Application of the activity concept in the physical chemistry of slags
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The a c t i v i t y coefficient, ) ' M A , may be defined for the d i s s o c i a t i n g e l e c t r o l y t e , M A , by the equation
THE
ion a c t i v i t y and the ion activity coefficient concepts have b e e n used in the t h e r m o d y n a m i c t r e a t m e n t of dilute aqueous s o l u t i o n s of e l e c t r o l y t e s for a long t i m e . T h e s e concepts have also b e e n extended to nonaqueous m i x t u r e s , m o l t e n s a l t s ~ and s l a g s . 2 It is, howe v e r , g e n e r a l l y a g r e e d ~ that single ion a c t i v i t i e s c a n not be e x p e r i m e n t a l l y d e t e r m i n e d and they cannot be c a l c u l a t e d without n o n l h e r m o d y n a m i c a s s u m p t i o n s . T h e r e f o r e it is i m p o r t a n t that in any work a p p l y i n g s i n g l e ion a c t i v i t i e s , the convention used should be c l e a r l y stated and a n a l y z e d . We will f i r s t b r i e f l y s u m m a r i z e the c l a s s i c a l i n t r o d u c t i o n of s i n g l e ion activity coefficients in aqueous s o l u t i o n s . B. DEFINITION OF SINGLE ION ACTIVITY COEFFICIENTS
~ # M A = R T In (CM +. C A - " •MA)
[2]
where c M § a n d CA- a r e c o n c e n t r a t i o n s of the ions M* and A- r e s p e c t i v e l y . (For m o l e c u l a r s p e c i e s the conc e n t r a t i o n t e r m is C M A ) . D i f f e r e n t c o n c e n t r a t i o n u n i t s m a y be used in this equation, m o l a r i t y , m o l a l i t y and so forth. The gene r a l l y m o s t r a t i o n a l 4 c o n c e n t r a t i o n units a r e cons i d e r e d to be the mole (ionic) f r a c t i o n s b a s e d on the s p e c i e s a c t u a l l y p r e s e n t in the s y s t e m . ( F o r d i f f e r e n t opinion s e e F r i e d m a n and KrishnanS). In a s i m i l a r way as in Eq. [1], the single ion a c t i v i ties aM* and a A - a r e u s u a l l y defined by the g e n e r a l equations: Ptvi§ = ~ / i + + R T
In aM +
[3]
and F o r s i m p l i c i t y we will c o n s i d e r only s o l u t i o n s of s y m m e t r i c a l b i n a r y e l e c t r o l y t e s of the type M A (although the r e s u l t s can be extended e a s i l y to u n s y m metrical salts). The m e a s u r a b l e t h e r m o d y n a m i c q u a n t i t i e s of i n t e r e s t in this connection a r e changes in c h e m i c a l p o t e n t i a l ApMA of a component M A in a m i x t u r e . The a c t i v i t y of M A , a M A , is defined by the equation: AIdd/1A = IJ{YIA -- lffl4A = R T
In a M A
[1]
where P~/A is the c h e m i c a l potential in the given m i x t u r e , and P~/A is the c h e m i c a l potential in the s t a n d a r d state where the activity, a~ by definition is set equal to unity. Equation [1] e m p h a s i z e s that the choice of a s t a n d a r d state u s u a l l y c o r r e s p o n d s to the s e l e c t i o n of a state in which the a c t i v i t y is put equal to unity. The a c t i v i t y of a component in a m i x t u r e can be e x p r e s s e d as a r a t i o of some p r o p e r t y of the solutio
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