WILLIAML. MARSHALL
346 possibilities must be examined carefully and compared with other factors that may have an influence on thermodynamic properties, particularly the effects of water structure breakdown, for a proper evaluation of the significance of the data. Such an evaluation is assisted by inspection of the temperature and concentration dependence of excess free energies, enthalpies, and entropies for both water and salt. A succeeding paper will deal with correlation of all available high-temperature osmotic coefficient data, calculation of activity coefficients and excess functions for salt as well as water, and some interpretations of the significance these
have for aqueous solutions at both high and low temperatures.
Acknowledgments. This work was performed under contract from the Office of Saline Water. We are indebted also to Mr. T. s. Bulischeck for assistance in construction of apparatus and conducting the experiments, and to many others a t Westinghouse Research Laboratories who contributed to various phases of the work. We also wish to acknowledge useful and informative discussions with Professors R. 34. Fuoss and H. S. Frank.
Complete Equilibrium Constants, Electrolyte Equilibria, and Reaction Rates1 by William L. Marshall Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 57890 (Received M a y 16, 1060)
Application of the complete equilibrium constant ( K O ) , which includes solvent as a reactant, has revealed recently several additional correlations of aqueous electrolyte behavior. Of particular importance, the conventionally derived standard state change in molar volumes (AV) between products and reactants (excluding solvent) is shown experimentally to be proportional merely to the compressibility of the solvent ; the significance of this relationship is discussed. All other conventional thermodynamic properties can be calculated as a function of both pressure and temperature from the variation of K O and IC (the assumed net change in waters of solvation) with temperature (only) and from the known pressure-volume-temperature behavior of the solvent. Analogous behavior for rate constants is considered, with the product being the activated complex. There appears to be no significant effect of viscosity on the complete constants within the precision of measurements. Several comparisons of the description of ionization behavior by means of K O , fugacity, and activity coefficients are presented. From these comparisons over wide ranges of pressure, temperature, and dioxane-water mixed solvent compositions, the overall utility of fugacity, with its defined relationship to chemical potential, is questioned in that the use of K O simplifies the description of electrolyte-solvent equilibria. A knowledge of fugacities (and/or activity coefficients) is unnecessary, and therefore the complete constant would appear to have much potential usefulness.
Complete Ionization Constants Isothermal ionization equilibria in aqueous fluids can be described by complete ionization constants (KO)
where KO and k (the assumed average net change in waters of solvation upon dissociation of solvated ion-pair species MA(H,O),) are found to vary only with temperature, K is a conventional constant (or quotient) that varies both with temperature and pressure, j , m, and n represent average waters of solvation, The Journal of Physical Chemistry
and all concentrations are expressed in moles per liter at a total pressure P.2-4 The conventional constant does not distinguish between contact ion pairs, ion pairs containing a discrete
(1) Research sponsored by the U. 9. Atomic Energy Commission under contract with the Union Carbide Corp. Presented before the Division of Physical Chemistry a t the 158th National Meeting of the American Chemical Society, New York, N. Y., Sept 7-12, 1969. (2) E. U. Franck, Z . Phys. Chem. (Frankfurt am Main), 8 , 107, 192 (1966). (3) W. L. Marshall and A. 8.Quist, Proc. Natl. Acad. Sci. U . S., 58, 901 (1967). (4) A. S. Quist and W. L. Marshall, J.Phys. Chem., 72, 1536 (1968).
EQUILIBRIUM CONSTANTS, ELECTROLYTE EQUILIBRIA, AND REACTION RATES number of water molecules between and those of any other degree of solvation. The parameter k , therefore, appears to be a statistical term representing the net change in solvation number, on ionization, from the average extent of solvation of the various ion pairs to a corresponding average for the ions. Calculated thermodynamic functions, like those ordinarily obtained from conventional coastants, must be considered on this basis. The conventional constant is obtained for the solute species in reference states at infinite dilution at the particular pressure on the system, and for H20 in a reference state of pure solvent at the same pressure. Under these conditions, the activity coefficients are always defined to be unity. Ordinarily at low temperature and atmospheric pressure, and at infinite dilution of electrolyte, the activity of water is taken also as unity (a constant) and is deleted from the equilibrium expression. I n the present approach, the activity of water is defined to be equivalent to its analytical molarity (CH~O).The standard states are therefore hypothetical 1M solutions for all reacting species (eq 1). With the above definitions, the standard states are functions both of temperature and pressure. We have found that virtually all ionization behavior in aqueous media adheres to this relationship not only at 25-800" at pressures to 4000 bars but also in dioxane-water solutions at 25-100' where dioxane is considered to be O simply the analytical an inert diluent and where C H ~is molarity of water in the mixed solvent4 (however, see Appendix). Although the standard free energies of reactants and products will indeed change with pressure, with the model (eq 1) and definitions used it would appear that the complete differences in these standard free energies (AGO) are invariant with pressure. By substituting 55.51d for [H20]in eq 1, where d is the density of water, taking the logarithm of the resulting equation, and differentiating with respect to pressure (P) a t constant temperature ( T ) , the following expressions are obtained In K = In
+ k In C H ~ O + k In 55.51 + k In d
=
KO
In
KO
(2)
(3) (4)
=
kp
(5)
where p is the compressibility of water. Thus, it is experimentally found that the isothermal change in the logarithm of a conventional ionization constant with pressure is merely proportional to the compressibility of the solvent, relating to the specific electrolyte equilibrium by the constant k. A stringent test of this relationship is shown in the lower section of Figure 1 where log K (molar ionization) for sodium iodide in an aqueous supercritical fluid is plotted against log CHZo at
, ,
ee 0 ,
347 log FUGACiTY ibors) 3 2
28
I
30
I
I
'
i
-5 13
44
15
34
I
'
36
T - 1
1
1
16
17
log CH 0 Lmole3/llterl
Figure 1. Contrast in the dependence of K(mo1ar ionization) for NaI on the fugacity and the molar concentration of water, 500-800".
several temperatures from 500 to 800" and at pressures from 1000 to 4000 barsax The linear relationships verify the adherence to eq 2-5 and reflect the dependence of the conventional constant K on the change in concentration of the substance water to maintain a truly constant KO. Figure 1 shows also that the slope k at high temperature becomes independent both of temperature and pressure for these particular 1-1 salt e q ~ i l i b r i a . 2 - ~ ~ ~ Fugacity and Concentration Comparative plots in the upper section of Figure 1 of the logarithm of the fugacity of water vs. the same values of log K(Na1) as in the lower section provide no linearity. With the use of fugacity, however, the standard state of water is taken to be invariant with pressure, and consequently pressure activity coefficients for solute species should be introduced to maintain pressure-independent standard states also for these species. These activity coefficients could be calculated in a manner to account for the nonlinearity in the plots of Figure 1, as discussed in the next section. By the definition of fugacity, its definedg relationship to chemical potentia1,'O and the defined direct proportionality of (5) (6) (7) (8) (9)
M. Eigen and K. Tamm, Z . Elektrochem., 66,93, 107 (1962).
G. Atkinson and S. Petrucci, J . Phus. Chem., 70, 3122 (1966). G. Atkinson and S. K. Kor, ibid., 71, 673 (1967). L. A. Dunn and W. L. Marshall, ibid., 73,723 (1969). G. N. Lewis, Proc. Am. Acad., 36, 145 (1900); 37, 49 (1901); 43, 259 (1907); 2. Phys. Chem. (Leipzig), 38, 205 (1901); 61, 129 (1907). (10) J. W. Gibbs, Trans. Conn. Acad. Sci. U. S., 3, 108, 343 (18761878).
Volume 74, Number 2 January 28,1970
WILLIAM L. MARSHALL
348 log FUGACITY (bars1
-4 0 I I
0
10
I
I
DIOXONEIwt
20
,
30
0
59
98
%I 50
96
70
7 1
I
+ f -20
-
