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Downloaded by NORTH CAROLINA STATE UNIV on December 9, 2012 | http://pubs.acs.org Publication Date: October 29, 1980 | doi: 10.1021/bk-1980-0133.ch029
Activity Coefficients, Ionic Media, and Equilibrium Constants R. M . PYTKOWICZ Oregon State University, Corvallis, OR 97330
In this work the concepts of ionic medium, effective ionic strength and free versus total activity coefficients are exam ined. Then they are applied to the study of permissible and incorrect translations of equilibrium constants from one medium to another. Ionic Media Ionic media are solutions of background electrolytes which are concentrated enough so that the activity coefficients of the electrolytes of interest do not change during processes which are occurring. Typical ionic media are a 1 m HClO or NaClO solution and seawater. Let us consider the dissolution-precipitation process in seawater in the following example. The normal concentrations of calcium and of carbonate in the near-surface oceanic waters are about [Ca+] = 0.01 and [C03 -] = 2X10 M. The CaC0 in solution is metastable and roughly 2u0% saturated (1). Should precipitation occur due to an abundance of nuclei, [C03 -] will drop to 10 M but [Ca ] will change by no more than 2%. There fore, the ionic strength of the ionic medium seawater will remain essentially constant at 0.7 M. The major ion composition will also remain constant. We shall see later what the implications are for equilibrium constants. 4
2
2
4
-4
3
2
-4
2+
I t i s i m p o r t a n t t o r e a l i z e t h a t one must t a k e i n t o c o n s i d e r a t i o n i o n a s s o c i a t i o n o f t h e i o n i c media e l e c t r o l y t e s b e c a u s e i t a f f e c t s t h e e f f e c t i v e i o n i c s t r e n g t h ( 2 ) . T h i s i n t u r n changes the a c t i v i t y c o e f f i c i e n t s o f t h e i o n s under s t u d y . The e f f e c t i v e i o n i c s t r e n g t h , I , o f a 2-1 e l e c t r o l y t e C A w h i c h a s s o c i a t e s i s g i v e n by e
I
e
2
=0.5{4[C
2 +
]
p
+ [ A - ] + [CA ]} F
where t h e s u b s c r i p t F r e f e r s t o f r e e s p e c i e s . I p l a y s a key r o l e i n e q u i l i b r i a .
(1)
+
We s h a l l
see t h a t
e
0-8412-0569-8/80/47-133-561$05.00/0 © 1980 American Chemical Society In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL
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APPLICATIONS
E l e c t r o l y t e s w h i c h o f t e n a r e c o n s i d e r e d t o be c o m p l e t e l y d i s s o c i a t e d b u t i n e f f e c t a r e n o t a r e NaCl and NaClO^ ( 3 ) .
Downloaded by NORTH CAROLINA STATE UNIV on December 9, 2012 | http://pubs.acs.org Publication Date: October 29, 1980 | doi: 10.1021/bk-1980-0133.ch029
Ion-Pairing In t h e p r e c e e d i n g s e c t i o n m e n t i o n was made o f i o n a s s o c i a t i o n ( i o n - p a i r i n g ) w h i c h , f o r the purposes o f t h i s paper, w i l l r e f e r to coulombic e n t i t i e s with o r without cosphere o v e r l a p . Experim e n t a l s u p p o r t f o r i o n - p a i r i n g has come from sound a t t e n u a t i o n ( 4 J , Raman s p e c t r o s c o p y [5) and p o t e n t i o m e t r y ( 2 , 3). Credibility has r e s u l t e d from t h e model o f Fuoss {§) a p p l i e c T by K e s t e r and Pytkowicz (7). Our method a t p r e s e n t i s n o t based upon t h e o r e t i c a l m o d e l s o r d e p a r t u r e s from i d e a l b e h a v i o r . I t c o n s i s t s i n the use o f p o t e n t i o m e t r i c d e t e r m i n a t i o n s and l i t e r a t u r e v a l u e s o f a c t i v i t y c o e f f i c i e n t s , s t a r t i n g w i t h HCI-HCI0^ e l e c t r o l y t e m i x t u r e s and w i t h t h e a s s u m p t i o n t h a t HCIO^ i s c o m p l e t e l y d i s s o c i a t e d s i n c e t h e a s s o c i a t i o n c o n s t a n t pK = 7 i s e x t r e m e l y s m a l l i n t h i s c a s e . A c o m p a r i s o n o f e x p e r i m e n t a l r e s u l t s w i t h t h o s e c a l c u l a t e d from t h e Fuoss (6>) t h e o r y i s p r e s e n t e d i n T a b l e I. The t h e o r y i s o n l y v a l i d a p p r o x i m a t e l y so t h a t t h e o r d e r o f m a g n i t u d e agreement i s f a i r l y g o o d , e x c e p t i n t h e c a s e s o f MgC0 ° and C a C 0 ° . Stoichiom e t r i c a s s o c i a t i o n c o n s t a n t s K* a r e t h e n o b t a i n e d from t h e a c t i v i t y c o e f f i c i e n t s , e x p r e s s i o n s f o r K*, and from e q u a t i o n s f o r t h e c o n s e r v a t i o n o f mass. The l a t t e r e x p r e s s t h e t o t a l c o n c e n t r a t i o n o f a g i v e n i o n as t h e sum o f t h e c o n c e n t r a t i o n s o f t h e f r e e i o n and o f t h e i o n - p a i r s . V a l u e s o f K* and o f t h e a c t i v i t y c o e f f i c i e n t s o f f r e e i o n s i n i o n i c media depend o n l y upon t h e e f f e c t i v e i o n i c s t r e n g t h a s i s shown l a t e r . 3
3
T a b l e I. A comparison o f s t o i c h i o m e t r i c a s s o c i a t i o n constants c a l c u l a t e d from t h e Fuoss [6) model w i t h Debye r a d i i and from t h e measurements o f J o h n s o n and P y t k o w i c z ( 3 ) . Ion
Pair
NaS
