A study of ion activities in ionic solutions
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I.
INTRODUCTION
IN 1923, Lewis and Randall tu introduced the concept of single ion activities for the study of aqueous solutions where activities are expressed by the Henrian scale. For instance, the activity of Na +, CI-, and NaC1 in the aqueous solution may be related so that a(NaC1) = a(Na+)a(cI -)
standard state has been established for an individual ion." This statement implies that Eq. [7] has become one condition that the "perfect ionic solution" has to meet. In order to avoid this problem in nonideal solutions, Grjotheim and co-workers 13'4'51 introduced the Temkin activity coefficient, 7(xv), for a compound XY to modify Eq. [2], i . e . ,
[ 1]
[81
a(xy) = T ( x y ) N x + + N y -
In molten salts, Temkin (1945) L21 applied statistical thermodynamics and obtained the expression of activity for a compound, XY, in terms of ion activities. For ideal ionic solutions, it becomes a(xy) = Nx++Ny =
a(x~+) = Nx++
[3a] [3b]
= Ny-
However, Temkin t21 also indicated that for nonideal solutions, this relationship might be adopted so that a(xv) = a(x++)a(v~ )
[4]
Y(xv) = 7(x ++)7(v ~)
[5]
For instance, for a solution consisting of two cations and two anions, Fe ++, Mn ++, O - , and S =, Eqs. [4] and [5] would lead to the unit value of equilibrium constant for the following displacement reaction in slag phase: (FeO) + (MnS) = (FeS) + (MnO) K 6 --
a(F,s~a(M.o) _ ( a w + * a s =) (a~a.++ao=) a(MnS)a(FeO)
[6] ~-~
1
[7]
(aMn++as - ) ( a F e + + a o - )
Thus, Temkin's conclusion may be quoted as follows: "the activities of individual ions can formally be introduced, in which case the activity of an ion in a perfect solution can be taken equal to its ionic fraction. In the general case of an ionic solution, however, no definite DUNCAN MA, Graduate Student, and W.-K. LU, Professor, are with the Department of Materials Science and Engineering, McMaster University, Hamilton, ON L8S 4L7, Canada. Manuscript submitted September 22, 1992.
METALLURGICAL TRANSACTIONS B
[9]
K6 - a(Fes)a(MnO) -- Y(FeS)")/(MnO) a(Mns)a (FeO)
[2]
where Nx+ยง and Nv- are the cation fraction of X ++ and anion fraction of y=[2,3l in each sublattice. Temkin pointed out that Eq. [2] might be comparable with Eq. [1 ] for a "perfect ionic solution." Then, activities of ions may be expressed for the molten salts:
a(v=)
Therefore, Eq. [7] becomes
"Y(MnS)T(FeO)
With such formalism, activity c o e f f i c i e n t s o f c o m p o u n d s in molten salts and slag have been extensively studied, and numerous articles can be found in the literature. In 1975, Elliott e t al. trl first used cation and anion activities as a part of the expression of equilibrium constants for slag/metal reactions. In their formulation, cation and anion activities were defined in their own sublattices. It should be pointed out that pure cations or pure anions by themselves do not exist in nature. Therefore, the standard state for activities of cations should include the state of the anion sublattice and v i c e v e r s a . From this consideration, Blander (1977) IT1 a
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