Effect of Pressure on Aqueous Equilibria - American Chemical Society

Chapter 7

Effect of Pressure on Aqueous Equilibria 1

2

Pradeep K. Aggarwal , William D. Gunter , and Yousif K. Kharaka

3

1

2

Battelle Memorial Institute, 505 King Avenue, Columbus, OH 43201 Oil Sands and Hydrocarbon Recovery, Alberta Research Council, P.O. Box 8330, Postal Station F, Edmonton, Alberta T6H 5X2, Canada Water Resources Division, U.S. Geological Survey, Mail Stop 427, 345 Middlefield Road, Menlo Park, CA 94025

Downloaded by UNIV LAVAL on September 30, 2015 | http://pubs.acs.org Publication Date: December 7, 1990 | doi: 10.1021/bk-1990-0416.ch007

3

A model based on the density of the solvent together with the "iso-Coulombic" form of reactions has been used to estimate the pressure dependence of ionization constants of aqueous complexes. This model reproduces experimentally determined pressure dependencies of several ionization constants of aqueous complexes. Calculated saturation states of calcite in seawater are ~500 cal (100°C, 0.5 kbar) and ~700 cal (100°C, 1.0 kbar) greater, and the temperatures of calcite saturation are ~80°C (0.5 kbar) and ~40°C (1.0 kbar) higher, than the values obtained when the effect of pressure on ionization constants is neglected. The equilibrium between aqueous solutions and minerals changes significantly with changes in pressure (1,2). To fully characterize the pressure dependence of such equilibria, we need to estimate the effect of pressure on the saturation state ( A G ^ ) of minerals: AG

d i f f

= RT In (Q/K)

(1)

where Κ and Q are, respectively, the solubility constant and activity quotient of the mineral; R is the gas constant; and Τ is temperature in kelvin. For example, the solubility reaction and Q for calcite are: ++

CaC0 (solid) = Ca + CO" " 3

In Q = In 2

(2)

3

+

In a ^ - - In a

^

(3)

where ai is the thermodynamic activity of the subscripted species; the activity of calcite is equal to one for a pure phase in its standard state. Equations 1 and 3 imply that estimates of the effect of pressure on the saturation state should evaluate the pressure dependencies of both the solubility constants and the thermodynamic activities of single ions. Thermodynamic activities of ionic species in aqueous solutions with ionic strength (I) < 0.01 molal (m) commonly are calculated using the ion-pair model (3), which is valid also for solutions with I < 0.1 m. In dominantly NaCl solutions, the ion-pair model can be used for I < 3 m with appropriate adjustments to the activity coefficients (4). The specific ion interaction model (5) may be more appropriate for solutions of high ionic strengths. The effect of pressure on the thermodynamic activities of single ions in this model can be estimated from the stoichiometric partial molal volume and compressibility data Q). However, a complete data set for all the ioninteraction parameters is not yet available for this model to be used in complex geochemical solutions. 0097-6156/90/0416-0087$06.00/0 c 1990 American Chemical Society

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

88

CHEMICAL MODELING OF AQUEOUS SYSTEMS II

Ion-ion interactions in the ion-pair model are treated by considering the formation of ion-pairs (or aqueous complexes). The effect of pressure on ion-pair formation is considered negligible for most geochemical calculations (6). This approach can lead to an erroneous estimate of the effect of pressure on the saturation states of minerals. A simple relationship based on the density of the solvent (7) which can be used to characterize completely the effects of pressure on aqueous solution - mineral equilibria is presented here. ESTIMATION OF PRESSURE EFFECTS Effect of Pressure on Solubility Constants


The pressure dependence of the equilibrium or solubility constant (K) for the congruent dissolution of a mineral, as in reaction 2 above, is given by: , (

d In Κ

v

y

dP

-AV°

N

) T

=

(4) RT

AV° is the molal volume change of the reaction in the standard state: ΔΥ° = Σ V? - Σ V°

(5)

where the subscripts refer to the products (P) or the reactants (R). The standard state for mineral species is the pure phase of unit activity at the temperature and pressure of interest. Standard state for the ionic species is the hypothetical ideal solution of unit molality referenced to infinite dilution. Standard molal volumes of minerals together with the coefficients of isobaric expansion and isothermal compressibility are available in several compilations (8,9). Standard partial molal volumes of uncomplexed ions are available at 25°C and 1 atm. Q); however, data are sparse for the coefficients of isobaric expansion and isothermal compressibility. Partial molal volumes of aqueous ionic species vary considerably with changes in pressure and temperature. The molar volume of an aqueous species can be split into a Coulombic and a nonCoulombic term. The non-Coulombic term consists of the intrinsic volume of the ion. The Coulombic term consists of the volume of solvation and the volume of collapse. The volume of solvation is related to the orientation of water dipoles around the aqueous species, and the volume of collapse is the component of the partial molal volume related to the collapse of the water structure in the vicinity of the aqueous species. The pressure and temperature dependence of the molar volume of aqueous species arises from a similar change in the electrostatic properties of the solvent Helgeson and co-workers (10,11) have proposed an equation of state based on the electrostatic properties of the solvent that can be used to estimate standard partial molal volumes of uncomplexed ions at elevated temperatures and pressures. Effect of Pressure on Ionization Constants To calculate the effect of pressure on the formation or ionization constants of aqueous complexes, the partial molal volume change of the ionization reaction must be known. Standard partial molal volumes (25°C, 1 bar) of some aqueous complexes are known, and can be used together with the molar volumes of uncomplexed ions to calculate AV. The Fuoss equation can also be used to estimate the standard molal volume change in ionization reactions (20,21): 3

b

K = 4Fla e N / 3000

(6)

b = Iz Ζ le / a£KT + - ο

(7)

f

where Kf = molar formation constant of an aqueous complex; Ν = Avogadro's number; κ = Boltzmann constant; a = distance of closest approach of ions; ε = dielectric constant; e = permittivity of the vacuum; e = electron charge; and Ζ = charge on the cation or anion in the ion pair. For a neutral complex, Equations 4, 6 and 7 result in:


7.

AGGARWALETAL.


ΔΥ =

89

Effect ofPressure on Aqueous Equilibria

b ( —=r~ ) - β

RT

(8)

β is the compressibility of the solvent and is used to convert Equation (6) from the molar to molal scale. To calculate the value of AV from Equation (8), b is first calculated from Equations (6) and (7) using the known formation constant of an aqueous complex. Estimates of volume change calculated from Equations 6-8 are in reasonably good agreement with measured values when the complexing dominantly is of outer-sphere type, e.g. MgSO?. However, large uncertainties result between estimated and measured values when a significant proportion of the ion-pairs are of innersphere type, e.g. CaSO? (22). The molar volume change in ionization reactions at higher temperatures and pressures cannot be calculated for most of the aqueous complexes because of a lack of data on isobaric expansion and isothermal compressibility coefficients. Entropy and heat capacity correlations have recently been used to generate equation of state parameters for estimating molal volumes of aqueous complexes at elevated temperatures and pressures (Sverjensky, 12). These coefficients are available for aqueous complexes only of univalent anions and, therefore, the pressure dependence of ionization constants at elevated temperatures cannot be estimated using Equation 4. Marshall and Mesmer (7) have used a relationship based upon the density of the solvent for calculating the pressure dependence of ionization constants: In K

P T

A V

In K° -

° RT β°

In - E E p°

(9)

where Ρ is the applied pressure and the superscript (°) indicates temperature Τ and the saturation vapor pressure of water; ρ and β are, respectively, the density and coefficient of isothermal compressibility of water; and AV is the molar volume change in the reaction. Equation 9 also cannot be used to estimate the pressure dependence of ionization constants when the term (AV°/RTB°) shows a temperature dependence (Fig. 1). The following technique can be used to alleviate this problem. The heat capacity change of "iso-Coulombic" reactions (reactions which are symmetrical with respect to the number of ions of each charge type) is nearly independent of temperature (13,14). Similarly, the molar volume change of "iso-Coulombic" reactions will be expected to display a relatively minor temperature dependence because most of the temperature-dependent changes in the Coulombic and non-Coulombic contributions to the volumes of individual ions will cancel out in the AV term. Thus, the 25°C value of AV can be used in Equation 9 if the reaction is "isoCoulombic", or is made so by the addition or subtraction of an appropriate number of water dissociation reactions. For example, the dissociation reaction of the aqueous complex H CO? can be written in the "iso-Coulombic" form (Reaction 12) by combining Reactions 10 and 11: 2

H CO? = HCO" + H 2

+

(10)

3

H0 = H 2

+

+ OH"

(11)

H CO? + OH" = HCO" + H 0 2

3

(12)

2

The isothermal pressure dependence of the equilibrium constant for (12) is given by:

ο 1ηΚρ,3 = 1ηΚ?

3

N

-

PP.T

" RT β°

I n — p°

(13)

where η = AV (25°C,lbar) - AV (25°C,lbar). Using available values of In Kp,„ the pressure dependence of the ionization constant of reaction 10 can be obtained: 10

In K

Pil0

u

= In K

P100°C). However, the calculated values below 200°C are generally within the error of measurement. Above 200°C, the deviations are higher than the experimental error. These deviations occur probably because the temperature dependence of AV is not completely eliminated by using the iso-Coulombic form of the reaction. Estimates of pressure dependence of the ionization constant of PbCl based on Equation 9 are compared in Table 1 with those obtained by using Equation 4 (12). Both approaches result in similar values for pressures up to 1000 bars. At higher pressures, estimated pressure dependence based on Equation 9 is lower, especially at higher temperatures. As mentioned earlier, disagreement at higher temperatures may be due to the temperature dependence of the reaction volume. In addition, the error of estimation in the data of Sverjensky (12) is unknown. 2

3

3

3

4


4

3

4

+

+

Table 1. Pressure dependence of the ionization constants of PbCl calculated using Equation 9 (from the data in Sverjensky, 12) log K - log K° 1000 bars P

Temp(°C)

500 bars

25 75 175

0.01 (0.00) 0.03 (0.01) 0.17 (0.12)

0.01 (0.00) 0.06 (0.01) 0.29 (0.22)

1500 bars 0.03 (0.03) 0.11 (0.01) 0.50 (0.23)

APPLICATIONS IN GEOCHEMISTRY The equilibrium or solubility constants for mineral dissolution reactions increase with increasing pressure, resulting in an increase in the solubility of the minerals (Fig. 6). The ionization constants for the aqueous complexes also increase with increasing pressure (Figs. 2-5), which results in an increase in the activity of the uncomplexed ions. Owing to the increased activity of the uncomplexed ions, the magnitude of the pressure correction for the saturation state of minerals is lower when the pressure effects on the ionization of aqueous complexes are taken into account as compared with no correction for changes in the ionization constants. These are general trends and the saturation state of individual minerals may change differently with increasing pressure, depending upon temperature and solution composition. To illustrate the effect of pressure on aqueous equilibria, the speciation and saturation states of minerals at higher pressures were calculated for a modified seawater and an oil-field brine from the Texas Gulf Coast (Table 2). The calculations were performed using the computer program SOLMINEQ.88 (16). SOLMINEQ.88 computes the distribution of species and saturation states of minerals using chemical composition, pH, and Eh at 25 °C. A description of the methodology for computing a high temperature pH is given in (17).




92

Figure 2. The effect of pressure on the ionization constants of the reaction H C 0 = H C 0 ~ + H . The experimental data were taken from ref. 27. The calculations were performed using the "iso-Coulombic" form of Equation 9. 2

+


3

3


7.

AGGARWAL ET AL.

93

Effect of Pressure on Aqueous Equilibria

0.6

500

1000

750

Pressure (bars) Figure 3. The effect of pressure on the ionization constants of the reactions H B 0 = H B 0 ~ + H £30) and H C 0 ~ = C 0 ~ ~ + H (31). The numbers in parentheses are for the references from which the experimental data were taken. The calculations were performed using the "iso-Coulombic" form of Equation 9. 3

+

+

3

3


3

2

3



94

Figure 4. The effect of pressure on the ionization constants of the reaction N H O H = N H + + O H ~ . The experimental data were taken from ref. 26. The calculations were performed using the "iso-Coulombic" form of Equation 9. 4


4

7. A G G A R W A L E T A L .

1 .

ι


95


ι

> '

1 '

H3PO4 Experimental Calculated

2000 bars

1000 bars Ρ = 500bars

0.0

50.0

_L 100.0

150.0

200.0

250.0

300.0

Temperature ( ° C ) Figure 5. The effect of pressure on the ionization constants of the reaction H P 0 = H P 0 ~ + H . The experimental data were taken from ref. 28. The calculations were performed using the "iso-Coulombic" form of Equation 9. 3

4

+


2

4


96


ι

I

ι

I

I

1

0 Anorthite, 1 kbar Δ Calcite, 1kbar

—

•

0

—

Calcite, 0.5kbar

/

6

-

4

2 Δ—-Δ-—~~^ ^^*^ '^ r

? 50

y

?

ι

150

250

ι

I 350

Temperature ( ° C )

Figure 6. Effect of pressure on the solubility constants of anorthite and calcite at higher temperatures based on data from (8).


7. AGGARWALETAL.


97

Table 2. Compositions of modified seawater and Texas Gulf Coast water used for illustrating the effect of pressure on aqueous equilibria (all concentrations are in mg/L, except pH) Component Ca Mg Na Κ Cl

so

4

Si0 Ba Fe Li Pb Sr F Β P0 Al* HS Total Inorg. Carbon pH(25 °C) Temp (°C) Pressure(bar)


2

4

2

seawater

Gulf Coast water (Pleasant Bayou #2) 9100 660 38000 840 80600 5.4 120 760 62 39 1.1 1020 1.4

422 1322 11019 408 19806 2775 4.28 0.02 0.002 0.19 8.33 1.42 4.45 0.06 0.001 10.23 24.85 8.2 25.0 1.0

0.001 0.5 216.9 4.91 150.0 800.0

* assumed for modeling purposes. Table 3. Standard molal volume change of ionization reactions of aqueous complexes used in SOLMINEQ.88 Complex

AV°

Complex

AV°

HC03 Al(OH)++ CH3COOH Ba(OH)+ CaHC03 + Cu(OH)+ Fe(OH)2 Fe(OH)++ Fe(OH)4HP04 KC03 Mg(OH) + MnSCH NaHC03 NH40H SrHC03 +

-28.7 -22.4 -11.2 -19.7 -31.6 -19.7 -5.7 -22.4 -85.7 -36.0 -19.8 -19.7 -7.1 -13.8 -28.8 -31.5

H4Si04 Al(OH)2+ BaC03 BaS04 Ca(OH)+ CuS04 FeS04 Fe(OH)2+ B(OH)4 H2P04 MgC03 MgS04 NaCl Na2S04 Sr(OH) + SrS04

-37.9 -43.2 -7.5 -7.1 -19.7 -7.1 -7.1 -43.5 -35.5 -25.9 -9.8 -7.4 -13.7 -7.1 -19.7 -7.1

AV°

Complex H2S Al(OH)4BaHC03 + CaC03 CaS04 Fe(OH) + FeCl ++ Fe(OH)3 H2C03 HS04 MgHC03 + MnHC03 + NaC03 NaS04 SrC03 ZnS04

-13.0 -64.3 -34.3 -10.6 -25.0 -19.7 -4.6 -64.6 -27.2 -14.8 -31.5 -34.0 -23.1 -15.8 -9.1 -7.6

The pressure dependence of mineral dissolution reactions in SOLMINEQ.88 is calculated using data from (8,11,18). The ionization constants at higher pressures for aqueous complexes are calculated using the "iso-Coulombic" form of Equation 9. The coefficient of isothermal compressibility and density of water are obtained from the data in (19). Molal volume change in the ionization reaction of aqueous complexes (Table 3) are obtained from experimental studies, when available, or are estimated based on Equations 6 to 8.


98


The effect of pressure on calculated pH, activities of several aqueous species, and saturation states of selected minerals for the seawater are listed in Table 4. The calculated pH at higher temperatures and 500 bars pressure is -0.1 unit lower than that calculated for pressures along the vapor saturation curve; at 1000 bars pressure, the pH is lower by -0.2 units (Table 4). At 500 bars pressure, the predicted saturation states of calcite are greater by -200 cal (ASI=0.15) at 25°C, and 1800 cal (AS 1=0.75) at 250°C, compared to those calculated without considering the effect of pressure on the ionization constants (Figure 7). Similar, but numerically larger, differences are seen for the saturation state of anhydrite.


Table 4. Calculated activities of ions and saturation states of minerals in modified seawater at higher pressures. "Sat." is the pressure of steam saturation; other pressures are in bars A. activities - log activity

+

H Ca Mg" Na CI SO, ca ++

+

3

Τ = 100 °C sat. 500 1000

Τ = 250 °C sat. 500 1000

7.10 2.74 2.00 0.54 0.50 2.73 6.22

6.02 3.24 2.38 0.70 0.68 3.23 9.53

6.99 2.70 1.97 0.53 0.49 2.66 6.04

6.90 2.67 1.95 0.51 0.48 2.59 5.88

5.74 2.95 2.18 0.61 0.59 2.82 8.54

5.87 3.06 2.27 0.65 0.63 2.97 8.95

B. saturation states AG*,, (cal) Mineral

a

b

c

Τ = 100 °C, Ρ = 500 bars Calcite 689 Anhydrite -192 Albite -7234

-165 -886 -8252

243 -699 -8556

Τ = 100 °C, Ρ = 1000 bars Calcite 689 Anhydrite -192 Albite -7234

-881 -1449 -9172

-160 -1107 -9754

Τ = 250 °C, Ρ = 500 bars Calcite 766 Anhydrite 4775 Albite -21967

-2700 3023 -23754

-900 4082 -24361

Τ = 250 °C, Ρ = 1000 bars Calcite -766 Anhydrite 4775 Albite -21967

-3059 1828 -25095

-1028 3502 -26200

pressure effects on

a: none; b: solubility constants; ç: ionization and solubility constants.



7. AGGARWALETAL.

Effect of Pressure on Aqueous Equilibria

99

Temperature (°C) Figure 7. The effect of pressure on the saturation state of calcite in modified seawater. The composition of seawater used in the calculations is given in Table 2.

The pressure dependence of the saturation state of albite is different than that of calcite or anhydrite. The magnitude of pressure correction for the saturation state of albite increases when the pressure correction for the ionization constants is taken into account, in contrast with a decrease observed in the case of calcite and anhydrite (Table 4). The calculated solubility of albite is a function of pH and the activities of aqueous N a \ A l , and Si0 (aq). The activities of N a \ A\ and Si0 remain nearly unchanged because (1) Na and A l complex mainly with CI and/or O H . The fraction of these complexes does not change measurably with a change in pressure; and (2) the effect of pressure on the ionization of silica species is relatively minor. Therefore, the change in the saturation state of albite upon considering the pressure dependence of ionization constants is due mainly to a change in pH. In the case of calcite and anhydrite, the effect of change in pH is countered by a corresponding change in the distribution of carbonate or sulfate species. This change in the distribution of species is responsible for the observed differences in the pressure dependence of the saturation states of albite, calcite, and anhydrite. An additional argument for considering the effect of pressure on ionization equilibria is presented in Figure 8. This figure plots calculated temperature and pressure conditions at which the modified seawater becomes saturated with calcite or anhydrite. At a constant pressure, the predicted temperature of mineral saturation is significantly different (higher for calcite and lower for anhydrite) when the effect of pressure on ionization equilibria are taken into account. This observation has important consequences for calculated geochemical models of water-rock interactions and ore deposition (23,24). The effects of pressure on the speciation and saturation states of minerals in the Texas Gulf Coast water are similar to those described above for the seawater. +++

+++

2

+

+++

2


±


100


I

I

I

0

50

100

L_

150

Temperature ( ° C ) Figure 8. A plot of the pressure-temperature conditions at which calcite and anhydrite are calculated to be in equilibrium with seawater.

CONCLUDING REMARKS The technique presented in this paper to estimate the pressure dependence of ionization constants is simple to use and requires minimal data. Excellent agreement is observed between the calculated and measured values of ionization constants of several aqueous complexes at higher pressures, at least up to 200°C. The discussion presented above shows that the effect of pressure on ionization constants must be considered in geochemical calculations of mineral-solution equilibria at low and high temperatures. ACKNOWLEDGMENTS The authors thank G.W. Bird, J. Hovey, F J . Millero, E.H. Perkins, and P.R. Tremaine for meaningful discussions, and J. Hovey, M. McKibben, D. Melchior, and J.D. DeBraal for reviews. Financial support for this work was provided in part by the Alberta Research Council. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Millero, F.J. Geochim. Cosmochim. Acta, 1982, 46, 11-22. Hemley, J.J., Cygan, G.L., d'Angelo, W.M. Geology, 1986, 14, 377-379. Garrels, R.M., Thompson, M.E. Am. J. Sci. 1962, 260, 57-66. Helgeson, H.C. Am. J. Sci. 1969, 267, 729-804. Pitzer, K.S. J. Phys. Chem., 1973, 77, 268-277. Seward, T.M. In Chemistry and Geochemistry of Solutions at High Temperatures and Pressures; Rickard, D. Wickman, F. Eds., Pergamom:New York, 165-181. Marshall, W.L., Mesmer, R.E. J. Soln. Chem., 1981, 10, 121-127. Helgeson, H.C., Delany, J., Nesbitt, H.W., Bird, D. Am. J. Sci. 1978, 278A, 1-229. Robie, R.A., Hemingway, B.S., Fisher, J.R. Bulletin U.S. Geological Survey, 1979, 1452, 1456. Helgeson, H.C., Kirkham, D. Am. J. Sci. 1974, 274, 1199-1261. Tanger, J., Helgeson, H.C. Am. J. Sci., 1988, 288, 19-98.


7. AGGARWALETAL.


101

12.

Sverjensky, D.A. In Thermodynamic Modeling of Geological Materials: Minerals, Fluids and Melts; Carmichael, I.S.E., Eugster, H.P., Eds., Mineralogical Society of America: Washington D.C., 1987, Vol. 17, pp 177-210. 13. Lindsay, W.T. Proc. 41st Intl. Water Conf.; Engineering Society of Western Pennsylvania, 1980, 284-294. 14. Murray, R.C., Cobble J.W. Proc. 41st Intl. Water Conf.; Engineering Society of Western Pennsylvania, 1980, 295-310. 15. Eugster, H.P. and Baumgartner, L., In Thermodynamic Modeling of Geological Materials: Minerals, Fluids and Metls; Carmichael, I.S.E., Eugster, H.P., Eds., Mineralogical Society of America: Washington D.C., 1987, Vol. 17, pp 367-404. 16. Kharaka, Y.K., Gunter, W.D., Aggarwal, P.K., Perkins, E.H., and DeBraal, J.D., SOLMINEQ.88: A computer program for geochemical modeling of water-rock interactions; U.S. Geological Survey, Water Resources Investigations Report, under review.


17.

Aggarwal, P.K., Hull, R.W., Gunter, W.D., Kharaka, Y.K. In Proc. Third Canadian/American Conference on Hydrogeology; Hitchon, B., Bachu, S. Sauveplane C.M., Eds., National Water Well Association: Dublin, Ohio, 1986, pp 196-203. 18. Helgeson, H.C. and Kirkham, D., Flowers, G. Am. J. Sci. 1981, 281, 1249-1516. 1974 19. Haar, L., Gallagher, J.S., Kell, G.S. NBS/NRC Steam Tables; Hemisphere: Washington, D.C., 1984; p318 20. Hemmes, P., J. Phys. Chem., 1972, 76, 895-900. 21. Fuoss, R. J. Am. Chem. Soc. 1958, 80, 5059-64. 22. Millero, F.J., Gombar, F., Oster, J., J. Soln. Chem., 1977, 6, 269-280. 23. Wolery, T.J., Calculation of Chemical Equilibrium Between Aqueous Solution and Minerals: the EQ3/6 Software Package, Lawrence Livermore Laboratory, 1979, Report UCRL-52658, p41. 24. Reed, M., Geochim. Cosmochim. Acta, 1982, 46, 513-528. 25. Marshall, W.L., Franck, E.V. J. Phys. Chem. Ref. Data, 1981, 10, 295-304. 26. Lown, D.A., Thirsk, M.R., Wynn-Jones, L. Trans. Farad. Soc. 1970, 66, 51-73. 27. Read, A.J. J. Soln. Chem., 1982, 11, 649-664. 28. Read, A.J. J. Soln. Chem., 1975, 4, 53-70. 29. Read, A.J. J. Soln. Chem.. 1988, 17, 213-224. 30. Kreamer, T.F., Kharaka, Y.K. Geochim. Cosmochim. Acta, 1986, 50, 1233-1238. 31. Ward, G.K., Millero, F.J. J. Soln. Chem., 1974, 3, 417-430. 32. Disteche, Α., Disteche, S. J. Electrochem. Soc., 1968, 114, 330. RECEIVED October 6, 1989


Effect of Pressure on Aqueous Equilibria - American Chemical Society

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