91 (1972) RECUEIL 1225

ACTIVITY COEFFICIENTS OF SINGLE IONS (V) IN ACETONE AND ACETONE- WATER MIXTURES

BY

D. BAX, C. L. de LIGNY and A. G. REMIJNSE (Laboratory for Analytical Chemistry*, State University, Utrecht)

A method for the estimation of standard chemical potential differences (Ap') of single ions for the transfer from one solvent to another, described previously, is further improved and applied to the transfer from water to acetone and acetone-water mixtures.

With some reservation a value of the surface potential x of acetone is derived.

1. Introduction

A method for the estimation of the difference of standard chemical potentials (Ap") of single ions in two solvents was described recently. The method was applied successfully to the transfer from water to N-methylformamide', methanol and methanol-water mixtures' and to ethanol and ethanol-water mixtures3. In the present paper the method is further improved and applied to the transfer from water to acetone and acetone-water mixtures.

2. Theory

In the foregoing papersZp3, it was shown that for hypothetical M+ and A- ions of equal radius the following equation holds for the transfer from solvent S to solvent S':

* Address: Croesestraat 77A. Utrecht. The Netherlands. c. L. de Ligny, Miss H . J . M . Dmesson and M . Alfenaar, Rec. Trav. Chim. 90, 1265 (1971). D. BKY, c'. L . t k Li,qnj. and M . A//kwtior, ihid 91, 452 (1972). D. BN.Y, C. L . t h L i g t ~ j . and A . G. R~nlijnsc,, ihid. 91, 965 (1972).

1226 D. Bax et ul.

where A& = Ap' of the H+ ion N = Avogadro's number e = elementarycharge 0 = quadrupole moment of the solvent molecules S and S',

respectively r +a = distance between the centres of the ion and of the solvent

molecules in the primary solvation layer p = dipole moment of the solvent molecules S and S, respect-

ively C; and C; are constants depending on the number of coordinated

solvent molecules around the M+ and A- ions.

Equation [l] can be rearranged to:

C;N k0, -- CiNe 0, A& - +A&, + iApi - ~

2 (r + 2 (r + q)"

The term (A& - $A&, + 3Api) can be determined experimentally, in our case for r values ranging from 1.81 8, (Cl-) to 4.09 8, (n-Bu4N)*. The last two terms of the left hand side of equation [2] can be calculated for any value of r, if q, k and 0, are known. The factor B can be calculated for the same values of r if q. and h, are known. From a plot of the left hand side of equation [Z] vs. B, A& and eS+ can be deter- mined.

* Me = methyl group n-Bu = n-butyl group Fic = ferricinium ion n-Pr = n-propyl group Foc = ferrocene Ph,B = tetraphenylboride ion.

Activiry coefficients of single ions ( V ) 91 (1972) RECUEIL 1227

3. Compilation of data for the determination of Ap" of single ions According to the theory the following data are required:

1. the values of A& - A& and h& + A&, 2. the values of the radii rA and rM, and

3. the values of a, p and 0 of H,O and of a and p of acetone.

3.1. Values of A& - A& and A& + A& Values of A& - A& and A& + A& have been computed from Ap" values of a number of electroneutral combinations of ions, and are given in Table I.

Avo values of K, Rb, Cs, Me4N, n-Pr4N and n-Bu4N perchlorates* for the transfer from water to acetone and acetone-water mixtures have been reported previously4. The same applies for Ap" values of KC1 for the transfer to acetone water mixtures5. The value for the transfer to acetone was computed from solubility data of KC1 in 80% and 100% acetone4. The solubility of KCl in acetone is known6, but not very accurately. Therefore both solubilities were redetermined.

Api - A&, + A&,,* for the transfer to acetone-water mixtures was calculated from Vedel's E values' of the Fic/Foc couble. For the transfer to acetone this quantity was determined by the authors. A&.,, was calculated from solubility data' as described previo~s ly~.~ .

Data on the solubility of K, Rb, Cs and NH4-Ph4B* in acetone and acetone-water mixtures are knowng. From these data A& - has been calculated as described previously4 **. Ap' of KReO, has also been calculated from solubility data. The solubility in water is known", the solubility in acetone was determined by the authors.

Ap" values of HX, where X=C1, Br and I have been calculated from E" data of the Ag,AgX electrode in water and in the solvent mixtures used. A review of these E" data has been published previously". *

** 4

5

6

See note on the previous page. The NH; ion behaves very strangely in acetone and acetone-water mixtures, accord- ing to these data. This fact raises some doubt on the reliability of these data. C. L. de Ligny, D. Bax, M . AlJenaar and Miss M . G . L . EIJerink, Rec. Trav. Chim. 88, 1 I83 (1969). D. Eax, M. Aljenaar and C. L. de Ligny, ibid. 90, 1002 (1971). A. Lannung, Z. physik. Chem. A161, 255 (1932).

' J. Vedel, Ann. Chim. 2, 335 (1967). * C. BarraquP, J. Vedel and B. TrPmillon, Bull. SOC. chim. France 3421 (1968).

A . N. Kirginisev and V. P. Kozitskii, Izvest. Akad. Nauk SSSR 6, 1 170 ( I 968).

D. Bax, C. L . de Ligny, M . Alfenaar and Miss N. J. Mohr, Rec. Trav. Chim. 91, 601 (1972).

l o G. R. Haugen and H . L. Friedman, J. Phys. Chem. 12, 4549 (1968).

M

K+

R

b'

cs+

M

e,N

+ n-

Pr,N

+ n-

Bu,

N'

Fic'

-168

2 k

45

-154

4 f

104

-144

4 f

105

- 8

58 f 1

04

A

- 1

373

f 57

8 -1

179 f 5

90

- 1 I

06 f 5

90

- 42

8 f 5

89

CI -

Br-

I-

ReO

; Ph

,B-

c10;

838 f- 2

33

8 * 7

-

420 * 9

-1

113

& 6

8

- 463

5

Tab

le I

1737

k 1

2 10

16 f 1

2 -

191 k

12

-116

7 k 6

7

- 87

26

Val

ues

of A

&

+ A

pl a

nd A

& - A

&

and

thei

r sta

ndar

d er

rors

for t

he tr

ansf

er

from

wat

er to

ace

tone

and

ace

tone

-wat

er m

ixtu

res,

at 2

5°C

(mol

ality

sca

le).

Val

ues

of th

e io

nic

radi

i hav

e be

en t

aken

fro

m re

fs.

1-3.

1.33

I .

48

I .67

2.

70

3.74

4.

09

3.30

1.81

1.

96

2.19

2.

45

2.65

4.

21

% ac

eton

e in

the

solv

ent

7.20

mol

e %

17

.1 m

ole

%

31.8

mol

e %

55

.4 m

ole

%

20.0

wt

40.0

wt

%

60.0

wt

80.0

wt

%

100

x A

& - A

&

[cal

.mol

e-'1

-557

f 1

1 -5

73

f 66

-4

81

f 66

-2

75

f 66

25

6 f

68

661 f 7

0 15

2

333 f

2 6

6f

7 -2

65 f

9 -6

09

k 4

9

- 20

90

-108

6 &

37

- 9

91 &

83

- 8

91 &

84

- 5

21 *

83

1381

& 8

7

- 1

06

- 1

494

f 26

-1

341

f 87

- 1

239

f 87

-

767 f 8

6 11

23 f 8

7

- 25

2

A&

+

Api

[ca

l.mol

e-'1

3744

f

12

2674

f

14

784

k

21

- 3

18 f

84

- 92

95

1262

2 f

23

1051

9 f

44

2951

f

585

1807

f

587

- 94

9 1

- h)

N

W

Activity coejjicients of single ions ( V ) 91 (1972) RECUEIL 1229

3.2. Values of a, p and 0 For water a = 1.4 A‘’ and p = 1.85 x ~ s u ’ ~ . For acetone a has been obtained by averaging the radius calculated from the van der Waals volumei4 (2.49 A) and the Lennard-Jones distance parameter”. Values of O,,,, are known12 (Table 11), OaOetone is equal to the slope of the line representing equation [2] (Table V). Calculations were made

on the basis of four different models for the solvation: I coordination number 4, hard sphere ions and solvent molecules,

I1 coordination number 6, hard sphere ions and solvent molecules, I11 coordination number 6, repulsion energy proportional to (r + a)-’,

r + a IV coordination number 6, repulsion energy proportional to exp. ---

P with p = 113

An infinite number of values of r may be used to calculate the line representing equation [23. Calculations with seven r values gave no substantial improvement over calculations with four r values. Therefore the following values were used: 1.81, 1.96,2.19 and 2.45 A corresponding with the radii of C1-, Br-, I- and ClO;.

Table I1

Values of the quadrupole moment of water and of the constants C3” and C,” in equations [ 1-33 for the four models chosen.

Model

IV

1.9 4

1.4 6

4 *.O I

C,“

135 64

-- Jz 9 8

- - ( 6 , / 5 + 1)

5 8

- - (6 , /5 + 1)

9 r + a - $ A 8 r + a

- - (6 , /5 + I )

H. I? Halliwell and S. C. Nyburg, Trans. Faraday SOC. 59, 1126 (1963).

Cleveland, Ohio (1963).

J. 0. Hirschfelder, C. I? Curtiss and R. B. Bird, “Molecular Theory of Gases and Liquids”, J. Wiley and Sons Inc., New York (1967).

I 3 “Handbook of Chemistry and Physics”, 44th Edn. Chemical Rubber Publishing Co.,

l4 A . Bondi, J. Phys. Chem. 68, 441 (1964).

I6 D. Cubicciotti, J. Chem. Phys. 31, 1646 (1959).

I230 D. Bax CI al

4. Experimental section

4.1. A&, and AP;Rco4 The solubility of KCI in 80% acetone was determined by evaporation of the saturated solution and weighing the residue. The solubility in 100% acetone was determined coulometrically as described by Krijgsrnan et al.". (We are indebted to these authors for performing the determination.) The solubility of KReO, in acetone was determined by evaporation and weighing. The results are given in Table 111.

4.2. A& - A&ic + A l i O c A& - A&= + Ap;= for the transfer from water to acetone ias been calculated from polarographic measurements as described previously3 with some modifications as specified.

The halfwave potential E, was measured against a Ag,AgCI electrode. A mixture of Et,NC104* (0.009 molal) and LiCl (0.001 molal) was used as carrier electrolyte. The standard potential of the Ag,AgCI electrode in acetone is known".

The results are as follows:

Ef,Fi; = - 606.8 mV AE& = 313.4 mV

A& - A& + = -4921 calmole-',

where Ef,Fic = polarographic halfwave potential of the Fic/Foc couple in acetone referred to the standard hydrogen electrode in the same solvent, AE& = E;: (in ace- tone) - EE: (in water) and E"* = standard potential of the Fic/Foc couple referred to the standard hydrogen electrode in the same solvent.

5. Results

S.1 Apo values of single ions in acetone The line representing equation [2] was calculated using the least squares method. The resulting values of A& and their standard errors, calcu- lated on the basis of the four solvation models, are given in Table IV. Values of Oacetone and their standard errors are also given in Table IV.

For further calculations the value of A& based on model I1 was used since it is approximately the average of the results of the four models used. The Ap" values of the other ions investigated, based on these data, are given in Table V.

* Et = ethyl-group. W. Krijgsrnan, W. P . van Bennekom and B. Griepink, Mikrochim. Acta 42 (1972).

Tab

le 1

11

Ap0

of K

C1

and

KR

eO,

for t

he tr

ansf

er f

rom

wat

er to

som

e so

lven

ts*.

d ~

g.c

m-~

]

0.85

0

0.79

0

0.79

0 0.

998

0.79

0

salt

m

A [m

ole.

kg

[A]

solv

ent-'

]

4.10

54

.09

x

4.10

12

x

4.10

31

.8

x

4.30

3.

99 x

4.30

13

.8

x lo

-,

KC

I K

Cl

KC

I K

ReO

, K

ReO

,

solv

ent,

acet

one

wt

%

msa

, [m

ole.

kg s

olve

nt-

'3 2R

T In

my*

[c

al.m

ole-

'1

KA

Ckg

.mo1

e-l:

AP"

[cal

.mol

e- '3

H20 + S

44

708

708 0.

77

708

80.0

100

100 0

100

(88.

40 k 0

.67)

x

12 x

10

-6**

(3

1.8

& 0

.3) x

10-

6t

4.08

x

(24.

0 f 0

.8)

x

* m

a, =

solu

bilit

y (m

olal

sca

le).

K,

= a

ssoc

iatio

n co

nsta

nt, i

n al

l cas

es ta

ken

equa

l to

that

of K

C10

, '.

d =

den

sity

of t

he s

atur

ated

sol

utio

n, ta

ken

equa

l to

that

of t

he s

olve

nt4.

A

= io

n si

ze p

aram

ete?

. m

=

u q

a,.

CL

=

deg

ree

of d

isso

ciat

ion.

th

e st

anda

rd e

rror

was

cal

cula

ted

as d

escr

ibed

pre

viou

sly4

. **

at 2

5°C

; by

linea

r in

terp

olat

ion

betw

een

18 an

d 37

°C.

***

final

val

ue A

&,

= 1

4000

_+ 58

0 ca

l.mol

e- '

t m

easu

red

in o

ur la

bora

tory

.

- 4

336

-134

82

- 1

2327

- 4

938

- 8

118

5426

k 43

' 14

572

1341

7***

0

3180

i 1

01

Tab

le I

V

Ap"

[kca

l.mol

e - '1

40.0

wt

%

60.0

wt

%

80.0

wt

%

100%

-1.8

1 0.

02

-2.9

1 f 0

.03

-4.2

3 f 0

.14

-4.4

0 f 0

.65

- 1

.90

5 0.

02

-3.0

1 f

0.02

-4

.43 f 0

.30

-4.9

1 f 0

.68

- 1

.88

& 0

.02

-3.0

4 f 0

.03

-4.4

3 f 0

.14

-4.1

9 f 0

.61

-2.1

2 It:

0.0

2 -3

.48 f 0

.02

-5.2

0 f 0

.13

-6.1

6 f 0

.14

Val

ues

of Ap,?, a

nd o

f OaC

CIo

nC

for

the

tran

sfer

from

wat

er to

ace

tone

and

ace

tone

-wat

er m

ixtu

res,

at 2

5°C

and

for

the

four

mod

els c

hose

n.

@BEeID

nF

x lo

z6 es

u

1.22

f 0

.25

0.13

f 0

.20

1.04

f 0

.28

0.64

f 0

.21

Mod

el

111

IV

20.0

wt

% -

-0.8

5 f 0

.02

-0.8

8 f 0

.02

-0.8

8 f 0

.02

-0.9

8 f

0.03

Activity coejjkients of single ions (V) 91 (1972) RECUEIL 1233

60.0 wt %

-3.1 -1.6 - 1.8 -1.9 - 2.3 -4.2

- 2.8 4.8 4.1 2.9 1.9

- 5.6

Table V

Values of Apo of single ions for the transfer from water to acetone and acetone-water mixtures, and from ethanol to acetone.

80.0 wt %

-4.4 -2.7 - 2.9 - 3.0 - 3.5

- 4.0 8.1 1.1 5.2 4.1

-4.9

I on

H+ K + Rb' cs+

Me,N' n-Pr4N+ n-Bu,N'

Fic+ C1- Br- I-

ReO; Ph,B-

c10;

~

20.0 wt %

-0.9 -0.3 - 0.3 - 0.4 -0.6 - 1.2 -1.6 - 1.1

1.2 1 .o 0.6 0.3

- 1.2

40.0 wt %

- 1.9 -0.8 - 0.9 - 1.0 -1.4 - 3.3

- 1.1 2.1 2.2 1.5 0.8

- 2.7

100%

- 4.9 - 3.5 - 3.1 - 3.8 - 4.5

- 4.4 17.5 15.4

7.8 6.1

- 4.6

ethanol 1

acetone

- 6.8 - 6.1 - 1.0 - 1.2 - 1.3

- 4.1 12.4 11.0

5.2 5.3 0.0

5.2. Avo values of single ions in acetone-water mixtures

Ap0 values for the transfer to the aqueous mixtures were calculated as described previously2 v 3 , but by a more mathematical procedure, i.e. by using the equation:

where x = molefraction of acetone in the solvent mixture. A& - $Ap; + *A& can be determined experimentally and the other terms on the left hand side of equation [3] can be calculated. Each value of A& - $A& + +ApI leads to a value of A&. The final value of A& and its standard error were calculated from the individual values of Ap; at four values of r (1.81, 1.96, 2.19, 2.45 A).

I234 D. Bus PI cr l .

l8 I 16

14

12

10

,:;;]I8 6

4

2

0

- 2

- 4

- 6 - 0 20 40 60 80 100 -

rnoleo/acetone

Fig. 1. Ap" of single ions as a function of the moles % acetone in the solvent*.

5.3. The surface potential of acetone Recent estimates of the surface potential xwater range from -0.4 to 0.1 Volt18. We prefer the value of -0.3 f 0.1 Volt1g. The surface potential of acetone can then be calculated by the equation:

* In previous articles of this series, Ap" of single ions was plotted against the wt % of the organic component in the solvent. In this case a plot against the moles % seem more satisfactory since the lines for the anions become almost straight lines.

In B. Case and R. Parsons, Trans. Faraday SOC. 63, 1224 (1967). '' C. L. de Ljgny, M. Alfenaur and N . G . vun rler Veen, Rec. Trav. Chim. 87, 585 (1968).

Acf iv i ty coeJJcienrs oj'single ions ( V ) 91 (1972) RECUEIL I235

Au& = A&, - FAX c41 where A@, = the difference of the standard real free enthalpy'* of the chloride ion in acetone and in water, 16.4 & 0.3 kcal.mole-' 'O. The corresponding value of A&, = 17.5 kcal.mole-' (Table V), conse- quently A x = xacetone - xwater = 0.05 & 0.04 Volt. With some reser- vation we find for xacetone = -0.25 f 0.1 Volt.

6. Discussion

The results found for acetone and its aqueous mixtures are very dif- ferent from those found for methanol and ethanol and their aqueous mixtures. In the present case, the Avo values of the negative and the positive ions differ considerably, those of the negative ions being positive (except for the very large Ph,B- ion) and those of the positive ions being negative. This is probably due to the charge density distribu- tion in the acetone molecule, combined with its spatial structure, which strongly favors solvation of positive ions over that of negative ions. A relatively large negative charge is localised on the oxygen atom, while the positive charge is delocalised over the propyl group.

Unlike the behaviour in methanol and ethanol and their aqueous mixtures, the hydrogen ion does not behave exceptionally, although it does seem to behave like a large ion.

It follows from these results that acetone should be classified as a protophylic rather than as a protophobic aprotic solvent ( c j ref. 21).

It is interesting to consider Ap" values for the transfer of ions from ethanol to acetone (Table V, last column). These solvents are nearly isodielectric, but the former is an amphiprotic solvent,. the latter a dipolar aprotic solvent.

The results for the cations demonstrate the protophylic character of acetone very clearly.

According to Parker2', for such a transfer Ap" of small anions will be positive, due to H-bonding in the amphiprotic solvent. This is borne out by the data, Ap" of CI- and Br- being very large and Ap" of ClO, and ReO,, which are only weak H-bond acceptors, being considerably smaller.

2o I. Zugdrska and Z. Koczorowski, Roczniki Chemu 44, 1559 (1970).

2 2 A . J. Parker, ibid. 25, 345 (1971). I. M. Kolthofl Pure Appl. Chern. 25, 305 (i971).

I236 D. Bax CI a/.

Ion

K+ Me,N+

CI- Br- clo;

Further, Parker expects that for large polarizable anions Apo will be negative, due to dispersion* forces in the dipolar aprotic solvent and unfavourable structural interactions with the highly structured amphi- protic solvent. The Ap” value of the Ph,B- ion shows that this is not true.

The ratio of Wulden products:

R” 2 4 R‘ 24 R 2 5

eqn. c51 eqn. PI

2.74 1.10 1.120 1.34 1.10 1.039 1.95 0.68 1.088 1.80 0.67 1 . 1 10 I .68 - -

hoqo (in H,O) hoqo (in acetone)

R = C5l

where h” is the limiting ion conductance, and qo is the viscosity of the solvent, informs us on the structure-making and structure-breaking ability of the ion in water as referred to the same ability in R” is the analogous ratio for ethanol/acetone. The ratio:

hoqo (in H20, 10°C) hoqo (in H,O, 45°C)

R’ =

informs us on the behaviour of the ion in water. Values of R, R” afid R’ are given in Table V1.

Table VI

The values of R’ show that the ions considered are all structure-breakers in water. It follows from the values of R that in acetone the ions are not structure-breakers, perhaps even (K’) structure-makers.

* The term due to dispersion forces in the Buckingham equation 23 for a single ion cancels out in equations 1-3, where the difference is taken of the free energy of two ions M and A (thought to have equal radius, polarizability and ionization potential). 23 A. D. Euckinghum, Disc. Faraday SOC. 24, 151 (1957). 24 R. L. Kay and D. F. Evans, J. Phys. Chem. 70, 2325 (1966). 2’ H . C. Erookes, M . C. E. Hotz and A . H. Spong, J. Chem. SOC. A, Inorg. Phys. Theor.

2410, 2415 (1971).

Aclivity corJjicients oJ singlo ions (V) 91 (1972) RECUEIL 1237

A large value of R is likely to correspond to a large negative value of AS", and therefore to a large value of Ap", as was found in the case of methanol and ethano12v3. It follows from Table V (6th column) that (apart from the K+ ion) this type of correlation does exist. However, R" and Apa for the transfer from ethanol to acetone are not correlated in this way. Probably, the contribution of the term -TAS" to Ap" is of relatively little importance in the latter case.

Applications for the single ion values of Ap" may also be sought in the explanation of equilibria involving these ions. An example is given below: For a weak acid HA, which dissociates according to HA H+ + A-,

1 RT In 10 (APG + AP: - APG'4) pK (in S) - pK(in H,O) = c71

where K is the dissociation constant of the acid. 2,4,6,2',4',6'-Hexanitrodiphenylamine (HNDA) dissociates thus:

HNDA o H + + NDA-. HNDA is a stronger acid in acetone-water mixtures with up to 42% acetone, than in water26. According to Dodd- Wing Fong and Grunwald, this is caused exclusively by the fact that the NDA- ion is better solvated in acetone-water mixtures in this range than in water, i.e. that A&DA- - A & N D A < 0. They state that the higher acidity of HNDA is even counteracted by the value of A& (which they presume to be > O ) . Comparison of their data with ours (Table VII) reveals that the higher acidity is caused more by better

Table VII

Thermodynamic data on the dissociation of HNDA

wt % acetone

76,5 100

APG + A&DA - APGND~: ApG ** [kcalmole- '3 [kcalmole-

-0.84 f 0.05 -0.51 f 0.02 -2.03 f 0.05 - 1.06 f 0.02 -0.34 f 0.14 -2.00 f 0.02

0.20 k 0.14 -4.15 & 0.3 0.75 f 0.14 -4.9 0.7

-0.33 f 0.05 -0.97 f 0.05

1.66 f 0.14 4.4 _+ 0.3 5.7 f 0.7

* Calculated from equation [7]. ** From Fig. 1. The errors in A& have been estimated by analogy with with the values

2 6 Dodd- Wing Fong and E. Grunwald, J. Phys. Chem. 73, 3909 (1969). given in Table IV.

I238 D. Bus ct ul.

solvation of the H+ ion than by that of the NDA- ion. In 42% acetone the value of A&DA- - AcL;;NDA is positive which indicates that the HNDA molecule is more solvated than the NDA- ion. The higher acidity is this case is caused exclusively by better solvation of the H + ion, in spite of counteraction by the NDA- ion.

7. Conclusions

The difference of the standard chemical potentials of single ions in water and in acetone and acetone-water mixtures, and the surface potential x of acetone, can be estimated with fair accuracy. Acetone is a protophylic, rather than a protophobic, solvent.

(Received February 23rd, 1972)