2986
The Journal of Physical Chemistry, Vol. 83, No. 23, 1979
Gupta
Thermodynamics of Electrolytes in Mixed Solvents. Application of Pitzer's Thermodynamic Equations to Activity Coefficients of 1:1 Electrolytes in Methanol-Water Mixtures A. R. Gupta Chemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay 400 085 (Received June 15, 1978; Revised Manuscript Received March 26, 1979)
Thermodynamic properties of 1:l electrolytes in mixed solvent systems have been investigated by using Pitzer's thermodynamic treatment of electrolyte solutions in aqueous medium. It has been shown that these equations are formally applicable to mixed solvents systems also. Using the same values for the b and a! parameters in the mixed solvents as in aqueous systems, we have evaluated the two parameters, PMX'O) and P&), governing the second virial coefficient P m Y for HC1, LiC1, NaC1, and KC1 in methanol-water mixtures. Very high negative values for f i ~ X ( ' ) and large positive values for PMX(O) have been obtained for alkali halides in these media. This behavior of fiMx(') and PMx(O) has been attributed to the role of the electrostatic interaction term in the second virial coefficients for electrolytes in these media. It has been shown that 2:2 electrolytes in an aqueous medium behave in a similar way. The variations of PMX(O) and PMX(l) with 1/D further suggest the presence of strong attractive forces in methanol-rich media, indicating ion association. Large negative values of @MX(') and ion association have been shown to be related.
Introduction Various modifications of the Debye-Huckel model proposed from time to time have met with varied success in predicting the thermodynamic properties of aqueous electrolyte ~olutions.l-~ Recently Pitzer4 has developed a system of equations for the thermodynamic properties of electrolyte solutions. These equations, though semiempirical in character, have been quite successful in predicting the properties of the electrolyte solutions at concentrations upto several molar. The important feature of these equations is that the second virial coefficients, which are independent of the ionic strength in Guggenheim$catchard5 equations, become a fynction of ionic strength. This arises because of the recognition of the dependence of short-range binary interactions on ionic strength. On the basis of these equations, Pitzer et aL6 have derived two parameters, PMX(O) and PMX'l), for each electrolyte MX in aqueous solutions. An analybis of these parameters for the various electrolytes in aqueous solutions showed that the principal contribution to P&l) comes from the short-range interactions of unlike charged ions while the short-range interactions of both unlike and like charged ions contribute to PMX(O).The radial distribution functions at hard core contact, namely, g+-(a),g++(a),and g-(a), thus contribute in weighted proportion to PMX(O) whereas only g+-(a) contributes to PMX(l).However, the problem which is not solved is the meaning, if any, of these adjustable parameters. Debye-Huckel, Guggenheim-Scatchand, and Pitzer's equations are all concerned with the interaction between ions in a dielectric medium. The specific property of the medium which explicitly occurs in the above equations is the dielectric constant and the specific interactions of the ions with the dielectric medium do not come into the picture, Therefore, these equations formally apply to any dielectric medium, Le., to any solvent including mixed solvents. The effect of changing the dielectric medium should be reflected in Pitzer's equations in A , (the Debye constant) and the two adjustable parameters, PMX(O) and Pm('). As A , is a constant for all electrolytes of the same valency type, the specific effects of changing the medium would be reflected in the two adjustable parameters. The 0022-365417912083-2986$0 1.OOlO
objective of the present investigation is to study the variations in these parameters for an electrolyte in different solvents in order to have a better understanding of these parameters and various interactions in such systems. In the present communication an attempt has been made to apply Pitzer's equations to the available data on the activity coefficients of 1:l electrolytes in methanol-water mixtures. The values for PMX'O) and PMX(l) for HC1, LiC1, NaC1, and KC1 in different methanol-water mixtures have been obtained and discussed in terms of the properties of the solvent mixtures.
Computation of PM#') and Phlx(l) in Methanol-Water Mixtures The relevant equations for single electrolyte activity coefficients derived by Pitzer4i6are
where uM and ux are the number of M and X ions in the formula, ZM and zx are their respective charges in electronic units, u = vM + ux, and m is the conventional molality. Other quantities are defined as follows:
(3) cMXy = Y2cMX'
(4)
where I , the ionic strength, 1/2CLmLz,2, A,, the DebyeHuckel coefficient for the osmotic function, 1/3 ( 2 a N o d l 1000)112(e2/DkT)3/2, d is the density of the solvent, D the dielectric constant, and all other symbols having their usual meaning. The values of parameter b = 1.2 and 01 = 2.0, found satisfactory for aqueous systems, were used for mixed solvent systems also. In aqueous systems, experi0 1979 American Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 23, 1979 2987
Thermodynamics of Electrolytes in Mixed Solvents
TABLE I : Properties of Water-Methanol Mixtures and Values of the Debye Constant ( A , ) soln no.
wt % MeOH
dielectric constant
1 2 3 4 5 6 7 8 9 10
0 10 20 30 40 50 60 70 80 90
78.3 74.18 69.99 65.55 60.94 56.28 51.67 47.11 42.6 37.91
density 1.000 0.98 24 0.9681 0.9536 0.9372 0.9185 0.8978 0.8751 0.8505 0.8239
thus obtained were usually in good agreement. However, some time it was noticed the values of PMX(O) and PMX(l) obtained were widely different. On further analysis it was found that all such values of PMX(O) and PMX(') originated from all the members of the set of simultaneous equations, containing a particular molality. As such these variations could be attributed to possible errors in the activity coefficient values for that molality. Neglecting such values for and PMX(l), we obtained the average values for these parameters taking into account the rest of the computed values. Table I11 gives the and PMX(l) values for the various electrolytes in different methanol-water mixtures.
A, 0.392 0.423 0.458 0.502 0.555 0.619 0.695 0.788 0.904 1.066
TABLE 11: Values of the Coefficients for A , and P M X ( ' ) in Eq 2 for Various Ionic Strengths ( b = 1.2; a = 2.0)
--
a
soln no.
ionic strength, m
1 2 3 4 5
0.02 0.05
Xa
0.10 0.20 0.50
Coefficient of A,.
b
Yb
__ -----___ 0.3822 0.9168 0.57 25 0.6929 0.7654 0.5974 1.0071 0.4863 1.6225 0.3281
Coefficient of p M X ( ' ) .
mental data for osmotic and activity coefficients to 6.0 M were fitted with these equations to determine the values for PMX(O), PMX(l), and CMX? However, experimental data for activity coefficients in mixed solvents rarely go beyond 0.5 m (or less) and the contribution of C M Xterm ~ a t low concentrations becomes negligible; as such this parameter has been set equal to zero for all systems in the present study. In order to apply these equations to mixed solvent systems, the density and dielectric constants of various mixed solvents are needed. The selected values for these quantities from the literature and the computed A , values for various systems are given in Table I. Akerlof s7 activity coefficient data for the various electrolytes in different methanol-water mixtures have been used. As the activity coefficient data for the various electrolytes in these mixed solvents is available only at three and four different molalities, no attempt was made to determine the two param. eters PMX'O) and /3MX(l) by least-square analysis; instead these parameters were computed for all possible combinations taking data a t two concentrations a t a time as described below. For 1:l electrolyte systems, with C M x set to zero, eq 1 reduces to In YMX = -A$ + m[2PMx(O)+ 2 P M X ( 0 ) y ] (5) where X and Yare constants, depending upon the ionic strength. The values for X and Y at various ionic strengths are given in Table 11. The set of equations for different values of m were then solved for the two unknown PMX(O) and P M X ( l ) , taking all possible combinations. The valyes
Discussion The most striking feature of these PMX'') and P M X ( ~ ) values is the negative Pm@) values for LiC1, NaC1, and KC1 in all the mixed solvents. These values become more negative as the methanol content increases. Even for HCl, PMX(l)values decrease as the methanol content increases and eventually, in solutions of high methanol content, they also become negative. PMX(O)values, on the other hand, are positive for all electrolytes in all solvent mixtures and increase with increasing methanol content in all cases. Numerically Prn(l) values are larger than Pm(0) in all cases except HC1. For LiCl, NaC1, and KC1, in all solvents, the ratio PMx(l)/PMx(o)ranges from -2.0 to -2.4. In this connection it is interesting to note that, on theoretical considerations, a ratio of 1.5 is expected for 1:l electrolytes in aqueous system^.^ The ~MX(l)/PMX(o)ratios observed in methanol-water systems are numerically close to this value values. but are of opposite sign because of negative In contrast to the behavior of PMX'O) and PMX(l) in mixed valsolvent systems, in aqueous systems PMX(O) and ues for these electrolytes (and most others) are positive, with PMX(l)larger than p,()'! Numerically large positive values for PMX(l)have been observed in electrolytes containing multiply charged ions. I t is rare that negative values for either PrnCo)or Pm(l) are encountered in aqueous systems. Thus, the most important feature which needs to be explained is the large negative value for P M X ( l ) for 1:l electrolytes in mixed solvent systems. Dependence of Pm(l) and Pm(0) on Dielectric Constant. The one property of the solvent medium which changes when methanol is added to water and also figures explicitly in the expressions for activity coefficients of electrolytes is the dielectric constant. In the discussion of hard core effects on osmotic and activity coefficients in terms of extended forms of the Debye-Huckel theory, Pitzer4 has pointed out that PMX(l) would be a function of K ~ ,As K~ involves the reciprocal of the dielectric constant, D, one could expect that PM#) would be a function of 1/D. The plots of P M X ( l ) vs. 1/D are shown in Figure 1. For HC1, one can see that all the points lie on a straight line. For other electrolytes there is a break in the linear plots and there are two distinct regions in NaCl and KC1 systems.
TABLE 111: Values of p(O) and p ( ' ) for HCI, LiCl, NaCl, and KCI in Various Methanol-Water Mixtures soln w t % no. MeOH p(O) -_-_____--___--__ 1 2 3 4 5 6 7 8 9 10
0 10 20 30 40 50 60 70 80 90
0.1775
HCl
LiCl p(') 0.2945
0.3838
0.1183
0.4423 0.5116 0.6046 0.7305
0.1358 0.0679 -0.0496 -0.2315
0.9989
-0.4937
NaCl
-
p(0)
p(')
0.1494 0.3714 0.5916 0.7498 0.9517 1.3177 1.9471 2.2644 3.4713 4.255
0.3074 -0.4051 -0.7584 - 1.1682 - 1.6839 -2.5794 -4.2539 -5.008 --8.201 -10.231
p(0)
0.0765 0.3905 0.6735 0.8949 1.2726 1.74 2.6388 2.971 4.563
KCI
- _ _ _
p(') 0.2664 - 0.3859 1.14 - 1.697 - 2.6543 - 3.844 -6.227 -6.978 11.217
pf") 0.04835 0.9497 1.8089 3.199 4.991 6.674 13.159 18.93 27.058 40.292
p(') 0.2122
- 1.6762 - 3.42 - 6.142 -9.713 12.744 -- 25.199 - 36.277 -51.848 - 77.13
2988
The Journal of Physical Chemistry, Vol. 83, No. 23, 1979
Gupta
31 4X
I I
001
c
OOP
003
t/D
1ID
8
(ID
Figure 1. for various electrolytes in methanol-water mixture as a function of dielectric constant.
Figure 2. PMx'O)for various electrolytes in methanol-water rnlxtures as a function of dielectric constant.
The break is not as distinct for LiC1. These breaks seem to indicate a more fundamental change in ion-solvent and ion-ion interactions. Up to 60-70% (w/w) methanol, there is a linear dependence with a comparatively small slope. There seems to be a linear dependence in the second region also, but this cannot be stated definitely as there are only two or three points in this region. All the same, an approximate value for the slope in that region has also been derived. The dependence of P M X ( I ) on 1/D in the first region (Le., before the break) can be described by the following equations: for no break P H c ~ (= ~ ) 1.03 - (57.5/D)
Radial Distribution Functions in Low Dielectric Constant Media. In a Monte Carlo study of the primitive model of electrolytes, Card and Valleau' have derived the radial distribution functions in aqueous systems. It was also noted in that study that the same functions computed on the basis of an exponential form of the Debye-Huckel theory were in good agreement with those derived from Monte Carlo calculations, up to -0.4 M concentration. The same exponential form of the Debye-Huckel equations have been used here for computing radial distribution functions at different dielectric constants. The relevant equations are
slope after the break
- 1000
P L ~ C ~=' ~ 8.493 ) -
slope after the break
-
slope after the break
- 31.96 7000
(637.5/D)
1750 &qa~l(l) = 10.8 - (840/0)
P K c I ' ~ )=
-
where
(2500/D)
There is no explicit dependence of PMX(O) on dielectric constant in Pitzer's thermodynamic treatment of electrolyte solutions. However, PMx(O) does have contributions from g+-(a),g++(a),and g-(a), which are functions of dielectric constant. The dependence of P(O, ) on the dielectric constant is shown in Figure 2. The behavior of ,f3MX('J vs. 1 / D plots is very similar to that for fm(l).plots, except that PMX(O) values increase with decreasing dielectric constant. The HC1 plot does not show any break; LiC1, NaC1, and KC1 plots show distinct breaks, approximately at the same dielectric constant values as PMX(l) plots for these electrolytes. Before the break, there is a linear dependence of PMx(O) on 1 / D in all cases. As the parameters &x(o) depend upon the values of the radial distribution functions (g+..(a) or g++(a)) the variations in g+-(a) or g++(a) with dielectric constant become important.
for 1:l electrolytes at molality m. Then the radial distribution functions g+- and g++ (= g--) are given by r 1a g++ = g-- = exp(-F(r)) r 1a r
