COMMUNICATIONS TO THE EDITOR
4022 TdH/dT correction factors,2 be fitted into the previously determined dielectric constant dependent functions,l should these changes also originate in conformational equilibration. However, the “best fit” value of the temperature dependent functions as evaluated by a least-squares method cannot be fitted to the dielectric-dependent functions because of the opposite signs of the curve directions discussed above. This method, therefore, affords a new criterion for the validity of free energy values determined by computer fittings to temperature-dependent functions, since the corresponding curve directions for all spectral functions in the temperature dependent vs. dielectric constant dependent functions must be related, pairwise, in sign if the spectral changes are due primarily to changes in the conforma,tional free energy. It has not been widely appreciated, though it is very well established, that temperature dependence in spectral changes of the magnitude described above can be exclusively ascribed to vibrational eff ects.‘jJ Since
the curves in Figures 1 and 2 cannot be accounted for in terms of an equilibrium constant compatible with the corresponding dielectric functions, it is probable that the effect of temperature on the population of methylene group torsional vibration levels makes the major contribution to the spectral changes observed here. The implications regarding conformational stability in ethylene sulfite would thus be consistent with the closely related observations that each of the separable geometrical isomers of a simple 4-substituted methyl analog of ethylene sulfite shows no chromatographically detectable inversion over long periods of time, and that the methyl and methylene resonance lines of the gemdimethyl analog, which are excellent probes of time averaging, indicate no conformational mobility.s (6) L. Petrakis and C. H. Sederholm, J . Chem. Phys., 35,1174 (1961). (7) K.C. Ramey and W. S.Brey, Jr., ibid., 40,2349 (1964). (8) J. G. Pritchard and P. C. Lauterbur, J . Amer. Chem. SOC.,83, 2105 (1961).
C O M M U N I C A T I O N S T O THE E D I T O R C o m m e n t s on the Paper “Activity Coefficients for Ionic Me1ts”l
Sir: Haase2 has proposed that an ideal ionic melt be defined as one in which the chemical potential of any ion j is taken as P$ = PO^
+ R T In
xj
(1)
where is the chemical potential of the pure liquid ion and xj is the ion fraction defined as the number of ions of j divided by the total number of species in the melt. For an ideal melt all of these species would be fully ionized. The proposal was made without reference to any statistical model, but in fact it corresponds to one for which in an ideal melt all ions mix randomly with each other regardless of charge. This can be shown from Haase’s eq 4, here slightly rearranged as Xu -2.0
Vl(1 Vl(1 - X)
2)
+
v22
(2)
I n a mixture of salts A and B of stoichiometric mole fractions (1 - x) and x, a is an ion found only in A. vl and v2 are the numbers of particles produced by the complete ionization of 1 formula weight of A and B; if A is Ce2(SO,),, VI is 5 N . The denominator thus conThe Journal of Physical Chemistry
tains all the particles in the melt. 22,the fraction of a in pure A, would be va/vll vu being the number of a ions in 1 formula weight of A. (22is used to normalize xu which would otherwise not equal 1 at II: = 0.) Ion fractions as in (2) will be referred to as the “total ion fraction” in this paper. The ion fractions for the other ions are defined in a similar fashion. Haase then derives expressions for the ideal activities of the component salts which are the products of the total ion fractions of the constituent ions. Basing the ion activities on the total ion fractions seems t o have been proposed first by Herasymenko and Speight in 1950,3 and then again by Bradley in 1962.4 While such a treatment is quite reasonable for a mixture of uncharged species it does not take into account the very strong Coulombic forces that tend to alternate ions of opposite charge. The Coulombic ordering has been observed experimentallys and predicted from a general theoretical modeL8 In 1945, long before this (1) Research sponsored by the U. S. Atomic Energy Commission under contract with Union Carbide Corporation. (2) R. Haase, J . Phys. Chem., 73, 1160 (1969). (3) P. Herasymenko and G. E. Speight, J.Iron Steel Inst. (London), 166, 169 (1950).
(4) R. 5. Bradley, Amer. J. Sci., 260, 374 (1962). (5) See, for example, M. Blander, Ed., “Molten Salt Chemistry,” Interscience Publishers, New York, N. Y.,1964, Chapter 2. (6) Reference 6, Chapter 3.
COMMUNICATIONS TO THE EDITOR
4023
evidence was available, Temkin’ proposed that in an ideal salt mixture the anions and cations should mix freely with themselves but not with each other; thus for a salt A,Y, the activity should be (3)
where ni is the number of particles i. This treatment is based on the assumption of charge alternation but does not require the use of any specific liquid model. A discussion of the Temkin and Herasymenko approaches may be found in ref 8. Although component activity coefficients are often given as (4) expressions for these activity coefficients may be derived from the Temkin equations. Haase refers to the system (AgN03, KzS04) which we abbreviate as (AY, B2Z). The Temkin ion fractions are
x*
=
1-x 1 x’
-*
+
xy = 1 -
XB =
2;
22 l + x
-
(5)
of independent mixing, based on charge alternation, is widely maintained. This principle is not compatible with Haase’s formulation of the ideal solution. It seems to me that the main reason for talking about ideal solutions a t all is to provide some insight into what is really happening, and that therefore one should avoid using a definition of an ideal solution which is in contradiction to what is thought to be physical reality. Acknowledgment. I wish to thank Drs. J. Braunstein and G. D. Robbins for helpful discussions of this subject . (7) M. Temkin, Acta Physicochem. URSS, 20, 411 (1945). (8) P.Gray and T. F$rland, Discussions Faraday SOC.,32,163 (1961). (9) W. J. Watt and M. Blander, J . Phys. Chem., 64, 729 (1960).
REACTOR CHEMISTRY DIVISION OAKRIDGENATIONAL LABORATORY OAKRIDQE,TENNESSEE37830
DAVIDM. MOULTON
RECEIVED JUNE 9, 1969
Reply to the Comments on the Paper “Activity Coefficients for Ionic Melts”
xz = x
so that the ideal activities are
Haase’s expressions are 2(1 - 2) aAY =
[
+
1’;
a OBiZ
=
(7)
In fact, the values predicted by these two sets of expressions are quite close. For example, a t x = 0.5 aAY
=
aAy =
0.167; aBzz = 0.222 (Temkin) 0.160; aB,z = 0.216 (total ion fraction)
so that either would fit the data as well despite the very different assumptions used in their derivation. However, it should also be noted that Watt and Blanderg have shown that when small amounts of K2S04are added to dilute solutions of AgN03 in KN03 the activity of AgNOa drops more than would be predicted by the dilution. They explain the deviation from the ideal (Temkin) activity with the use of the asymmetric approximation to nonrandom mixing, indicating association of the Ag+ and 502- ions; thus it is doubtful that this system can be regarded as ideal from any point of view. The ideal fused salt mixture can be defined to be consistent with the Temkin picture. Admittedly it is not settled whether modifications should be made for mixtures of ions of different charge, such as adding vacancies to the lattice, but in any case the principle
Sir: Moultonl has critically examined my proposal2 of a redefinition of activity coefficients for binary ionic melts. I n particular, he compares my definition of an ideal ionic melt with that given by Temkin. First of all, I should like to stress that the purpose of my paper was to develop a useful definition of activity coefficients. I did not discuss any statistical theory at all. In particular, I did not mention the Temkin model. Indeed the statistical interpretation of thermodynamic properties of ionic melts is an involved matter subject to continuous discussion. Thus the Temkin model and its extensions to melts containing ions of different charge numbers are still debated, but the practical question of a convention about activity coefficients cannot be postponed until agreement is eventually reached with respect to the statistical model to be used for ionic melts. That is the reason why I wrote the paper without any reference to molecular models. In order t o proceed in a logical way, let us briefly discuss the following problems: (a) the meaning of the word (‘ideal ionic melt”; (b) the definition of activity coefficients for any ionic melt; (c) the analytical representation of activity coefficients; and (d) the interpretation of activity coefficients. As far as I am aware, there are the following definitions of an ideal ionic melt in the literature: (1) a melt ideal with respect to the components, that is to say a (1) D. M. Moulton, J . Phys. Chem., 73,4022 (1969). (2) R.Haase, $bid., 73, 1160 (1969).
volume 78, Number 11 November 1060
