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11 Thermodynamics of Preferential Solvation of Electrolytes in Binary Solvent Mixtures Downloaded by MONASH UNIV on December 4, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/ba-1976-0155.ch011

A. K. COVINGTON Department of Physical Chemistry, University of Newcastle, Newcastle-upon-Tyne, NE1 7RU, U.K. Κ. E. NEWMAN Department of Chemistry, University of Keele, Keele, Staffs, ST5 5BG, U.K.

The solvation changes of an ion, as the composition of a binary solvent is varied, can be treated on the basis ofnsuccessive equilibria wherenis the solvation number. From a detailed consideration of the thermodynamics of preferential solvation, it is possible to define a free energy of preferential solvation ∆G and relate it to the more familiar free energy of trans fer, ∆G determinable for a neutral combination of ions from emf measurements. The treatment can be modified to include a case of change of solvation number and to non-statis tical distribution of the solvated species. When separate sol vent NMR signals from solvation shells can be detected or mixed solvates isolated, a further development enables a satis factory explanation to be given for the observed distribution of solvated species. ө

ps

ө

ps

T

he problem of understanding the processes which occur w h e n a gaseous i o n is put into a solvent such as water has c o m m a n d e d the attention of chemists for more than 80 years. It is a k e y to the understanding of the properties of solutions and is of far reaching technological a n d theoretical importance. If the solvent is m a d e u p of two or more components, preference m a y be shown for one of these components b y the cations, anions, or both. This is the p r o b l e m of preferential solvation or of solvent-sorting i n the i m m e d i a t e v i c i n i t y , the co-spheres (I ), of the ions.

T h e r m o d y n a m i c methods, per se, are of l i m i t e d use, although they have been used extensively to u n r a v e l problems as complex as these. Nevertheless, 153

In Thermodynamic Behavior of Electrolytes in Mixed Solvents; Furter, W.; Advances in Chemistry; American Chemical Society: Washington, DC, 1976.

154

THERMODYNAMIC

BEHAVIOR O F E L E C T R O L Y T E S

studies must be made on a sound thermodynamic, or statistical thermodynamic, framework. It is the purpose of this review to provide first the thermodynamic basis for such studies and then to indicate how progress can be m a d e i n understanding ion-solvent interactions (2, 3, 4, 5, 6) using spectroscopic methods, particularly N M R i n c o m b i n a t i o n w i t h classical t h e r m o d y n a m i c studies.

Basic Thermodynamic

Treatment

G r u n w a l d , B a u g h m a n a n d K o h n s t a m ( G B K ) , i n a n appendix to a classic paper on vapor pressure studies of solvation i n dioxane a n d water mixtures (7), Downloaded by MONASH UNIV on December 4, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/ba-1976-0155.ch011

presented a n outline of a t h e r m o d y n a m i c treatment of the solvation of ions i n a mixed solvent.

It is convenient to start f r o m their general treatment but to adopt

a different nomenclature, used previously (3). Consider a homogeneous solution of w° moles of water, p ° moles of a cosolvent P and a moles of a solute X .

T h e G i b b s free energy of the system at

constant temperature and pressure is g i v e n f o r m a l l y b y G = au\ + w >

w

+

P > p

(1)

and is independent of whether the solute is considered solvated or not. However, this is not true of the solute c h e m i c a l potential. If the solvation n u m b e r of X is n w for pure water and n p for pure P , the general solvated species can be written as X W j P j where 0 ^ j ^ n w a n d 0 ^ i ^ np. T h e fraction of X existing as this general ij species is denoted b y so that average solvation numbers for water and P can be d e f i n e d nw np

hw = E

E jn

(2)

; = 0 i=0 nw np

h? = E

E iij

(3)

;=0i=0

and

= 1. A general treatment based on different solvation numbers for water and P, although physically very plausible, becomes impossibly difficult to handle later and some simplification is necessary. It w i l l be assumed that the solvation number is the same i n both pure solvents, i . e . , n w = n p = n . T h e general species now referred to as the i t h species, can be w r i t t e n as X W _ i P j a n d 0 < i < n . n

Also the average solvation n u m b e r = h = E *0t

and

E 4>i = 1

(4)

(5)

Considering now the variously solvated species i w i t h c h e m i c a l potentials ft, the free energy of the system G , can n o w be expressed as


11.

COVINGTON AND NEWMAN

155

Preferential Solvation of Electrolytes

G = a^faui

+ pjup + w/iw

(6)

where JLIW, MP are the c h e m i c a l potentials of W a n d P respectively. But w = w ° - a 2 ( n -i)(t>i p =

p

(7)

°

(

8

)

since the solvent has lost molecules w h i c h are considered part of the solute species.

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Substituting Equations 7 a n d 8 into 6 gives G = a^iUi

+ (p° — a S i ^ i W + (w° — a Z ( n — i)0o° •

(35)

— 1 +

[(K

Z

n terms

1 / n

Y ) * f l (n + 1 - i)/i] i= 1

but the denominator of Equations 34 and 35 is a b i n o m i a l expression. 0 , ° = (K^YY

ft

[(n + 1 -

Thus

+ K^nY)'

(36)

i=l

and

0o° = 1/(1 + K

Y)

1 / n

(37)

n

U t i l i z i n g Equations 36 and 37, a n d noting the identity n\/[(n-i)\i\]

(38)

= fl(n + l-i)/i

l

and also E q u a t i o n 5, one can s i m p l i f y E q u a t i o n 28 to AG

t ( x )

e m i x

= 20 ° i i

A

i

e e , e c

- Mo w) (

nRT l n / p W ) ~ B T Z i ^

e e , e c

0

+ 2(i0 /n)(AG i

l n x f °/f ? F

f

F

o

p s

e

-

- R T 2 ( n - i)i°

X l n [ ( l - x ) / w 7 / w ' ] + R T 2 i 0 i ° l n K / » Y - n R T l n (1 + K 1

P

1 / n

Y)

(39)

where a l l summations are between i = 0 a n d n .

Relation with Experiment NMR

Solute I o n S h i f t .

T h e N M R c h e m i c a l shift, a measure of changed

magnetic field at the resonating nucleus, is caused b y perturbations of the electron cloud around that nucleus. F o r organic molecules such effects m a y extend through several c h e m i c a l bonds, p a r t i c u l a r l y for conjugated systems where the 7r electron orbitals are fairly polarizable. H o w e v e r , for ionic solutes, the effects of solvent on the solute nuclei c h e m i c a l shift are u n l i k e l y to extend b e y o n d the first layer of solvent. A n y g i v e n arrangement of solvent persists for only a very short time ( 1 0 ~ sec for a l k a l i metal halides) so the observed c h e m i c a l shift c a n n


160

THERMODYNAMIC

BEHAVIOR O F

ELECTROLYTES

be f o r m u l a t e d as the weighted average of the c h e m i c a l shifts arising f r o m a l l possible arrangements of solvent a r o u n d the ion (13).

H e n c e , if the i t h species

has an intrinsic shift of 6 , the observed shift 6 is g i v e n b y t

5 =

(40)

t t=l

T o proceed further it is necessary to m a k e assumptions about how the various 5i terms are interrelated.

It w i l l be assumed (2, 3) that the contribution to the

shift f r o m each P or W molecule is additive. T h e c h e m i c a l shift 5 m a y be ex-


pressed i n terms of the shielding constants (14) 6 =

a -

(41)

j mor

i

t

t

90.6 72.6 63.8 54.9 44, 45

61.1 50.3 37.2 42

60.7 51.9 43.0 46

have studied ^ C l , B r , and I chemical shifts i n A N - w a t e r as w e l l as uv C T T S iodide a n d b r o m i d e bands. Bloor a n d K i d d (45) have obtained N a shifts, a n d Stockton a n d M a r t i n (46) have used a proton N M R technique similar to that of C o g l e y a n d co-workers to obtain apparent association constants for an ion i n A N - r i c h solutions. C o m p a r i s o n of observed a n d calculated values of A G ° is shown in Table III. Agreement is good i n spite of the experimental uncertainties in the data d e r i v e d f r o m both t h e r m o d y n a m i c a n d spectroscopic sources. It is encouraging that solvation trends w i t h c h a n g i n g ion size are predicted well. 3 1

1 2 7


2 3

t

D I O X A N E A N D W A T E R . G r u n w a l d and co-workers ( G B K ) (7) used a vapor pressure method to obtain the differential of the free energy of transfer of a solute w i t h respect to solvent mole fraction at 50 w t % dioxane. O n the basis of what has now become k n o w n as the large-ion assumption (8), they separated cation and anion effects by equating the free energies of transfer for tetraphenylborate and tetraphenylphosphonium ions. T h e y concluded that N a was preferentially solvated by dioxane, a surprising result then, but less unexpected n o w that complexes of the alkali metals w i t h polyethers have been discovered (dioxane +

0-2

0-4

0-6

mol f r a c t i o n dioxan

Figure 9. Infinite dilution Na shifts in dioxane and water mixtures (47). Vertical bars indicate the experimental uncertainty 2S


11.



173

is a cyclic diether). Figure 9 shows ^ N a chemical shifts of N a l i n dioxane-water mixtures (47). Solubility problems restrict the studies to X? = 0.3. T h e data are limited and experimental uncertainties are large, but the evidence clearly supports the preferential solvation of N a b y dioxane not water. A n approximate value for the c h e m i c a l contribution to the free energy of transfer can be estimated as —18 ± 9 k j m o l (assuming n = 4). +

- 1

A f a i r l y large n u m b e r of solvents of such p u r i t y

N O N A Q U E O U S SYSTEMS.

as to make reasonably precise p h y s i c o c h e m i c a l measurements possible are now available (48). Knowledge of the physical properties of mixtures of these is often Downloaded by MONASH UNIV on December 4, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/ba-1976-0155.ch011

l a c k i n g except where one component is water. formation is being accumulated.

G r a d u a l l y , however, more i n -

Greenberg and Popov (49) have made the first

systematic study of the solvation of N a ions using N a shift measurements i n +

2 3

all b i n a r y mixtures of seven solvents (nitromethane ( N M ) , acetonitrile, hexamethylphosphoramide, dimethylsulfoxide, p y r i d i n e (Py), a n d tetramethylurea). Results were analyzed i n terms of E q u a t i o n 66 to obtain the free energies of preferential solvation and b y the location of the equi- or iso-solvation point (20). This is the point at w h i c h both solvents participate equally i n the solvation shell. It occurs at the composition at w h i c h the chemical shift lies m i d w a y between the values for the pure solvents, hence at 5 / 5 = 1/2 i n E q u a t i o n 65. H o w e v e r , the P

5 values do not relate to i n f i n i t e d i l u t i o n but to a finite concentration (0.5 M ) of sodium tetraphenylborate.

T h e concentration dependence m a y be slight, but

in v i e w of the low dielectric constant of m a n y of these solvents i o n pairs w i l l be present a n d the dependence w i l l then be non-linear.

T h e observation that d i f -

ferent salts apparently do not extrapolate to the same infinite dilution value (50) causes concern.

N o r m a l i z e d results (5/5p) for acetonitrile as c o m m o n solvent

are shown i n Figure 10. F r o m the values of free energy of preferential solvation, a d d i t i v i t y checks are possible.

F o r example,

NM A N AG Py ««— N M Py « — A N Py

AN(calc)

p s

© > - 4 . 4 1 =*= ° ° = -5.51 ± 0.13 k J mol" =-2.10 ± 0.47 k J mol" 2 3

k

J

m

r

l

1

1

=-1.10 ± 036 k J m o F

1

A l t h o u g h just outside the estimated errors, this a d d i t i v i t y check is encouraging (bearing i n m i n d the reservations mentioned above).

Some systems d o

not give very good straight line plots with Equation 68. Hence, additivity checks i n v o l v i n g these are suspect.

F u r t h e r w o r k of the comprehensive, systematic

nature of G r e e n b e r g a n d Popov is necessary.

Nonstatistical Distribution of Solvated Species T h e introduction of the last t e r m i n E q u a t i o n 27, the statistical factor for the n u m b e r of ways of arranging i P molecules a n d (n — i ) W molecules i n the



Figure 10. Normalized Na chemical shifts in some binary solvent mixtures involving transfer from acetonitrile (49). DMSO = Dimethylsulfoxide; HMPT = Hexamethylphosphotriamide; TMU = Tetramethylurea; MeN0 = Nitromethane; Py = Pyridine 2S

2

solvation shell, leads to E q u a t i o n 33 relating values to the constant for the overall process a n d hence to a statistical distribution of the solvated species, as shown i n F i g u r e 11. H o w e v e r , the process of substituting solvent molecules P for W i n the solvation shell m a y not take place w i t h e q u a l facility for each step. Thus the solvent exchange process m a y become more or less energetically favorable as the shell becomes richer i n P. In the general case, some simplification is necessary. T h e constant for the first step c o u l d be assumed to be very m u c h larger than those r e m a i n i n g (9), w h i c h m a y then be related statistically. A m o d i f i e d m o d e l has been adopted (5), i n w h i c h the free energy change for substitution of one W by one P changes by RT l n k for each successive step. A related approach has been used i n another connection b y Stokes a n d Robinson (51) a n d the treatment is also similar to Bjerrum s spreading factor (x) introduced to explain variation i n the ratios of successive constants i n c o m p l e x - i o n e q u i l i b r i a (12). It m a y be noted that x = k~ / ; B j e r r u m applied x to each step but here k is applied to the second a n d subsequent steps only. 1

2



11.


Figure

11.


175

distribution

of solvated species for K = 1.0 and n = 4

K/+!

ki(n — i)

K/

(i+ l ) ( n - i + l)

Statistical

T h e ratio (71)

and for the i t h step _

K

i + 1^

=

J t
w h i c h c a n be obtained f r o m the e x p e r i m e n t a l values of 0i i n the region where no b o u n d acetone c a n be detected i n the spectra, it is possible to obtain K = (1.1 ± 0.4) X 1 0 " . 3

± 3 kJ m o l . - 1

W i t h n = 6, this leads to A G ^ / = - 6 3

Some values of 0 d e r i v e d f r o m T o m a a n d c o - w o r k e r s ' experit

mental results (62) for 185 K and Z = 1.6 are included i n Table I V , but it has been assumed that the water to m a g n e s i u m concentration ratio was slightly greater than stated.

Using a 220 M H z instrument, these workers (62) were able to resolve


11.



Species i n M g ( C 1 0 ) — A c e t o n e — W a t e r 4

187

System

2

in parentheses)


03 0.01 0.04 0.12 0.19 0.27 0.32 0.24 0.12 0.03

0

(0.01) (0.02) (0.08) (0.16) (0.25) (0.31) (0.23) (0.11) (0.04)

0.04 0.08 0.15 0.24 0.31 0.32 0.24 0.10 0.03

4

(0.02) (0.06) (0.12) (0.24) (0.31) (0.32) (0.23) (0.09) (0.03)

0s 0.18 0.32 0.36 0.36 0.30 0.19 0.06

0 0.78 0.59 0.45 0.25 0.12 0.05

(0.18) (0.30) (0.37) (0.39) (0.33) (0.22) (0.09)

6

(0.80) (0.63) (0.49) (0.28) (0.15) (0.06)

further the spectra involving the 4 (dihydrate) species a n d to detect its isomeric forms (53) shown below.

T h e presence of such isomeric solvates m a y account for the a s y m m e t r y noted (62, 6) when carrying out the curve resolution of the 9 0 - M H z spectra, but, within the accuracy attainable, the effect is barely significant.

There are discrepancies

i n the values for the intrinsic shifts of the solvated species recorded b y a l l three groups of workers (but differences between successive solvates are more satisfactory).

T o m a a n d co-workers calculated (62) the theoretically expected a n d

isomeric differences between successive solvates, obtaining reasonable agreement w i t h observed values (Table V ) . S i m i l a r calculations w o u l d be possible w i t h the system A l ( C l 0 4 ) 3 i n D M S O - H 0 studied b y O l a n d e r , M a r i a n e l l i , a n d L a r s o n (63), but the actual 2

experimental results are not available.

The M g

2 +

system i n m e t h a n o l - w a t e r

has been studied several times (64, 65) a n d appears to be more complex i n the interpretation of the spectra obtained.

A g a i n detailed systematic measurements

at one temperature a n d a range of solvent compositions are not available.


188

THERMODYNAMIC

Table V . ATo. of Moles WaterlMg

2+


6 5 4 3 2 1

BEHAVIOR O F

ELECTROLYTES

Observed C h e m i c a l Shifts o f M i x e d Solvates o f M g Acetone—Water (5/ppm)

2 +

in

Reference 62

6

61

7.08 7.00 6.89 6.76 6.61 6.45

7.16 7.02 6.96 6.84 6.67 6.50

7.12 7.03 6.95 6.84 6.66 6.50

Calc,

62

7.08 (assumed) 6.98,6.93 6.84,6.79 6.71,6.67 6.58,6.54 6.45 (assumed)

It is interesting to speculate whether confirmatory experiments on the M g system i n acetone-water could be made using ^ M g resonance.

2 +

It was concluded

(6) that for K = 10~ the distribution of 0*° values would be that shown i n Figure 3

20 a n d hence the interesting region where m a x i m a i n fa values occur is experimentally inaccessible because of the extremely l o w water concentrations ( x w

l-OO

005

Ol mol fraction of woter Journal of the Chemical Society, Faraday I

Figure 20. Predicted variation of fa ° values with mol fraction of water for K = 10 ~ in magnesium perchlorate-acetone-water system. 3


11.


189


< 10~ ) w h i c h w o u l d have to be attained. 2

T h e weak signals f r o m

2 5

M g w i t h an

isotopic abundance of 10% makes the experiment even m o r e d i f f i c u l t . E . L . K i n g a n d co-workers (66, 67, 68) have studied the solvation of C r ions i n w a t e r - m e t h a n o l , - e t h a n o l , a n d - d i m e t h y l s u l f o x i d e mixtures.

3 +

Species

containing up to six bound organic molecules have been separated f r o m each other b y cation exchange c o l u m n procedures. values of this section.

If the C r

these are effectively fa ° values.

3 +

Analysis of these species yields the fa

concentration is low i n the o r i g i n a l solution,

Attempts to fit K i n g s data for these three systems

yield K = 0.07(MeOH), 0.03(EtOH), and 0.2(DMSO).

T h e last is illustrated i n

F i g u r e 21. T h e fa values were calculated f r o m Equations 36 a n d 37 (with y


replaced b y y? as necessary) b y selecting a value of K b y trial a n d error w h i c h most closely fits all the fa data.

F o r clarity, only a few experimental points have

been shown on F i g u r e 21, the scatter b e i n g consistent w i t h the estimated experimental error.

This approach contrasts with King's analysis to obtain e q u i l i b r i u m

quotients for the f o r m a t i o n of the solvate species m a k i n g correction f o r solvate mixture non-ideality.

As a result, the quotients for the successive equilibria were

f o u n d to be m e d i u m dependent.

Discussion and Criticisms of the Present Approach T h e basic assumption of the present treatment is that the c h e m i c a l shift of an ionic nucleus is dependent on its immediate magnetic environment and hence gives a measure of changes i n the p r i m a r y solvation sphere of the i o n as the composition of the b u l k solvent m i x t u r e is changed.

A n obvious l i m i t a t i o n of

the treatment is the need to assume a value for n , the solvation n u m b e r , if spectroscopic and t h e r m o d y n a m i c data are to be compared.

It must be stressed that

this solvation n u m b e r is s i m p l y the n u m b e r of solvent molecules i m m e d i a t e l y surrounding the ion. This w i l l not necessarily be the same as the solvation number determined b y other methods (69) w h i c h take into account b o n d i n g interactions. A n y configuration about a n a l k a l i metal ion w i l l have a very short l i f e t i m e , a n d it is unrealistic to think i n terms of rigid solvation shells.

In contrast, some workers

consider cesium ions u n h y d r a t e d i n aqueous solution, a n d the h y d r a t i o n of the chloride ion is often set to zero i n order to split into ionic contributions the results f r o m methods w h i c h measure h y d r a t i o n numbers for salts.

Solvation numbers

d e t e r m i n e d f r o m r a d i a l distribution functions d e r i v e d f r o m x-ray scattering experiments (34, 70) are the most appropriate to the present considerations.

It

is unfortunate that there remains some disagreement between the experts about the analysis a n d interpretation of such data (71).

A further distinction should

be made between ordered and disordered solvation shells (46) d e p e n d i n g on the strength of the i o n - m o l e c u l e interaction (72).

A trend m a y occur i n a series of

increasing ionic radius, but there w i l l certainly be a clear distinction between, for example, a solvated N a a n d a n A l +

3 +

nation positions for solvating molecules.

i o n w i t h octahedrally directed c o o r d i T h e r e i n lies the p r o b l e m of whether


T H E R M O D Y N A M I C BEHAVIOR

OF

ELECTROLYTES


190


11.


191


to take into account the symmetry of such solvates i n a consideration of the likely behavior of ions f o r monodentate vs. bidentate solvating molecules. T h e solvation numbers of ions such as M g

2 +

, Al

3 +

, and B e

2 +

mined by low temperature P M R techniques as mentioned earlier.

m a y be deterT h e solvation

number for small spherical ions m a y be determined i n certain circumstances using a titration technique suggested b y V a n Geet (15).

It is based o n the competition

by water for the solvation sphere of s o d i u m ions i n t e t r a h y d r o f u r a n ( T H F ) measured b y ^ N a shifts.

T h e salt must contain a large anion, w h i c h is assumed

to be u n h y d r a t e d d u r i n g the titration; otherwise a sum of h y d r a t i o n numbers w o u l d be d e t e r m i n e d .

T h e assumptions m a d e b y V a n Geet are basically those


of the present treatment.

H i s apparent constant is for the reverse of the e q u i -

l i b r i u m of E q u a t i o n 21 a n d c a n be i d e n t i f i e d as 1 / K [ P ] , where [P]j? is the free F

T H F concentration, effectively constant i n the early stages of the titration. U s i n g Equations 88 a n d 47 a n d r e c o g n i z i n g that 1 - — = - 2 (n -

= — —

n

Op

(92)

n[Aj7

where S ( n — i ) 0 i is the average solvation n u m b e r of W , that is, the n u m b e r of moles of bound W per mole of solute ion X , then, or alternatively f r o m E q u a t i o n 65, 1 - - * 6p

— 1 + K[P] /[W]

(93)

l

F

F

This can be rearranged, since Z = [ W ] j / [ X ] r , to Z

K[P]

l-d/d

?

U

F

[X] b/b T

?

This is E q u a t i o n 14 of V a n Geet (15) i n the present nomenclature.

A plot

( F i g u r e 22) of the left h a n d side against 1 /b gives n f r o m the intercept, w h i c h can be located w i t h reasonable accuracy if the slope is s u f f i c i e n t l y h i g h .

For

sodium tetraphenylborate, least squares data f i t t i n g gave n = 3.0 or 3.7 f o r 0.75 or 0.48 mol/1 solutions, respectively.

T h e presence of i o n pairs w o u l d interfere

w i t h this method but it was concluded they were not present i n T H F . It remains to be seen whether this m e t h o d c a n be used f o r other ions i n different solvents. T h e second basic assumption of the present treatment concerns the intrinsic c h e m i c a l shifts or shielding constants of the m i x e d solvate species. proportional to the amounts of co-solvent P w h i c h they contain. evidence for the v a l i d i t y of this comes f r o m the studies of A l

3 +

These are

Some further

solvates b y D e l -

p u e c h a n d co-workers (58), w h o f o u n d that w h e n substituting a water molecule by an organic l i g a n d shift changes were a p p r o x i m a t e l y a d d i t i v e (3.5 p p m per substitution) as shown i n T a b l e V I . Some of the data analysed using the approach of the present treatment have related to solute chemical shift or u v peak m a x i m a shifts measurements at finite solute concentrations.

I n order to assume that i o n - i o n interactions do not i n -


THERMODYNAMIC


5

K>

BEHAVIOR O F

15

ELECTROLYTES

20

z/(l-6/6p)

Journal of the American Chemical Society

Figure

Table V I . No. of Moles Water/Al 3+

2 7

22. Evaluation of n for Na THF-H2O after Van Geet (15)

in

+

A1 Chemical Shifts (ppm) o f A l N i t r o m e t h a n e (58) P = PO(OMe)

MePO(OMe),

3

6 5 4 3 2 1 0

3 +

0 3.7 6.7 10.0 14.0 17.5 20.5

Solvates i n

HPO(OMe)

2

0 3.5 6.8 10.1 14.8 17.5 20.2

0 3.3 6.6 9.1 14.0 15.9 17.7

Journal of the Chemical Society, Chemical Communications

02

04

0-6

OS

Figure 23. Effect of solute concentration on the derivation of K from chemical shift or peak maxima shift data, upper full line m' = 0 (infinite dilution), K = 5 (assumed); — m/ = 1; m = 2; lower full line m' = 3 (the apparent value of K falls to 3.61) r


11.



193

terfere, any solute concentration dependence on the shifts should be checked and, if necessary, extrapolation to zero solute concentration c a r r i e d out.

A second

effect of using data relating to finite solute concentrations is that the solvent mole fractions i n the b u l k solvent m a y be significantly different f r o m stoichiometric solvent mole fractions because of the quantity of solvent i n the ionic solvation spheres.

This was discussed i n connection w i t h G r e e n b e r g a n d Popov's studies

described earlier.

F a i l u r e to observe this difference especially w h e n K is very

large or very small can lead to significant errors as illustrated i n F i g u r e 23, w h i c h was p r o d u c e d b y a computer iterative procedure based on the solution of


E q u a t i o n 65 w i t h 95, m'n

yp

Y„-

/ r

.

(«/8p) 5

5

5

- • - s s i '

(95)

1

1

- " / "

1

where m' is the aquamolality of the solute ion. T h e error i n A G for m' = 1 a n d K = 0.5.

p s

e /

is about 12%

F i n a l l y , m e n t i o n must be m a d e again of the apparent compensation of activity coefficient terms so that the solvent mixture is effectively treated as ideal. The experimental evidence f r o m the constancy of the right hand side of Equation 66 w i t h variation of solvent composition for a variety of solvent mixtures irrespective of the solute is strong. It is supplemented b y a simple treatment, ignoring solvent activities, of the directly d e t e r m i n e d fa data f r o m the w o r k of K i n g . These l e n d support to modifications to the theory postulating non-statistical distribution of K values or change of solvation number w h e n the right h a n d side of E q u a t i o n 64 is not apparently constant. F u r t h e r light is shed on this p r o b l e m x

by treating preferential solvation b y the K i r k w o o d - B u f f theory (73) w h i c h w i l l be the subject of a paper presented elsewhere (74). There is a discrepancy between the results arising f r o m the choice of standard states i n the two treatments, w h i c h suggests that a shortcoming of the thermodynamic treatment is the failure to take into account v o l u m e changes i n the solvation shell as its composition changes. M o l e c u l a r m o d e l considerations suggest that for some systems the v o l u m e c o u l d change b y a factor of u p to ten. T a b l e V I I collects the results for all monovalent i o n systems for w h i c h spectroscopic data are available. Studies of preferential solvation are still at a stage comparable to the establishment of Raoult's a n d H e n r y ' s laws for b i n a r y nonelectrolyte solutions. Correlation w i t h thermodynamic data is encouraging for isodielectric solvent systems, but further consideration of the electrostatic terms necessary i n the discussion of other systems is r e q u i r e d . It is h o p e d that this present work, which coordinates, correlates, and advances progress made by other workers (7, 18, 19, 20, 45, 46, 61, 62, 66, 67, 68), w i l l stimulate systematic exp e r i m e n t a l investigations of suitable systems b y both spectroscopic a n d therm o d y n a m i c methods.


194

THERMODYNAMIC

Table V I I . Ion Li Li Li Na Na Na Na Rb Rb Cs Cs Cs Cs 19p 19p 19p C1 C1 CI C1 Big,. Br- (CTTS) 12 7J I- (CTTS) 127J N 0 - (n - 7T*) N O 3 - (n -> 7T*) 7

7 7

2 3

2 3

2 3 2 3

8 7

8 7


, 3 3

1 3 3 1 3 3

1 3 3

35

35

3 5 3S

3

Preferential Solvation*

Solvent

mixture

H 0*-H 0 H 0-DMSO DMA-DMSO* H 0-H 0 H 0*-MeOH AN-H 0* en*-H 0 H 0-H 0 * H 0*-MeOH H 0-H 0 * H 0-DMSO* H 0-sulpholane* H 0*-MeOH H 0-D 0 H 0-H 0 * H 0-MeOH H 0-H 0 H 0*-MeOH H 0*-AN H 0-DMSO H 0-MeOH AN-H 0* AN-H 0* AN-H 0* H 0-DMSO* DMSO*-H 0 AN-MeOH* 2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

BEHAVIOR O F ELECTROLYTES

2

2

2

2

2

K

k

0.49 0.98 1.25 0.98 0.60 0.31 2.3 1.96 0.70 2.81 1.04 2.09 0.77 1.0 2.38 0.96 1.0 0.68 0.07 1.0 1 0.17

2 4 4 2 3 45 45 2 32 2 4 16 16 24 2 29, 32 2 30 44 44 30 77

0.35 2.5 1.68 0.5

0.75 0.5 1.26 0.7

44 44 1 78

2

2

2

2

Ref.

1 1.38 1 1 1 0.8 0.8 1 1 1 1.12 1.25 1 1 1 1 1 1 0.9 1 1 0.75

The preferentially solvating component is indicated by an asterisk (*). K is for the formation of a solvated species containing the second mentioned solvent component. CTTS = charge transfer to solvent. a

The treatment has wide applicability to coordination chemistry and to other solution phenomena.

F o r example, aspects of it have been a p p l i e d b y L i l l e y to

an explanation of salting-out a n d salting-in phenomena (75) a n d to weak interactions i n b i n a r y nonelectrolyte mixtures i n a t h i r d solvent (76).

Ackno wledgmen ts This work was supported b y grants f r o m U n i l e v e r , L t d . , Port Sunlight R e search Laboratory, a n d the Science Research C o u n c i l . C o n t r i b u t i o n s to this research were made b y G . A . Porthouse, I. R. L a n t z k e , T . H . L i l l e y , Jennifer M . T h a i n , and A . D . Covington. O u r thanks are given especially to the last two w h o contributed some of the figures illustrating this review. W e are also grateful to J. C l i f f o r d , D . G . H a l l , W . H . Beck, R. A . Matheson, a n d R. A . Robinson f o r valuable a n d stimulating discussions d u r i n g the course of the development of the research, to E . L . K i n g (Boulder, Colorado) for d r a w i n g our attention to the


11.



195

problems arising f r o m the s y m m e t r y of m i x e d mono-bidentate complexes, to A. I. Popov for letting us see his results prior to publication, and to J. W . Akitt and M . N . S. H i l l for help w i t h the experimental N M R aspects. O n e of us ( A . K . C . ) thanks the R o y a l Society a n d the U n i v e r s i t y of Newcastle-upon-Tyne for travel grants w h i c h made possible the presentation of this paper at the 170th A C S M e e t i n g i n C h i c a g o .


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THERMODYNAMIC BEHAVIOR O F ELECTROLYTES

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