, the agreement should be

considered satisfactory but not superior to

results obtained from DO values in pure

NaCl solutions.

Pawlikowski and Prausnitz (1983, 1984)

have also given ion-specific Setschenow

constants at 25C although electrolyte con-

centrations are expressed as molality (mol

kg-). Unfortunately for limnologists, no

data are given for Mg2+ or C032-, greatly


14/16

248

Sherwood et al.

Table 7. Comparison of equilibrium DO concentrations measured in seawater and Laguna Tamaulipas,

Mexico (Copeland 1967) and predicted with Eq. 25 and 29.

--

----

--

W (mg iter-)

--

Temp. COOCll

(cl

(g Is-l)

25 ,zst

s5*

1508

220*

37 105*

l iO$

2> 0$

MWlSURd

Eq. 25 A*

6.60 6.79 -0.19

4.62 4.79 -0.17

3.50 3.40 +0.10

2.81 2.13 +0.68

3.85 3.90 -0.05

3.12 3.01 f0.11

2.50 2.96 +0.54

Predicted

----

Eq. 29

CL*

--

6.75 -0.1s

4.69 -0.01

3.27 40.23

1.98 to.83

* Difference between m c;lsured and predicted DO values.

f Seawater.

# Laguna Tamaulipas, h&&o.

limiting application of these results to nat-

ural

waters. They have, however, produced

equations to predict the variation of Set-

schenow constants with temperature over

the range 0-6OC. These equations are based

partly on theoretical considerations and have

the form

k = aIs + a2J + (hs + ~2S~Wk)gas

(30)

where

k,

is the ion-specific Setschenow con-

stant (kg mol-*),

T

is Kelvin, (e/k)gas s the

Lennard-Jones parameter for O2 (118 K),

and a s, a2s,&, b,, are ion-specific coeffi-

cients.

DO values were predicted for a 2007~ so-

lution at 0C (3.02 mg liter-), 25C (2.46

mg liter-), and 40C (2.19 mg liter-) using

Eq. 30 and th-e coefficients for NaCl. They

differ by -0.32, 0.01 and 0.01 mg liter-

respectively worn values predicted by Eq.

.25. Although coefficients for Eq. 30 are giv-

en for Na+, K+, and Cl-, they are insufficient

to allow its application to most natural wa-

ters. We are .currently working with lim-

nologically important salts to overcome this

deficiency.

One final Iboint should be made about

predicting DQ concentrations. Because of a

lack of consensus among researchers, values

for DO, salt concentrations, and Setsche-

now constants are reported in both volume-

based (e.g. ml; liter-) and mass-based con-

centrations units (e.g. mol kg-). Although

it may be de&able for all concentrations to

be given in temperature-independent units

based on mass (e.g. mg kg- or mol kg-),

the convenience of volumetric glassware in

laboratory procedures means that this goal

commonly is not achieved. Accordingly, to

get most access to published data, limnol-

ogists must have accurate density tables for

a particular water body. Ideally, equations

of state that give the variation of density

with salinity and temperature should be cal-

culated. Such equations are known, for ex-

ample, for seawater (Miller0 and Poisson

198 1) and Dead Sea brines (Krumgalz and

Miller0 1982). Changes in relative ionic

composition over time may complicate de-

termination of the equation of state for a

body of water.

Conclusion

The constancy of relative ionic compo-

sition of estuarine and marine waters has

made possible the preparation of precise

(a0.02 mg liter-) solubility tables for ox-

ygen (e.g. Weiss 1970). A general table of

comparable precision and simplicity for hy-

persaline lakes cannot be achieved at pres-

ent because of the great variability in their

ionic composition. This variability affects

the equilibrium concentration of oxygen.

Nevertheless, since most saline lakes are

dominated by NaCl, a table based on DO

solubility in pure NaCl solutions has some

utility. A table of this sort can be generated

with Eq. 25. The data given shpuld be gen-

erally reliable to within 0.2 mg liter- DO

for lakes dominated by NaCl (L70% by

mass).

It is possible, in theory, to predict DO

concentrations for salt mixtures such as hy-


15/16

Oxjrgen in hype73aline waters

persaline natural waters. In practice, re-

stricted data mean that this approach pres-

ently offers no advantages over the use of

DO concentrations estimated from model

NaCl solutions. Research to determine ion-

specific Setschenow constants over a range

of temperatures for ions of limnological sig-

nificance is needed to change this situation.

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of lentic surIa

d.o. in hyper saline water

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