15 Computational Techniques of Ionic Processes in Water-Organic Mixed Solvents BUDDHADEV SEN—Department of Chemistry, Louisiana State University, Baton Rouge, L A 70803 RABINDRA NATH ROY and JAMES J. GIBBONS—Department of Chemistry, Drury College, Springfield, MO 65802 DAVID A. JOHNSON—Department of Chemistry, Spring Arbor College, Spring Arbor, MI 49283 LOUIS H . ADCOCK—Department of Chemistry, University of North Carolina, Wilmington, NC 28401
A curve-fitting computational technique for the computation of the standard potential of Ag-AgCl electrode in mixed solvents has been developed. The equations generated from experimental data parallel the mathematical form of Gronwall, LaMer, and Sandved's extended Debye-Hückel Equation for symmetrical electrolytes. Application of this technique to a large number of systems has yielded excellent results. The curve-fitting computational technique has been extended to ionic equilibrium processes. Generated equations seem to support Born'selectrostatic model in a dielectric medium as a first approximation. The power of the curve-fitting technique rests on the fact that it does not assume any physical model: it only assumes that the experimental data are good and then proceeds to explore which mechanistic model best rationalizes the empirical equation.
" j p v u r i n g the past t w o decades t h e t h e r m o d y n a m i c s o f c h e m i c a l processes i n m i x e d a n d n o n a q u e o u s solvents h a v e b e e n s t u d i e d e x t e n s i v e l y b y a l a r g e n u m b e r o f w o r k e r s ( I ) . S u c h studies h a v e m e r i t i n t h e i r o w n r i g h t , aside f r o m t h e fact that these studies h a v e e x t r e m e l y i m p o r t a n t practical implications.
I n s t u d y i n g v a r i o u s types o f c h e m i c a l e q u i l i b r i a
a n d i n s t u d y i n g k i n e t i c s , i t is sometimes necessary t o u s e m i x e d - o r g a n i o 0-8412-0428-4/79/33-177-215$08.50/l © 1979 American Chemical Society
216
THERMODYNAMIC BEHAVIOR OF ELECTROLYTES
H
aqueous solvents i n o r d e r to a v o i d c o m p l i c a t i n g processes s u c h as h y d r o l y s i s , u n d e s i r e d c o o r d i n a t i o n , c o m p e t i n g reactions, i n s o l u b i l i t y , etc. H o w e v e r , w e are not c e r t a i n i f the use of m i x e d solvents does not, i n its w a k e , create m o r e p r o b l e m s t h a n it solves ( 2 ) .
I n fact, A m i s a n d H i n t o n
state " A s p e r p l e x i n g as the s e a r c h f o r a s t r u c t u r a l d e f i n i t i o n of w a t e r i s , t h e e c c e n t r i c p h y s i c o - c h e m i c a l p r o p e r t i e s of m i x e d - a q u e o u s at times e v e n m o r e b a f f l i n g " ( 2 ) .
solutions is
W e w i l l not pursue the complex role
of m i x e d solvents o n r e a c t i o n rates, a n d therefore o n m e c h a n i s m s , except i n s t a t i n g that t h e b u l k d i e l e c t r i c constant of the m i x e d solvent is one of t h e i m p o r t a n t parameters of every p r o p o s e d t h e o r y
(2).
T h i s c h a p t e r is c o n c e r n e d p r i m a r i l y w i t h the c o m p u t a t i o n of p o t e n tials of a c e l l u s i n g the h y d r o g e n electrode as a p r o b e for s t u d y i n g i o n i c e q u i l i b r i u m processes i n m i x e d - o r g a n i c - a q u e o u s
solvent systems.
Com
p u t a t i o n of a n u m b e r of other t h e r m o d y n a m i c f u n c t i o n s of the i o n i c process u n d e r i n v e s t i g a t i o n or of the solvent u s e d is r a t h e r s t r a i g h t f o r w a r d o n c e the s t a n d a r d p o t e n t i a l of the m e a s u r i n g c e l l has b e e n c a l c u l a t e d . T h e r e f o r e , f r o m t h e e x p e r i m e n t a l p o i n t of v i e w the m o s t i m p o r t a n t objective is to d e v e l o p a m e t h o d f o r c o m p u t i n g the s t a n d a r d p o t e n t i a l of the c e l l f r o m e x p e r i m e n t a l e m f d a t a . T h e first p a r t of this c h a p t e r presents o u r endeavors i n that d i r e c t i o n . C o m p u t a t i o n of t h e t h e r m o d y n a m i c e q u i l i b r i u m constant ( a n d
AG°)
of a n i o n i c process is q u i t e s i m p l e o n c e t h e s t a n d a r d p o t e n t i a l of
the
r e l e v a n t c e l l has b e e n d e t e r m i n e d . E n t h a l p i e s a n d entropies of t h e process c a n b e c a l c u l a t e d w h e n s u c h e q u i l i b r i u m constant d a t a are a v a i l a b l e over a r a n g e of temperatures. H o w e v e r the i m p o r t a n c e of s u c h t h e r m o d y n a m i c d a t a , e v e n w h e n o b t a i n e d b y r i g o r o u s e x p e r i m e n t a l p r o c e d u r e s , is g r e a t l y r e d u c e d i f t h e d a t a cannot b e r e f e r r e d to a n a r b i t r a r i l y a c c e p t e d
common
r e f e r e n c e state. T h e s e c o n d p a r t of this c h a p t e r presents c o m p u t a t i o n a l methods
for c o n v e r t i n g the t h e r m o d y n a m i c d a t a o b t a i n e d i n a m i x e d
solvent to t h e c o r r e s p o n d i n g t h e r m o d y n a m i c d a t a i n a reference
system
w h i c h i n this case is aqueous m e d i u m c o n t a i n i n g t h e e q u i h b r i u m i o n i c process at i n f i n i t e d i l u t i o n . A l a r g e v o l u m e of the e x p e r i m e n t a l d a t a c i t e d w e r e o b t a i n e d b y the a u t h o r s . I n o r d e r to p r e v e n t t h e c h a p t e r f r o m b e c o m i n g u n w i e l d y , w e h a v e b e e n selective r a t h e r t h a n c o m p r e h e n s i v e i n r e v i e w i n g the p e r t i n e n t l i t e r a t u r e . A l s o , the b a c k g r o u n d t h e o r e t i c a l treat m e n t has b e e n k e p t b r i e f w i t h t h e a s s u m p t i o n t h a t the r e a d e r is m o r e o r less conversant w i t h s u c h m a t e r i a l .
Computation
of Standard
Potential
T h e w o r k i n g c e l l is Pt, H
2
(1 a t m ) |HC1 ( m ) , S ( X ) , H 0 (Y) | A g C l - A g 2
I
15.
SEN E T AL.
Water-Organic
Mixed
217
Solvents
i n w h i c h S represents t h e o r g a n i c c o m p o n e n t o f t h e solvent, X a n d Y a r e w e i g h t percents o r m o l e fractions o f t h e t w o solvent c o m p o n e n t s , a n d the o t h e r s y m b o l s h a v e t h e i r u s u a l significance.
I n t h e i r classic m o n o
g r a p h (3) H a r n e d a n d O w e n h a v e e x t e n s i v e l y s u m m a r i z e d m o s t o f t h e earlier w o r k o n t h e cells of T y p e I i n c l u d i n g t h e i r o w n c o m p r e h e n s i v e w o r k u s i n g t h e d i o x a n e - w a t e r s y s t e m . T h e y f o u n d that as t h e d i e l e c t r i c constant o f t h e solvent decreased, t h e c o n t r i b u t i o n o f G r o n w a l l , L a M e r , a n d S a n d v e d ' s ( G L S ) (4,5) e x t e n d e d terms f o r t h e D e b y e - H i i c k e l E q u a tion c o u l d n o longer b e ignored i n extrapolating to obtain the limiting v a l u e o f E ° . H a r n e d a n d O w e n (for details see R e f . 5) h a v e d e m o n s t r a t e d g r a p h i c a l l y t h e effect o f i g n o r i n g t h e h i g h e r - o r d e r t e r m s b y p l o t t i n g E ' 0
and E ° ' — E
ext
against the m o l a l i t y of H C l i n C e l l I w i t h v a r y i n g per
centages o f d i o x a n e ( F i g u r e 1 ) . E°' — E ° +
f(m)
and E
is t h e
ext
e x t e n d e d terms c o n t r i b u t i o n . O b v i o u s l y , e x t r a p o l a t i o n o f t h e E
0
/
vs m
p l o t is u n s a t i s f a c t o r y f o r a solvent system c o n t a i n i n g e v e n 4 5 w t % d i o x a n e ( D = 38.48) o w i n g to t h e c u r v a t u r e o f t h e plots i n t h e i m p o r t a n t
0.0660 0.0650 0.0640 0.0630 Ε
0 1
0.1640 0.1630 0.2035 0.2025 0
0.01
0.02
m The Physical Chemistry of Electrolytic solutions
Figure 1. Extrapolation of emf (V) in dioxane-water mixtures computed by the Debye-Huckel extended equation. The percentages are those of weight percent of dioxane (5).
218
THERMODYNAMIC
low molality region.
E°'
— E
solvents c o n t a i n i n g 45 w t %
BEHAVIOR
OF ELECTROLYTES
H
plots s e e m to b e q u i t e satisfactory i n
e x t
(D =
38.48) o r m o r e of d i o x a n e ;
e v e n these plots are u n s a t i s f a c t o r y i n a 7 0 %
dioxane m e d i u m .
however, Harned
a n d others a t t e m p t e d to i m p r o v e the e x t r a p o l a t i o n m e t h o d b y i n t r o d u c i n g contributions
from
mass
action
and
d i s s o c i a t i o n of
the
acid i n
low
dielectric medium. L e t us n o w c o n s i d e r t h e e x p l i c i t expression for E bs of C e l l I 0
E
ohs
=
E°
_
2RT-lny m ±
( 1 )
R e a r r a n g e m e n t of E q u a t i o n 1 leads to £«
b8
+
- ^
lnm = E°
- * ψ - ] η γ
(2)
±
E q u a t i o n 2 was proposed b y L e w i s a n d R a n d a l l ( 6 ) even before the a d v e n t o f the D e b y e - H i i c k e l t h e o r y for t h e e v a l u a t i o n of e x t r a p o l a t i o n of L H S of E q u a t i o n 2 against f ( m ) y
±
Ε ° by
the
because b y definition
—» 1 as m - » 0. H o w e v e r , s u c h extrapolations f a i l e d to y i e l d p r e c i s e
v a l u e s of E ° b e c a u s e t h e plots d i d not p r o d u c e t h e d e s i r e d s t r a i g h t lines. T h e m o s t c o m m o n m e t h o d of e x t r a p o l a t i o n is to substitute a n expression f o r In y
±
from the D e b y e - H i i c k e l theory ( 7 ) , a n d the two most frequently
u s e d s u b s t i t u t i o n s are logy
±
—-S
( f )
(r)* +
B'm
(3)
and
where 1
Ρ
Γ =
1 . 2 9 0 X 10°
£
(
)
(6)
W
1 „
35.56
(7)
(DT)i
T h e t e r m a° is f r e q u e n t l y c a l l e d the i o n - s i z e p a r a m e t e r or a p p a r e n t i o n i c d i a m e t e r , B is a n e m p i r i c a l l y fitted coefficient. r
I n r e a l i t y , h o w e v e r , B ' has
i m p o r t a n t t h e o r e t i c a l significance i n i n t e r i o n i c a t t r a c t i o n t h e o r y , a n d i t is a h i g h e r - o r d e r f u n c t i o n of t h e i o n - s i z e p a r a m e t e r .
15.
Water-Organic
SEN ET AL.
Mixed
219
Solvents
A l s o a c o m p a r i s o n of t w o a l t e r n a t i v e expressions for l o g y
±
given b y
E q u a t i o n s 3 a n d 4 is of interest. A close e x a m i n a t i o n of these equations w i l l r e v e a l c e r t a i n i n h e r e n t weaknesses of t h e l i n e a r e x t r a p o l a t i o n m e t h o d for t h e e v a l u a t i o n of E ° , e v e n w h e n u s i n g t h e e x t e n d e d terms. F i r s t , t h e l i n e a r e x t r a p o l a t i o n w i l l r e q u i r e a precise
v a l u e of
D , the
constant of the solvent, w h i c h i n p r i n c i p l e is e x p e r i m e n t a l l y F r e q u e n t l y , h o w e v e r , i t is c o m p u t e d or b y g r a p h i c a l i n t e r p o l a t i o n .
dielectric
measurable.
b y U s i n g some e m p i r i c a l f u n c t i o n
S e c o n d l y , t h e u n c e r t a i n t y of t h e i o n - s i z e
p a r a m e t e r is significant a n d n o r e l i a b l e m e t h o d of c o m p u t a t i o n n o r is i t d i r e c t l y m e a s u r a b l e
exists,
experimentally.
T h i s d i l e m m a l e d us to investigate the f e a s i b i l i t y of e x t r a p o l a t i o n for t h e e v a l u a t i o n of E ° .
a nonlinear
F o r t h e sake of b r e v i t y , w e
will
n o t r e p r o d u c e h e r e the d e t a i l e d m a t h e m a t i c a l d e r i v a t i o n s of G r o n w a l l , L a M e r , a n d S a n d v e d s e x t e n d e d terms of the D e b y e - H i i c k e l theory. c a n find these derivations i n t h e i r o r i g i n a l p a p e r (4) Owens
classic m o n o g r a p h .
F o r a d e s c r i p t i o n of the b a s i c
assumptions
a n d the p h y s i c a l m o d e l of the i n t e r i o n i c a t t r a c t i o n t h e o r y one consult
Harned
Gurney
(8,9).
and
Owens
monograph
as
well
as
the
±
should
work
F o r the electrolytes of s y m m e t r i c a l v a l e n c e t y p e , the e x t e n d e d t i o n for In y
One
or i n H a r n e d a n d
of
equa
is expressed as
[uffe] · [i 5
X s
{κα)
~
4 F s
(κα)
]+
higherterms
(8)
i n w h i c h ζ is the v a l e n c e ( w h i c h for s y m m e t r i c a l electrolyte, |z+| =
|z.|),
cz is t h e i o n i c charge, D is the d i e l e c t r i c constant of the solvent, k is B o l t z m a n n constant, Τ is absolute
t e m p e r a t u r e , κ is a v e r y
important
f u n c t i o n i n the i n t e r i o n i c a t t r a c t i o n t h e o r y a n d has the d i m e n s i o n s of a reciprocal
distance,
a n d l/κ
is r e l a t e d to the p o t e n t i a l of
the
ionic
atmosphere a n d it is e x p l i c i t l y g i v e n b y /_4ττ^Ν_
y
^lOOODkT
J
7
( V
) ;
U p o n s u b s t i t u t i o n of the n u m e r i c a l values of the constants, E q u a t i o n 9 for s y m m e t r i c a l electrolytes at 25 ° C b e c o m e s
—
«
=
-j=
V
c
cm
(10)
220
THERMODYNAMIC
BEHAVIOR OF
ELECTROLYTES—Π
i n w h i c h c is t h e m o l a r c o n c e n t r a t i o n of a n i o n . O b v i o u s l y , i n a n o r m a l s o l u t i o n 1/K is of the o r d e r of a m o l e c u l a r d i a m e t e r , a n d i t varies i n v e r s e l y w i t h the s q u a r e root of c.
I n E q u a t i o n 8, a is t h e m e a n d i s t a n c e
of
a p p r o a c h of the ions. It is q u i t e o b v i o u s t h a t the first t w o terms of t h e
right-hand
side of
E q u a t i o n 8 represent D e b y e - H u c k e l ' s first a p p r o x i m a t i o n as expressed b y E q u a t i o n 4. T h a t i s , ι l
n
Μ)
^ =
κ
2
-2DkTT+^
n
n
/ i n
.
or
in which 35.56 X 1 0 ' a
ακ
A
A
~ ( T ) * ~ =
.
8
(DTV
35.56 X a ° ( )ΐ ι Ρ Γ
0 a
. i n
,
a
m
C
m
( 1 2 )
ο Angstroms x
(7)
T h e o v e r a l l r e a c t i o n i n C e l l I u n d e r the d e f i n e d s t a n d a r d c o n d i t i o n s is H C l (1 m) + A g ( s ) — A g C l ( s ) +
1/2 H ( p — 1 a t m ) 2
(13)
T h e electrical work done b y C e l l I under standard a n d reversible condi tions is a m e a s u r e of the s t a n d a r d free e n e r g y c h a n g e of R e a c t i o n 13. T h u s -AG°
=
(14)
1SSFE
0
i n w h i c h E ° , t h e s t a n d a r d p o t e n t i a l , is expressed b y
S° with E
o b 8
£obs + ~
In m + ?ψ·
lny
(15)
±
b e i n g t h e m e a s u r e d p o t e n t i a l of t h e w o r k i n g C e l l I . I t s h o u l d
b e e m p h a s i z e d here that the s t a n d a r d c e l l is a n i m a g i n a r y d e v i c e i n w h i c h m =
a =
y
±
=
1. T h e i n t e r i o n i c a t t r a c t i o n t h e o r y essentially accounts
f o r t h e n o n i d e a l i t y of the solutions of s t r o n g electrolytes (i.e., c o m p l e t e l y d i s s o c i a t e d ) i n a d i e l e c t r i c m e d i u m , a n d this n o n i d e a l i t y is expressed b y γ . ±
I n solutions of h i g h d i e l e c t r i c constants ( D >
e x t e n d e d terms
(in Equations 3 and 4)
38), Debye-Huckel's
adequately
account
f o r this
n o n i d e a l i t y (cf. F i g u r e 1 ) . H o w e v e r , as t h e d i e l e c t r i c constant decreases, t h e c o n t r i b u t i o n s o w i n g to t h e h i g h e r terms of E q u a t i o n 8 c a n n o l o n g e r be ignored.
15.
Water-Organic
SEN ET AL.
Mixed
221
Solvents
A t this stage w e w i l l o m i t a l l of the c o m p l i c a t e d a n d r a t h e r t e d i o u s m a t h e m a t i c a l d e r i v a t i o n s . R o y a n d J o h n s o n (10,11,12,13)
have shown
t h a t G L S E q u a t i o n 8 c a n b e r e d u c e d to a p o l y n o m i a l i n κ; t h u s In y
— A"* +
±
B ' V +
C'V + D ' V +
. . .
(16)
i n w h i c h the constants A " , B " , etc., e m e r g e f r o m t h e v a r i o u s
series
i n v o l v e d i n t h e G L S e q u a t i o n . I t has b e e n s h o w n e a r l i e r ( E q u a t i o n s 9 a n d 10) t h a t κ is p r o p o r t i o n a l to t h e square r o o t of i o n a l s t r e n g t h o r c o n c e n t r a t i o n ( m o l a r or m o l a l ) . E q u a t i o n 16 c a n b e r e w r i t t e n as In γ
±
— A ' r o * + B ' r a + Cm™
S u b s t i t u t i n g the v a l u e of In γ
+
. . .
(17)
f r o m E q u a t i o n 17 i n t o E q u a t i o n 2, one
±
obtains
#obs + ^ψ-
In m =
£° -
?ψ-
(A'm* + B ' m + C m / 3
2
+
. . .) (18)
or Sobs +
^ l ^ l n m — E°
+ Ami + Bm + Cm / + 3
2
. . .
(19)
Γ T h e coefficients
of E q u a t i o n 19 consist essentially of a n u m b e r
of
constants a m o n g w h i c h are d i e l e c t r i c constant D of the m e d i u m a n d t h e i o n - s i z e p a r a m e t e r . I t has b e e n m e n t i o n e d e a r l i e r t h a t i n d e t e r m i n a c y of the v a l u e of a m a k e s p r i o r c o m p u t a t i o n of constants i m p o s s i b l e .
There
are also d o u b t s a b o u t t h e r e l i a b i l i t y of the v a l u e s of D i n m a n y instances. A n u m b e r of i m p o r t a n t conclusions m a y b e d r a w n f r o m E q u a t i o n 19. T h e s e are as f o l l o w s . 1. ( E + R T / F In m ) is a p o l y n o m i a l f u n c t i o n i n p o w e r s of ra* w h i c h w i l l cause a p l o t of the l e f t - h a n d side vs. m* to b e c u r v e d i n w a r d s , a n d w i l l a s y m p t o t i c a l l y a p p r o a c h E ° as ra* - » 0. o b 8
2. I t is o n l y u n d e r s p e c i a l c o n d i t i o n s t h a t a p l o t of t h e l e f t - h a n d side vs. ra* p r o d u c e s a straight fine; a n d a l l e x p e r i m e n t a l e v i d e n c e seems to i n d i c a t e t h a t s u c h s p e c i a l c o n d i t i o n s exist f o r d i l u t e solutions of s t r o n g electrolytes ( p a r t i c u l a r l y 1-1 e l e c t r o l y t e s ) i n solvents of h i g h d i e l e c t r i c constant w h e r e the s u m of c o n t r i b u t i o n s of terms c o n t a i n i n g p o w e r s of m* greater t h a n 1 are i n s i g n i f i c a n t . T h e D e b y e - H i i c k e l e x t e n d e d e q u a t i o n i n c l u d e s t h e t e r m c o n t a i n i n g the s e c o n d p o w e r of m*. 3. T h e c o n t r i b u t i o n s f r o m h i g h e r o r d e r terms of m* r a p i d l y b e c o m e significant as |z+| = |z.| b e c o m e s l a r g e r t h a n 1, a n d as a b e c o m e s s m a l l e r w i t h the d e c r e a s i n g v a l u e of the d i e l e c t r i c constant.
222
THERMODYNAMIC BEHAVIOR OF ELECTROLYTES
II
B e c a u s e of the f o r e g o i n g c o n c l u s i o n s , w e d e c i d e d t o a b a n d o n the l i n e a r e x t r a p o l a t i o n m e t h o d a n d i n v e s t i g a t e t h e prospects of a c u r v e - f i t t i n g t e c h n i q u e for the e v a l u a t i o n of E° fitting
of C e l l I . I n o r d e r t o use t h e c u r v e -
t e c h n i q u e , i t is necessary to assume t h a t a set of r e l i a b l e a n d p r e c i s e
e m f d a t a f o r the c e l l r e a c t i o n i n the l o w - c o n c e n t r a t i o n r e g i o n say f r o m 10" m x
to 1 0 " m ) is a v a i l a b l e . W i t h t h e fine i n s t r u m e n t a t i o n a v a i l a b l e 4
t o d a y , the f o r e g o i n g e x p e c t a t i o n is e x p e r i m e n t a l l y a t t a i n a b l e . I t also is a s s u m e d t h a t the set of e x p e r i m e n t a l e m f d a t a c a n b e best fitted to a p o l y n o m i a l of e x p l i c i t f o r m , Y — A
0
+ AiX +
Ax 2
2
+ A z 3
w h i c h is a n a n a l o g of E q u a t i o n 19.
3
+
. . . +
(20)
Ax n
n
I n u s i n g the p o l y n o m i a l f o r
c o m p u t a t i o n of E ° , y is r e p l a c e d b y E
oh9
+
the
R T / F In rru, a n d χ is r e p l a c e d
b y mK I n the a c t u a l case, the v a l u e of t h e s u b s c r i p t η m u s t b e a r b i t r a r i l y fixed, a n d its a r b i t r a r y v a l u e n e e d not b e fixed a n y h i g h e r t h a n necessary i n o r d e r to save
computation time.
However,
computation must
be
c o n t i n u e d a n d i n c l u d e h i g h e r - a n d h i g h e r - o r d e r e d terms u n t i l a l l t h e e x p e r i m e n t a l d a t a c a n b e fitted to the a p p r o p r i a t e p o l y n o m i a l p r o d u c i n g a s m o o t h p l o t . T h e first a p p r o x i m a t i o n of E q u a t i o n 20 is y =
A
0
+
Αχχ,
w h i c h is a n a n a l o g of the D H - e x t e n d e d e q u a t i o n as m e n t i o n e d e a r l i e r . T h e coefficients A i , w h i c h w e r e d e t e r m i n e d b y the m e t h o d of least squares a n d t h e s t a n d a r d error of t h e d e p e n d e n t v a r i a b l e y, w a s c o m p a r e d w i t h a p r e d e t e r m i n e d m a x i m u m tolerance.
H i g h e r - o r d e r terms m u s t b e t a k e n
i n t o c o n s i d e r a t i o n , i f necessary, to h a v e the error f a l l w i t h i n the m a x i m u m tolerance. A m o d i f i e d G a u s s i a n e l i m i n a t i o n t e c h n i q u e w a s u s e d to solve t h e r e s u l t i n g set of l i n e a r equations.
I n our computation, w e used
a
s t a n d a r d I B M p r o g r a m ( r e v i s e d I B M 7.0.002). O b v i o u s l y , the c u r v e - f i t t i n g p o l y n o m i a l for t h e c o m p u t a t i o n of E°
of
C e l l I m a y b e w r i t t e n e x p l i c i t l y as
£obs +
in which A
0
or? rp =γIn m — A
— E°,
0
+ Aim* + A m + A m / 2
3
3
2
t h e s t a n d a r d p o t e n t i a l of t h e c e l l .
+ . . .
It was
(21)
never
necessary to use m o r e t h a n f o u r terms f o r the systems w e i n v e s t i g a t e d . W e w o u l d l i k e to e m p h a s i z e o n c e a g a i n that i t is i m p o r t a n t t h a t E q u a t i o n 21, w i t h the c o m p u t e d coefficients, a c c o m m o d a t e s a l l e x p e r i m e n t a l d a t a ; t h a t is, the c a l c u l a t e d [ E
o b 8
+
2 R T / F In m ] is w i t h i n t h e p r e d e t e r m i n e d
t o l e r a n c e l i m i t of e x p e r i m e n t a l [ E
o b s
+
2 R T / F In m] for a l l v a l u e s of m
i n the g i v e n s y s t e m at the g i v e n t e m p e r a t u r e . I n fact, i n o u r o p i n i o n , the systems f o r w h i c h s u c h a fit c a n n o t b e o b t a i n e d s h o u l d b e v i e w e d w i t h s u s p i c i o n , a n d this c r i t e r i o n m a y b e t a k e n as a n i n d i c a t i o n of presence of
15.
SEN E T AL.
Water-Organic
Mixed
223
Solvents
interactions other t h a n c o u l o m b i c i n t e r a c t i o n s a m o n g ions a n d ions, a n d ions a n d solvent d i p o l e s . D u r i n g o u r investigations w e e x p e r i e n c e d s u c h d e v i a t i o n s w h e n a c e t o n i t r i l e w a s u s e d as the o r g a n i c c o m p o n e n t i n C e l l I . W e w i l l m a k e a f e w b r i e f c o m m e n t s a b o u t t h e use of a c e t o n i t r i l e as t h e solvent c o m p o n e n t later i n this c h a p t e r . F i g u r e s 2 a n d 3 represent t y p i c a l plots of E' ( = E
- f 2 R T / F In m)
o b s
vs. ra* i n m i x e d solvents w i t h a l o w ( 8 . 6 8 % ) a n d a h i g h ( 8 9 . 0 0 % ) p r o portion of organic component
(10,11,12,13).
T h e p r o n o u n c e d increase
i n the c u r v a t u r e of the plots w i t h i n c r e a s e d o r g a n i c c o m p o n e n t ( decreased b u l k d i e l e c t r i c c o n s t a n t ) is q u i t e o b v i o u s . R o y a n d his co-workers
(14-28)
have used the curve-fitting poly
n o m i a l t e c h n i q u e f o r the c o m p u t a t i o n of E° of C e l l I c o n t a i n i n g a v a r i e t y of m i x e d - s o l v e n t systems.
S o m e of t h e v a l u e s of E ° m
( m o l a l s c a l e ) of
C e l l I (29) are c o m p i l e d i n T a b l e I . E x t e n s i v e e x p e r i m e n t a l d a t a o n b u l k d i e l e c t r i c constants of m i x e d a q u e o u s - o r g a n i c solvents are n o t a v a i l a b l e . S t a n d a r d p o t e n t i a l s of C e l l I w i t h h m i t e d d i e l e c t r i c d a t a a r e c o m p i l e d i n T a b l e I I . P l o t s of s t a n d a r d p o t e n t i a l vs. ( 1 / D T ) * are s h o w n i n F i g u r e 4. T h e d a t a w e r e p l o t t e d o n t w o different scales f o r a c l e a r d e m o n s t r a t i o n of t h e t r e n d . T h e e n t i r e r a n g e of p o t e n t i a l a n d d i e l e c t r i c d a t a , ( 1 / D T ) * , w e r e p l o t t e d as o p e n circles a n d the r a n g e p o t e n t i a l d a t a f r o m 1 4 9 - 2 2 2 m V a n d t h e c o r r e s p o n d i n g d i e l e c t r i c d a t a w e r e r e p l o t t e d as o p e n squares o n a m o r e
expanded
scale ( F i g u r e 4 ) . O b v i o u s l y , f o r t h e case i n w h i c h t h e b u l k d i e l e c t r i c constant of the solvent is greater t h a n 40, t h e s t a n d a r d p o t e n t i a l of C e l l I is a l i n e a r f u n c t i o n o f ( 1 / D T ) * , as w o u l d b e e x p e c t e d f r o m the a p p r o x i m a t i o n of D H - e x t e n d e d t h e o r y .
cantly deviate from the straight-line plot. 163 m V , 9338 ( Ι / λ / D T ) ;
1(/VDT).
first-order
O n l y three d a t a points s i g n i f i These points correspond to
149 m V , 8834 ( l / V Ô T ) ;
a n d 2 0 3 m V , 7417
T h e first of these p o i n t s corresponds to 4 5 w t %
dioxane
( D = 3 8 ) ; i t is the t h r e s h o l d r e g i o n of f a i l u r e of l i n e a r i t y ; also t h e d a t u m itself seems to b e suspect.
T h e other t w o p o i n t s m a y n o t b e c o n s i d e r e d
b e y o n d the r e a l m of e x p e r i m e n t a l error. I t w o u l d b e i n t e r e s t i n g to c o m p a r e t h e slopes of s u c h e x p e r i m e n t a l plots w i t h those c a l c u l a t e d f r o m t h e theory.
H o w e v e r , i t is safe t o c o n
c l u d e t h a t i n m i x e d solvents w i t h a b u l k d i e l e c t r i c constant greater t h a n 40, first-order c o u l o m b i c i n t e r a c t i o n s are t h e o n l y significant i n t e r a c t i o n s a m o n g t h e ions a n d ions, a n d ions a n d solvent m o l e c u l e s a s s u m i n g t h a t there are n o c h e m i c a l i n t e r a c t i o n s .
I n solvents w i t h l o w e r
dielectric
constants h i g h e r - o r d e r interactions, a n d p e r h a p s e v e n n o n c o u l o m b i c i n t e r actions, b e c o m e i n c r e a s i n g l y significant. A s e x p e r i m e n t a l i s t s , w e d o n o t w a n t to speculate any further, a n d i n m a k i n g the foregoing comments, i t has b e e n t a c i t l y a s s u m e d t h a t o n e of t h e c o m p o n e n t s system is w a t e r .
of t h e b i n a r y
224
THERMODYNAMIC
BEHAVIOR
OF ELECTROLYTES
0.2400 h
0.2300
u 0.2200
0.2100
0.05
0.10 0.15 0.20 0.25 0.30 rmJ / 2
Figure 2. Variation of emf [E' = E + (2RT/F) In m] with mohlity and temperature in 8.68% monoglyme o°c 0b8
0.1200 h
0.0800
0.0400
-0.0400
-0.0800
-0.1200
Figure
3. Variation of emf (Ε') with molality temperature in 89.00% tetrahydrofuran
and
II
15.
Water-Organic
SEN ET AL.
Table I. Solvent Compo sition Wt% Organic Component
rp 0
δ
100
Component:
ethane
45
(11,21)
0.2089 0.2009 0.1684 0.1099 -0.06039
Tetrahydrofuran D = 7.6
(12,28)
0.21368 0.20933 0.22160 0.20375 0.19828 0.21062 0.17060 0.16572 0.18662 0.09310 0.07330 0.11163 -0.00279 -0.02582 -0.05689 Component: D =
Isopropanol 1941
0.01878 - 0 . 0 0 4 3 5 -0.1122 -0.1249
0.2029
0.20864
1-Butanol 0.20350
Component: tert-Butanol D = 16.62 (30°)
0.2159 0.2083 0.1963 0.1444
(22,23) 0.1958
-0.06863
Component:
0.21028 Organic
0.2101
(15,20)
-0.02269 -0.1338
Component: 1-Butanol D -17.51
0.2168 (10°) -0.04027 Organic
10 20 40 70
35
0.2155 0.2209 0.2090 0.2158 0.1794 0.1905 0.1262 0.1449 -0.01125 - 0 . 0 3 9 5
0.23467 0.21662 0.20365 0.12600 0.03397
-
25
1,2-Dimeihoxy D = 6.8
0.2272 0.2242 0.2053 0.1688 0.025O
Organic 5
15
Component:
Organic 95 100
(°C) !
Organic 8.98 18.21 47.20 73.03 89.00
225
Solvents
Standard Potential (Ε™° Volts) of A g - A g C l Electrode (Cell I) Computed by the C u r v e - F i t t i n g Method
Organic 8.68 17.81 46.52 67.03 88.80
Mixed
0.2102 0.2013 0.1897 0.1354
0.2061 0.1957 0.1845 0.1251
0.1883 (40°) -0.10802
(1A) 0.19488
0.18272
(12) 0.2002 0.1909 0.1764 0.1105
0.1919 0.1862 0.1665 0.1025
226
THERMODYNAMIC
Table I . Solvent Compo sition Wt% Organic Component
δ
— — — — — — —
15
Component:
1-Propanol D = 20.33
— —
Component: D =
0.08569 0.04065 Component:
— — —
0.2309 0.2289 0.2266
Organic
Component:
— — — Organic
0.2314 0.2312 0.2271 Component: 0.23081 0.22643 0.2341
II
Propylene 64.4
, 45
24, 25) 0.2008 0.2034 0.1862 0.1940 0.1577 0.1689 0.1116 0.1289 0.0060 0.0461 -0.00319 -0.02047 -0.1333 -0.1500
(17,18)
0.06674 0.02077 Carbonate
0.04149 0.05089 0.00956 - 0 . 0 0 7 7 6 (19)
=
0.2260 0.2240 0.2190 D
5 — 10 — 0 (pure w a t e r as solvent) (29)
35
(10,21,
Glycerol 40.1
0.07868 0.02605 D
5 10 20
25
0.2212 0.2157 0.2093 0.2099 0.2053 0.1998 0.1917 0.1849 0.1729 0.1568 0.1461 0.1362 0.0971 0.0777 0.0583 0.04542 0.03363 0.02105 -0.0854 -0.1043 -0.1200
Organic 5 10 20
f°C) y
0
Organic 95 100
OF ELECTROLYTES
Continued
Τ
Organic 10 20 40 70 90 95 100
BEHAVIOR
Dimethyl 46.7
0.2209 0.2188 0.2132 Sulfoxide
0.2150 0.2125 0.2082
0.2080 0.2049 0.1990
(13)
=
0.2255 0.2210 0.2186
0.2179 0.2148 0.2117
Dimethylformamide D—36.71 0.22735 0.22307 0.2286
0.22139 0.21487 0.2224
0.2102 0.2093 0.2076
0.2036 0.2029 0.1990
(16) 0.21507 0.21063 0.2156
0.20476 0.20038 0.2083
I n c i d e n t a l l y , s u c h plots ( F i g u r e 4 ) m a y b e u s e d to c o m p u t e a p p r o x i m a t e v a l u e s of the b u l k d i e l e c t r i c constants of w a t e r - o r g a n i c m i x e d solvents f r o m t h e e m f m e a s u r e m e n t s p r o v i d e d that the b u l k d i e l e c t r i c constant is h i g h e r t h a n 40. I n fact, f o r a u t o - i o n i z i n g solvents this m a y be a convenient method, a n d our calculations have s h o w n that such c o m p u t e d v a l u e s are w i t h i n 5 - 7 % of t h e e x p e r i m e n t a l values.
Figure
4. 9
Variation of the standard potential of Cell I with (1/ΌΎ)$ at 25°C. Range of D , 78-36. (Ο), E, 55-220 mV (1/DT)K 6559-13909; (Π), E, 100-220 m V , (1/ΌΊ)\ 6559-9059.
Scale:
228
T H E R M O D Y N A M I C BEHAVIOR O F ELECTROLYTES
Table I I . Wt % of Organic Component 5 10 10 20 20 40 20 40 60 80 90 45 70 82 100
Act Me Act Me Act Me Diox Act Me Me Me Diox Diox Diox Water
Π
Standard Potentials (Molal Scale) of Cell I and the B u l k Dielectric Constants of the Solvents"
D 75.9 74.1 73.1 69.99 67.6 60.94 60.79 54.6 51.67 42.60 35.76 38.48 17.69 9.53 78.48
E,° (V)
(V)
No. of Obser vations
Std. Error x i o
15 18 15 7 15 8 10 14 9 7 9 10 10 7 8
0.94 0.47 4.45 0.82 1.00 1.59 0.70 1.25 0.5 1.80 3.20 0.57 0.39 1.24 0.52 0.19
0.2190 0.21925 0.21535 0.21532 0.21565 0.2160 0.2094 0.20914 0.2095 0.20818 0.19682 0.1968 0.20303 0.20301 0.18595 0.18616 0.1818 0.18120 0.1492 0.14895 0.1135 0.1148 0.16358 0.16331 0.06395 0.06408 -0.0415 -0.0339 0.2224 0.22238 0.2221
4
Deg. Equa tion 2 3 2 3 3 3 3 3 4 4 2 5 5 3 2 3
Τ = 25°C. Act = acetone, Diox = dioxane, M e = methanol, D = dielectric constant, E\° and E» Figure 6. The linear range of the ionization constants of the acids vs. the dielectric constant func tion at 25°C. ethanol-water (O); methanol-water (A); 2-methoxyethanol-water; dioxane-water (D); acetone-water, glycerol-water, 2-propanol-
r.(A)
r(A)
1.3 1.1 1.1 1.0 1.0 1.2 1.2 1.3 1.1 1.7 1.2 1.2 0.9 1.2
4.3 4.1 4.1 4.0 4.0 4.2 4.2 4.3 4.1 4.7 4.2 4.2 3.9 4.2 4.0 4.4 5.0
3.0 A .
First ionization constants for dicarboxylic acids.
a l t h o u g h of the same o r d e r of m a g n i t u d e , w i l l b e different for different acids as t h e y i n c l u d e s m a l l b u t significant c o n t r i b u t i o n s o w i n g to n o n c o u l o m b i c i n t e r a c t i o n s e v e n i n solvents of h i g h - b u l k d i e l e c t r i c constants (cf. T a b l e V I I ) . T o o m a n y factors s u c h as the d i p o l e m o m e n t s , p o l a r i z a b i l i t y , s t r u c t u r e , L e w i s a c i d i t y a n d b a s i c i t y of the solvent m o l e c u l e , a n d l o n g - r a n g e q u a n t u m m e c h a n i c a l i n t e r a c t i o n s are i n v o l v e d i n d e t e r m i n i n g t h e v a l u e s of β. T h e r e f o r e , i t w i l l b e f u t i l e to a t t e m p t a p u r e l y t h e o r e t i c a l c o m p u t a t i o n of β regardless of t h e s o p h i s t i c a t i o n of t h e m o d e l .
A s the
v a l u e of the b u l k d i e l e c t r i c constant b e c o m e s less t h a n a c e r t a i n c r i t i c a l v a l u e (e* < 4 0 ) , the c o n t r i b u t i o n of n o n c o u l o m b i c i n t e r a c t i o n s increases rapidly and B o r n s model becomes inadequate. A f e w c o m m e n t s o n the v a l u e s of r. a n d (r+ + are necessary.
r . ) (cf. T a b l e V I I I )
I n c r e a s i n g h y d r o c a r b o n content decreases the h y d r o p h i l i c
p r o p e r t y of t h e a n i o n (cf. f o r m i c , a c i t i c , p r o p a n o i c , b u t a n o i c , 3 - m e t h y l b u t a n o i c , a n d b e n z o i c a c i d s ) r e s u l t i n g i n the decrease of h y d r a t i o n ; t h e t r e n d e v e n t u a l l y levels off.
H y d r o p h i l i c s u b s t i t u t i o n increases h y d r a t i o n
( cf. acetic, c h l o r o a c e t i c , c y a n o a c e t i c , g l y c o l i c a c i d s ; cf. g l u t a r i c , s u c c i n i c , a n d m a l o n i c a c i d s ; cf. b e n z o i c a n d s a l i c y c l i c acids ) . A l s o n o t e t h a t r . is smallest for b e n z o i c a c i d a n d largest f o r m a l o n i c a c i d . T h e s e t r e n d s c a n not be fortuitous. F i n a l l y , i t seems p e r t i n e n t to m a k e s o m e c o m m e n t s o n t h e trends of v a l u e s of the constants b , b ' , a n d β ( cf. T a b l e V I I I ) of t h e e m p i r i c a l
15.
SEN E T AL.
Water-Organic
E q u a t i o n s 29, 30, a n d 3 1 .
Mixed
245
Solvents
F o r acids of the same class b o t h b ' a n d β
g e n e r a l l y f o l l o w the t r e n d of p K ; t h e y are i n f l u e n c e d s i g n i f i c a n t l y b y t h e a
s u b s t i t u e n t g r o u p as m i g h t b e expected.
N o s u c h t r e n d is o b s e r v e d
for
the v a l u e s of b . I n c o m p u t i n g b , the p r o g r a m d i d not a t t a c h a n y s p e c i a l w e i g h t to the p o i n t s i n the l i n e a r regions of the plots, h e n c e b v a l u e s are w e i g h t e d b y p o i n t s i n the c u r v e d r e g i o n of the plots, w h e r e a s b ' a n d β v a l u e s w e r e c o m p u t e d b y u s i n g d a t a f r o m the g r a p h i c a l l y s e l e c t e d l i n e a r r e g i o n of the plots.
It is i n t e r e s t i n g t o n o t e t h a t b y a s s u m i n g r . to
be
1.2 A , t h e o r e t i c a l β v a l u e turns out to b e 141 w h i c h is d e f i n i t e l y of t h e same o r d e r v a l u e s r e p o r t e d f o r β i n T a b l e V I I . deviations
are
obviously
i m p o r t a n t difference
caused
between
by
S m a l l b u t significant
noncoulombic
interactions.
E q u a t i o n s 30 a n d 31 s h o u l d b e
One noted;
E q u a t i o n 30 is e x p l i c i t l y r e f e r e n c e d to w a t e r , whereas i n p r i n c i p l e , E q u a t i o n 31 is a p p l i c a b l e f o r a n y t w o solvents. C u r v e - f i t t i n g c o m p u t a t i o n t e c h n i q u e w a s a p p l i e d for t h e c a l c u l a t i o n of f o r m a t i o n constants of c a l c i u m lactate i n m e t h a n o l - w a t e r , water, and glucose-water calculation
of
the
systems
average
(60)
formation
ethanol-
w i t h excellent results. constant
K
a v
I n the
( = (Ki · Κ ) * ) ,
β
2
t u r n e d out to b e a b o u t 190 f o r the m e t h a n o l - w a t e r system, 192 f o r t h e e t h a n o l - w a t e r system, a n d 185 for the g l u c o s e - w a t e r system. T h e v a l u e of b ' w a s 204. W e b e l i e v e t h a t a c o m p i l a t i o n of b ' a n d β values f o r acids w i l l e n a b l e one to c a l c u l a t e either p K
a
o r p K * k n o w i n g one a n d the solvent d i e l e c a
t r i c , w h i c h i n t u r n m a y be d e t e r m i n e d g r a p h i c a l l y f r o m E ° vs. ( 1 / λ / D T ) m
plots f o r C e l l I . I t s h o u l d also b e p o s s i b l e to classify t h e acids o n the basis of b ' or β v a l u e s .
T h e s e c o m m e n t s s h o u l d a p p l y also to
weak
i o n i c complexes.
Glossary of Symbols A = a c h a r a c t e r i s t i c constant as d e f i n e d b y E q u a t i o n 7 A , A ' , A " = constants of t h e p o l y n o m i a l Β, Β', B " =
constants of t h e p o l y n o m i a l
B ' = a constant of D H e x t e n d e d t h e o r y e q u a t i o n C , C , C " = constants of t h e p o l y n o m i a l c = molarity D = b u l k d i e l e c t r i c constant of the s o l v e n t i n t h e
first
p a r t of t h e c h a p t e r D H = Debye-Hiickel E°
= s t a n d a r d p o t e n t i a l of t h e p a r t i c u l a r c e l l
•Eobs =
e m f of t h e p a r t i c u l a r c e l l w h e n p a r t i a l pressure of h y d r o g e n is one a t m o s p h e r e
e =
e l e c t r o n i c c h a r g e i n t h e s e c o n d p a r t of the c h a p t e r
246
THERMODYNAMIC BEHAVIOR OF ELECTROLYTES II F = Faraday 0
A G ° , A G * , &G °*
= s t a n d a r d free e n e r g y c h a n g e ; asterisk i n d i c a t e s t h a t
t
the solvent contains a n organic component or i t may be nonaqueous G L S = Gronwall, L a M e r , and Sandved k = B o l t z m a n n constant m = molality Ν = Avogadro's number p K a = i o n i z a t i o n constant o f a n a c i d i n p u r e w a t e r p K a * = i o n i z a t i o n constant o f a n a c i d i n a n o r g a n i c - w a t e r m i x e d solvent o r i n a n o n a q u e o u s s o l v e n t R = gas constant S ) = l i m i t i n g t h e o r e t i c a l slope o f r a t i o n a l a c t i v i t y coeffi ( f
cient i n interionic attraction theory; a function of γ , D , a n d Τ as expressed b y E q u a t i o n 5 Τ = temperature i n K e l v i n X,Y
= function of D H extended theory equation ζ = valence of a n i o n s
2
Γ = i o n a l strength, 2 C i Z i ι y = m e a n m o l a l a c t i v i t y coefficient t
y ο = m e a n m o l a l a c t i v i t y coefficient at infinite d i l u t i o n i n the s o l v e n t i n d i c a t e d c = e l e c t r o n i c c h a r g e i n t h e first p a r t o f t h e c h a p t e r c, c* = b u l k d i e l e c t r i c constant o f t h e s o l v e n t i n t h e s e c o n d part of the chapter ν = t o t a l n u m b e r o f ions f r o m a s i n g l e e l e c t r o l y t e Vi = n u m b e r of ions o f a k i n d A l l other s y m b o l s a r e c l e a r l y d e f i n e d w h e r e t h e y a p p e a r i n t h e text.
Literature Cited 1. Hogfeldt, E . , Martell, A. E . , "Stability Constants," Supplement No. 1, Special Publication No. 25, The Chemical Society, London, 1971. 2. Amis, E. S., Hinton, J. F., "Solvent Effects on Chemical Phenomena," Vol. 1, Chap. 4, Academic, New York, 1973. 3. Harned, H. S., Owen, Β. B., "The Physical Chemistry of Electrolytic Solu tions," 3rd ed., Chap. 11, Reinhold, New York, 1958. 4. Gronwall, T. H., LaMer, V. K., Sandved; K., Phys. Z. (1928) 29, 358. 5. Harned, H. S., Owen, Β. B., "The Physical Chemistry of Electrolytic Solu tions," 3rd ed., Chaps. 3, 4, 11, Reinhold, New York, 1958. 6. Lewis, G. N., Randall, M., "Thermodynamics," Revised by K. S. Pitzer, L. Brewer, McGraw-Hill, New York, 1961. 7. Harned, H. S., Owen, Β. B., "The Physical Chemistry of Electrolytic Solu tions," 3rd ed., Chaps. 5, 10, Reinhold, New York, 1958.
15.
SEN ET AL.
Water-Organic Mixed Solvents
247
8. Gurney, R. W., "Ions in Solution," Dover, New York, 1962. 9. Gurney, R. W., "Ionic Processes in Solution," Dover, New York, 1962. 10. Roy, R. N., "The Activity and Other Thermodynamic Properties of Hydro chloric Acid in Tetrahydrofuran-Water Mixtures," Ph.D. Dissertation, Louisiana State University, 1966. 11. Johnson, D. Α., "The Activity and Other Thermodynamic Properties of Hydrochloric Acid in Monoglyme-Water Mixtures," Ph.D. Dissertation, Louisiana State University, 1966. 12. Johnson, D. Α., Sen, B., J. Chem. Eng. Data (1968) 13, 376. 13. Roy, R. N., Sen, B.,J.Chem. Eng. Data (1967) 12, 584. 14. Roy, R. N., Vernon, W., Bothwell, A. L. M., J. Chem. Soc. A (1971) 1242. 15. Roy, R. N., Vernon, W., Bothwell, A. L. M., Gibbons, J.,J.Electrochem. Soc. (1972) 119, 694. 16. Roy, R. N., Vernon, W., Gibbons, J. J., Bothwell, A. L. M.,J.Electroanal. Chem. (1972) 34, 345. 17. Roy, R. N., Bothwell, A. L. M., J. Chem. Thermodyn. (1971) 3, 769. 18. Roy, R. N., Vernon, W., Bothwell, A. L. M., J. Chem. Soc. Β (1971) 2320. 19. Roy, R. N., Gibbons, J. J., Bothwell, A. L. M., J. Electroanal. Chem. (1972) 34, 101. 20. Roy, R. N., Vernon, W., Bothwell, A. L. M., J. Electroanaly. Chem. (1971) 30, 335. 21. Roy, R. N., Vernon, W., Gibbons, J. J., Bothwell, A. L. M., J. Chem. Soc. A (1971) 3589. 22. Roy, R. N., Vernon, W., Bothwell, A. L. M., J. Chem. Soc., Faraday Trans. 1 (1972) 68, 2047. 23. Roy, R. N., Vernon, W., Bothwell, A. L. M., J. Chem. Thermodyn. (1971) 3, 883. 24. Roy, R. N., Bothwell, A. L. M., Gibbons, J. J., Vernon, W., J. Chem. Soc., Dalton Trans. (1972) 530. 25. Roy, R. N., Vernon, W., Bothwell, A. L. M., Electrochim. Acta (1972) 17, 1057. 26. Ibid. (1972) 17, 5. 27. Ibid. (1973) 18, 81. 28. Roy, R. N., Vernon, W., Bothwell, A. L. M., Gibbons, J. J., J. Chem. Eng. Data (1972) 17, 89. 29. Bates, R. G., Bowen, V. E., J. Res. Natl. Bur. Stand. (1954) 53, 283. 30. Harned, H. S., Owen, Β. B., "The Physical Chemistry of Electrolytic Solu tions," 3rd ed., Chap. 15, Reinhold, New York, 1958. 31. Wiberg, Κ. B., "Physical Organic Chemistry," John Wiley, New York, 1964. 32. Feakins, D., "Physico-Chemical Processes in Mixed Aqueous Solvents," F. Franks, Ed., American Elsevier, New York, 1969. 33. Harned, H. S., et al.,J.Am. Chem. Soc. (1936) 58, 1912. 34. Ibid. (1939) 61, 2374. 35. Ibid. (1941) 63, 2579. 36. Harned, H. S.,J.Phys. Chem. (1939) 43, 275. 37. Dunsmore, H. S., Speakman, J. C., Trans. Faraday Soc. (1954) 50, 236. 38. Grunwald, E., Berkowitz, B. J.,J.Am. Chem. Soc. (1951) 73, 4939. 39. Glover, D. J., J. Am. Chem. Soc. (1965) 87, 5279. 40. Shedlovsky, T., Kay, R. L., J. Phys. Chem. (1956) 60, 151. 41. Patterson, Α., Felsing, W. Α.,J.Am. Chem. Soc. (1942) 64, 1480. 42. Parton, Η. N., Rogers, J., Trans. Faraday Soc. (1942) 38, 238. 43. Morel, J. P., Bull. Soc. Chim. Fr. (1966) 2112. 44. Dippy, J. F. J., Hughes, S. R. C., Rozanski, A.,J.Chem. Soc. (1959) 1442. 45. Reynaud, R., C. R. Hebd. Seances Acad. Sci., (1966) 263C, 105. 46. Feakins, D., French, C. M., Chem. Ind. (1954) 1107. 47. Moore, R. L., Felsing, W. A., J. Am.Chem.Soc.(1947) 69, 2420. 48. Felsing, W. Α., May,Μ.,J.Am.Chem.Soc.(1948)70, 2904.
248
THERMODYNAMIC BEHAVIOR OF ELECTROLYTES II
49. Adcock, H. L., "The Determination of the Ionization Constants of Weak Acids in Mixed Solvent Systems. A Study of Medium Effects," Ph.D. Dissertation, Louisiana State University, 1970. 50. Sen, B., Adcock, H. L.,Anal.Chim. Acta (1970) 50, 287. 51. Kielland, J.,J.Am. Chem. Soc. (1937) 59, 1675. 52. Robinson, R. Α., Stokes, R. H., "Electrolytic Solutions," Academic, New York, 1959. 53. Tuck, D. G., Diamond, R. M., Proc. Chem. Soc., London (1958) 236. 54. Glueckauf, E., Trans. Faraday Soc. (1955) 51, 1235. 55. Conway, Β. E., Bockris, J. O'M., Linton, H., J. Chem. Phys. (1956) 24, 834. 56. Sienko, J. M., Plane, R. Α., Hestes, R. E., "Inorganic Chemistry," W. A. Benjamin, New York, 1965. 57. Wicke, E., Eigen, M., Ackermann, T., Ζ. Phys. Chem. (New Series) (1954) 1, 340. 58. Dennison, J. T., Ramsey, J. B., J. Am. Chem. Soc. (1955) 77, 2615. 59. Harned, H . S., Owen, Β. B., "The Physical Chemistry of Electrolyte Solu tions," 3rd ed., Chap. 12, Reinhold, New York, 1958. 60. Sen, B., Gibbons, J. J.,J.Chem. Eng. Data (1977) 22, 309. 61. Harned, H. S., et al.,J.Am. Chem. Soc. (1938) 60, 2130. 62. Ibid. (1936) 58, 1908. 63. Ibid. (1939) 61, 44. 64. Feakins, D., French, C. M.,J.Chem. Soc. (1956) 3168. 65. Harned, H. S., Thomas, H. C.,J.Am. Chem. Soc. (1936) 58, 761. 66. Oiwa, I. T.,J.Phys. Chem. (1956) 60, 754. RECEIVED February 13, 1978.
