Contribution of Non Coulombic Forces to Ion-pair Formation in some Non-aqueous Polar Solvents

BY J. BARTHEL, R. WACHTER AND H.-J. GORES

Department of Chemistry, University of Regensburg, W. Germany

Receiced 2nd May, 1977

Ion-pair formation of alkali and tetra-alkylanimoniun salts i n propanol, acetonitrile and propylene carbonate has been investigated with the help of precise conductivity measurements in dilute solutions

in the temperature range from -45 to ‘25°C.’ The temperature dependence of the association constant, K A , yields the therniodynamic data AG:, AH: and AS: which are divided into a coulombic ion-ion and a residual term. Contributions from ion-solvent interaction depend on the nature of the solvent and the electrolyte compound. The distances of closest approach of the ions in the ion-pairs are compared with crystallographic radii (alkali salts) or radii deduced from the ionic size (tetra-alkylammonium salts).

< c <

Conductance data on the investigated electrolyte solutions have been evaluated with the help of the set of equations

A = .[Ao - SVZ f EUC log EC f Jl(Rl)xc + J@2)t13’2~3’2] ( la)

In y A = 0. ( I d ) As usual A is the experimentally determined molar conductance of the solution at

electrolyte concentration c and A,, the molar conductance at infinite dilution. The coefficients S, E, J1 and J2 depend on the ion-distribution functions and the boundary conditions on which the theory is based. A tabular survey of the expressions appro- priate to the different theories has been catalogued.2 Without prejudice to recent attempts to explain the value of KA from the form of the distribution function used to set up the initial conductance equation, this quantity may actually still be considered in the framework of eqn (1) as introduced ad hoc in order to define the concentration tlc of free ions in the solution. Q is the degree of dissociation, y i the mean activity coefficient in the molar scale of the dissociated part of the electrolyte and y A that of the associated part, IC the Debye parameter and R, the distance parameter of the activity coefficient. q is given by eqn (3).

In so far as the equation set (1) is only used to determine K A without regard to the structure of the coefficients J,(R,) and J2(R2), KA is independent of the theoretical con- cept behind eqn ( la) . If, however, such an evaluation is not possible, a fundamental question arises about the significance of the distance parameters R, and Rz, which are derived from J1 and J2 and which must 5e compatible with R, in eqn (lc). Internal consistency of the equations requires [cf. ref. (2) to (6)]

R1 = R2 = R, = R. (2)

286 C O N T R I B U T I O N O F N O N C O U L O M B I C F O R C E S

E X P E R I M E N T A L

Precise A-c-T data in the temperature range -45 to + 2 5 T are obtained by a stepwise increase of concentration. This method enables the A-c-T diagram to be constructed by isologuous sections.lJ For this purpose the highly purified solvent is introduced into the measuring cell under protective gas. The conductance of the solvent is measured for the different temperatures of the programme. The first electrolyte concentration is then pre- pared in the mixing chamber by adding a definite amount of the electrolyte compound, After mixing thoroughly, the temperature programme is repeated with the new solution. The highest electrolyte concentration envisaged is reached after eight or ten concentration steps.

This technique requires a quick and highly accurate setting of the temperatures of the temperature programme. The construction of the thermostat and its temperature control has been described el~ewhere.'~' With this equipment a quick and reproducible (AT < K) setting of each temperature of the programme is guaranteed. No temperature oscillations can be observed and short time deviations are below K.

The measuring cell is in an arm of an a.c. bridge built according to present standards of technol~gy. '~~

Solvents and electrolytes were thoroughly purified, impurities were analysed and so far eliminated as not to disturb the envisaged accuracy of measurement.l

RESULTS Data analysis was achieved with the help of different conductance equations and

under varying conditions. This preliminary investigation was made in order to esti- mate to what extent KA values are conditioned by conductance theory. Some repre- sentative examples are listed in table 1.

TABLE 1 .-COMPARISON OF CONDUCTANCE DATA FROM DIFFERENT EVALUATIONS

Ao

fJA electro- /W cmz KA R1

lyte eqn mol-' 5 1 Jz (mol-' dm3 18, A. propanol (25'C); q = 13.68 8,

LiCl FHFP4 20.007 2032 -6733 265 10.1 10.0 0.001 FJ 4 20.003 1692 -5780 276 10.6 10.2 0.001 FJ 3 20.038 (2046) -9 677 309 (13.7) 13.1 0.005

Pr4NI FHFP4 26.282 3 266 -14 751 516 14.1 12.3 0.005 FJ 4 26.279 2905 -13 663 525 14.7 13.8 0.005 FJ 3 26.274 (2765) -11 729 516 (13.7) 12.9 0.005

B. acetonitrile (25°C); q = 7.77 A KI PFPP 3 186.69 (4 209) -14 388 19.5 (7.8) 6.5 0.026

FJ 3 186.64 (3072) -8952 17.5 (7.8) 8.2 0.018

Me4NI PFPP 3 196.51 (4 399) -14 387 32.3 (7.8) 6.3 0.013 FJ 3 196.48 (3 241) -7 844 32.7 (7.8) 7.6 0.010

C. propylene carbonate (25°C); q = 4.28 8, LiC104 PFPP 3 26.751 (100) - 257 1.4 (4.3) 4.9 0.004

FJ 3 26.75 (69) - 154 1.3 (4.3) 5.5 0.004

The first column of table 1 indicates the equation on which the data analysis is based and its underlying conditions. FHFP means an evaluation according to the

J . B A R T H E L . R . W'ACHTER A N D 1I.-J. G O R E S 287

equation of Fuoss and Hsia' as developed by Fernandez-Prinig in the form of eqn (la); FJ contains the coefficients E, J1 and J2 as given by Justice5 on the basis of the Fuoss theory including the Chen expression for the E-coefficient; and PFPP indicates that the Pitts' equationlo in ternis derived by Fernhndez-Prini and Prue" is applied. Each evaluation contains the activity coefficient eqn (Ic) in the form given by Bjerrum

Data analysis was at first performed by determining Ro, J,, J2 and KA by a least squares method without making use of eqn (2). The values R, and R2 were then cal- culated separately from the appropriate coefficients. This procedure is indicated in table 1 by a symbol 4 placed after the specification of the equation, e.g. , FHFP 4. FHFP 4 and PFPP 4, of course, yield identical coefficients A,,, J,, J2 and KA. Any deviation of FJ 4 is due to the E-term of this equation. The resulting variation of KA is not significant.

A symbol 3 after the specification of the equation means that, according to a sug- gestion of Justice,, data analysis is conducted with fixed S, E and R1 values to deter- mine A,,, J2 and KA. Here we make use of eqn (2) and postulate R1 = R,, and, to be consistent with the preceding treatment of data, we fix R, = R, = q. The corre- sponding J,-value, Jl(q), is listed in parenthesis.

The four coefficients evaluated show that for all salts in propanol (including those of table 2 which are not listed in table 1) the same result is obtained, namely R, M R2 M

R, = q and the compatibility condition, eqn (2) , is thus satisfied. The three para- metric fit FJ 3, therefore, yields cornperable results for all salts.

The significance of this investigation becomes evident when we review the conduc- tance data of solutions with acetonitrile or propylene carbonate as solvents. The four parametric fits FHFP 4, FJ 4 and PFPP 4 lead to small or zero KA-values. Highly precise A, c-data do not allow the separation of KA- and Jl-contributions. Electrolytes in propylene carbonate may be treated as completely dissociated. In acetonitrile this kind of evaluation is not successful. The procedures FJ 3 and PFPP 3, however, yield comparable association constants and satisfy the compatability con- dition, eqn (2)) which for these cases is as follows: R2 = Rl with R1 = R, = q. KA and R2 as obtained by the data analysis according to FJ,3 together with the appropriate values of q, E, and Tare listed in table 2.

From a chemical point of view the hypothesis R = q is not always quite satis- factory. It may be tolerated as long as q is greater than the distance of closest approach a of the ions which, in the case of spherically symmetric ions, can be identi- fied with the centre-to-centre distance of hard spheres, e.g., KI, R,NI. For non- symmetric ions like MeBu,N+ or C3H,0- we choose the shortest possible distance between the localised positive and negative charges to be the distance of closest ap- proach, e.g., the distance I- . . . Me . . . N + in MeBu,NI. These values are listed as the a-parameters in table 2. They are identified with crystallographic radii as far as these exist or else are calculated from bond length^.^^,'^ The latter procedure is only possible for tetra-alkylammonium salts with methyl and ethyl groups. a- Parameters for bigger ions such as Pr,N+, Bu,N+ etc . , are calculated from the molar volumes of the corresponding isosteric alkanes, i.e., Pr,C, Bu,C etc.13 For a 2 q, both four- and three-parametric evaluations become meaningless if R = q. The treatment of such solutions as solutions of completely dissociated electrolytes, however, would be a misrepresentation. We exclude these cases from the present discussion of ion-pair formation.

288 C O N T R I B U T I O N O F N O N C O U L O M B I C F O R C E S

TABLE 2.-ASSOCIATION CONSTANTS K,/mol-' dm3 AND DISTANCE PARAMETERS &/A OF VARIOUS SALTS IN PROPANOL, ACETONITRILE AND PROPYLENE CARBONATE FROM

CONDUCTANCE MEASUREMENTS

A. propanol (s = 6.90 .&)la

temperature -40°C -30°C -2O'C -1OT 0°C +lO°C +25"C

&rl 31.28 29.35 27.52 25.86 24.19 22.66 20.48

q/A [eqn (311 11.45 11.71 11.99 12.28 12.64 13.02 13.68

Pr,NI K A 475 f 1 457 f 1 447 f 1 445 i 1 452 & 1 469 i 1 516 f 1 a = 6.68 A R, 12.5 12.2 12.0 12.1 12.2 12.5 12.9

4 2.2 2.3 2.4 2.5 2.7 2.8 3.0

Bu.NI K A 471 f 7 456 & 8 448 i 8 447 f 7 456 i 8 471 f 13 514 f 8 a = 7.10 8, Rz 16.1 15.3 14.7 14.4 14.1 14.3 14.4

i-Am4NI K A 554 3 529 f 3 516 i 3 510 i 3 514 f 3 527 f 3 570 f 3 a = 7.10 8, RP 14.3 14.0 13.7 13.6 13.6 13.6 13.9

-Am,BuNI K A 537 + 2 516 i 1 504 & 1 500 f 1 506 i. 1 521 i 1 565 f 1 a = 7.10 8, Rn 13.5 13.1 12.8 12.7 12.8 12.9 13.2

MeBu,NI K A 563 & 1 539 f 1 528 1 2 527 1 1 536 f 1 558 5 1 615 i 2 a = 5.64 A R, 13.0 12.8 12.6 12.4 12.6 12.6 13.1

EtBu,NI K A 492 rt 5 476 f 5 468 i 4 466 i 4 473 f 3 495 f 3 543 f 3 u = 6.17 A RZ 12.9 12.5 12.4 12.4 12.5 12.5 12.9

Me2BuzNI K A 590 i 4 571 1 3 563 f 3 564 i 2 578 i 2 603 i 2 673 f 2 a = 5.64 8, RI 12.9 12.4 12.2 12.0 12.1 12.3 12.7

~

KI K A 8 9 i 2 1 0 7 i 2 1 2 8 i 2 1 5 6 i 3 1 9 2 f 3 2 3 9 f 3 3 4 3 i 5 a = 3.52 8, Rz 13.3 13.4 13.5 13.6 13.9 14.1 14.5

LiCl K A 74 i 1 87 f 1 106 f 1 129 i 1 162 f 1 206 f 1 309 & 2 a = 2.49 8, R, 11.3 11.5 11.7 11.9 12.2 12.5 13.1

B. acetonitrile (s = 5.12

temperature -40°C - 3 5 T - 2 5 T - 1 5 T -5°C +5"C + 1 5 T +25"c

48.21 47.11 45.00 43.03 41.15 39.38 37.69 36.07

q/A [ e m (311 7.43 7.45 7.48 7.52 7.57 7.63 7.69 7.77 ~~

Me,NI K A 31.4 1 0.3 31.4 i 0.2 30.9 1 0.1 30.7 5 0 2 ZC.8 5 0.2 31.1 ii 0.2 31.7 0.2 32 .71 0.2 a = 5.64 8, R, 7.2 6.9 7.1 7.3 7.4 7.6 7.6 7.6

a:: 2.2 2.2 2.3 2.4 2.4 2.4 2.4 2.4

KI K A 10.0 k 0.1 10.3 i 0.2 11.0 i 0.2 11.9 f 0.3 13.0 k 0.2 14.3 i 0.3 15.7 f 0.3 17.5 f 0.2 a = 3.52A Rt 7.9 7.9 8.0 8.1 8.1 8.2 8.3 8.2

KC104 K A 19.7 & 0.2 20.2 i 0.2 21.3 i 0.2 22.6 f 0.2 24.2 f 0.2 25.5 f 0.2 27.2 f 0.3 29.3 i 0.2 a = 3.70 8, Rt 6.8 7.0 7.0 7.0 7.0 7.4 7.5 7.5

C. propylene carbonate (s = 5.40

temperature -49.2 -35°C -25°C -15°C -5'C +5"C + 1 5 T + 2 5 T

Er' 85.89 82.59 79.41 76.36 73.48 70.65 67.99 65.42

q/A [ e m (31 4.26 4.25 4.24 4.24 4.24 4.25 4.26 4.28

LiClO. K A 0 0.2 i 0.3 0.4 i 0.2 0.9 f 0.2 1.0 f 0.1 1.1 i 0.1 1.4 i 0.2 1.3 i 0.1 a = 3.66 8, R, 8.1 7.3 7.2 6.1 6.1 5.8 4.8 5.5

KPF6 K A 0 0 . 5 i 0 . 1 0 . 6 i O 1 0 . 7 5 0 . 2 0 .8 f0 .1 1 . 3 i 0 . 1 1.2fO.l 1 . 3 i 0 . 1 a = 3.08, R, 9.3 7.1 6.8 6.7 6.6 5.8 6.1 6.0

J . B A R T H E L , R . W A C H T E R A N D H. -J . G O R E S 289

DISCUSSION

In conductance theory, as expressed by the set of eqn (l), association has been introduced by an ad hoc hypothesis which can be interpreted as a thermodynamic equilibrium

C+ -' A- z [ C + A - ] (4) where C+ is the cation, A- the anion and [C+A-] the ion-pair. As a consequence of this thermodynamic hypothesis, ions and ion-pairs must be considered as defined chemical entities. The equilibrium position of the process in eqn (4) expressed with the help of the appropriate chemical potentials p i ( p , T ) as

PCC'A-I - P C ' - P A - = ( 5 )

(6)

leads to eqn (lb) with

-RTln K A = pUOCc+A-l - &+ - p i - .

The quantities py are the partial molar Gibbs energies of the pure chemical compounds at infinite dilution. As usual the right side of eqn (6) can be expressed as AG;, eqn (7)

AG; = -RTln KA. (7) Thus AG; is the molar Gibbs energy to form an ion-pair from the initially infinitely separated ions. As a thermodynamic function, AG; can be divided into a coulombic ion-ion (AGQ and a residual (AG;) energy term 2 ,7

AG; = AGZ + AG;

K, = KiKP: = KZ exp [-AGJRT].

(8)

(9)

leading to a formal separation of these contributions in the association constant

As y ; + 1 and yA -+ 1 with vanishing electrolyte concentration,

1--o! KA = lim -. c-0 c

Eqn (10) is the link between a thermodynamic and a statistical-mechanical treatment of the association problem. In combination with eqn (9) it shows that with vanishing concentration the residual energy term AG; does not tend towards zero.

In order to express eqn (10) in terms of statistical-mechanics we adopt an expression of Falkenhagen and Ebeling lS initially derived for purely coulombic interaction forces in a more general context16

4000 N L m r'w(r) exp [- U(r)/kT] dr. 1 - x - --

C

As in the treatment of Falkenhagen and Ebeling w(r) is a weight function that satisfies the conditions

w(r ) + 1 if r -+ a and w(r ) + 0 if r -+ cc

and indicates to what extent paired states of oppositely charged ions are to be con- sidered bound in the sense of ion-pairs. Different assumptions have been made

290 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 F O R C E S

about w(r).'j For our purpose we choose w(r) to be a step function

1 i f r < c d r 0 if r >, d. w(r) =

The lower limit of the integral in eqn (11) is the distance of closest approach in the sense defined in the preceding section. U(r) is a complex function containing contri- butions of ion-ion, ion-dipole, induction-, dispersion- and repulsion forces as tabu- lated by Ke1bg.l' Since an actual separation of these distance and angular dependent functions is not possible we follow a proposal of this author and set

4+) + e2 U ( r ) = - - 4 m O ~ , r

This suggests that the ion-ion interaction is slightly modified by p(r), e.g. , by a local permittivity or by a structural screening factor and a residual term y(r). In the present context we suppose p(r) = 1 and y(r) = U* = const. Then eqn (1 1) can be written as2.'

-= I - u 4000 R N exp (-AG;/RT)[ r 2 exp [ e2 ] dr C 4neoc,rkT

because the quantity NU* may be regarded as AG;. Thus

K: = 4000 R N [ r2 exp [4nEoerrkT] e2 dr.

Eqn (1 5 ) is identical to Prue's association ~ o n s t a n t . ~ A further approach to this problem is due to M.-C. Justice and J.-C. Justice who

have stressed the possibility of applying the Friedman-Rasaiah theory in the frame- work of the conductance equations, eqn (1). On the basis of a charged square-well model18 they have obtained the expression

I-a a + l - = 4000 n N [exp (- h + - /kT) r z exp (2qlr) dr + C a

which relates (1 - a)/c to more than one type of ion-pair. It can be formally derived from eqn (1 1) and (13) using w(r) as a two step function.

Inspecting table 2, the existence of non-coulombic forces in ion-pair formation can be deduced from the abnormally low &values of the tetra-alkylainmonium salts (e.g., Pr,NI/PrOH and Me,NI/AN) which are obtained when the measured associa- tion constant K A is identified with eqn (15), d = q, and the lower limit a = a: of the integral is used for adaptation. Furthermore, tetra-alkylammonium salts yield log KA against T-l diagrams with minima. This observation cannot be explained from a purely coulombic ion-ion interaction.

In order to examine the nature of these interactions we use eqn (14) in the form

In KA + 3 In (c,T) - In Q(b) = In KO - AH"/RT + AS*/R (1 7) where Q(b) is the tabulated integral of the Bjerrum theory [cf. ref. (13)], b = 2q/a. KO = 4000 ~ N e ~ ( 4 n e ~ k ) - ~ and AG* = A H" - TAS". Eqn (17) implies setting d = q as required by the use of the activity coefficient eqn (lc) with R, = q for the evaluation

J . B A R T H E L , R . W A C H T E R A N D H.-J. GORES 29 1

of conductance data. On the other hand d = q means satisfying a chemical assump- tion for tetra-alkylammonium salts and LiCl in propanol and for KI and KC104 in acetonitrile. The dimensions of solvent molecules are such that a choice of d = a + s [cf. table 21 yields values of d w q. From this point of view paired states of oppositely charged ions are considered as ion-pairs if the ions have approached to within a distance smaller than the dimension of a solvent molecule.

Fig. 1 and 2 contain plots B(T) =f(T1) according to eqn (17), B(T) = log KA + 3 log ( E J ) - log Q(b), for propanol and acetonitrile solutions. All tetra-alkyl- ammonium salts (fig. 1) yield straight lines with positive slopes indicating that AH: < 0 and independent of temperature. Hence AS: is independent of temperature, too. In contrast to this behaviour all alkali salts (fig. 2) yield curves indicating AHA. > 0; temperature independence of AHA. is not always assured. Fig. 1 and 2 suggest the use of AH:-values as the appropriate parameters for a first classification of non- coulombic interactions.

0.7

0.6

0 . 3

3.5 4 0 4 . 5

lo3 K T

FIG, 1 .-Plot of B(T)against T-I according to eqn (17) for tetra-alkylammonium salts in propanol(0)

( e ) Me2Bu2N+I-, (f) MeBu,N+I-; EtBu,N+I-, (g ) Me4N+I-. and acetonitrile (a). (a) i-AmaN+I-, (b) i-Am,BuN+I-, (c)BudN+I-, (d)Pr4N+I-,

292 C O N T R I B U T I O N O F N O N C O U L O M B I C FORCES

1.0

0.9

- Yo != 0.8 4

0.7

0.6

3.5 4.0 4.5

I O ~ K I T

FIG. 2.-Plot of B(T) against T-' according to eqn (17) for alkali salts in propanol (0) and aceto- nitrile(O). (a)Cs+PrO- (B, = 13.0),(b)K+I- (B, = 12.7),(c)K+ClOh(BO = 13. O),(d)Li+[oz]C1-

(B, = 13.0), ( e ) K+I- (B, = 12.8).

Table 3 contains the results derived from fig. 1 and fig. 2. The AGi-values are obtained from the measured K,-values in table 2 with the help of eqn (7). The dis- cussion of the residual potentials AG:, AH: and AS: has to take into account that values of the parameters a and s are conditioned by the method of their determination and are sure only within limits of 10-15%.

An important part of the energy of formation AG; of an ion-pair is the residual part AG:. For alkali salts AH: > 0, but this heat required for ion-pair formation is com- pensated by an adequate increase of entropy in the process described by eqn (4). The ionic solvation shells loosen oriented solvent molecules during this process. From AH: < 0 and always small AS:-values in the ion-pair formation of tetra-alkylammo- nium salts it follows that the interaction between the solvent around ions, ion-pairs and these species is of a different nature. There is no solvation shell comparable to that of alkali salt ions. Interaction forces are mainly dispersion forces. The absolute value of entropies AS: in table 3 ought not to be discussed at the present state of our in- vestigation, only their relative values can provide information.

In table 3 we have added for the salts KI and LiCl values indicated by the symbol

J . BARTHEL, R . WACHTER A N D H.-J. GORES 293

TABLE 3 .-THERMODYNAMIC DATA O F ION-PAIR FORMATION

-40°C < 6’ < +25”C e = 2 5 ~ AH: AS; AG; AG;

electrolyte 4 d /J mol-’ /J mol-l K-l /J mol-l /J mol-‘

A. propanol

Pr4NI

i-Am4NI i-Am,BuNI Me B u N I

Me2Bu2NI KI

BLI~NI

EtBuSNI

LiCl

CsOPr *

6.68 4 -6 800 7.10 4 -6 900 7.10 4 -7 500 7.10 4 -7 300 5.64 4 -6 200 6.17 4 -6 200 5.64 4 -6 000 3.52 4 +3 500 3.52 a t s; 4 (f3900) 2.49 4 >O 2.49 a + s; 4 (>O) 5.30 4 + 7 400t 3.20 4 +8 300

~~

-8.0 -8.0 -8.4 - 8.4 -6.7 - 6.7 -5.0

t13 .4 (+ 14.7)

<O (<O)

+32t +- 36

~~

-4 400 -4 500 -4 900 -4 900 -4 100 -4 100 -4 400 - 460

(- 500) +3 300

(+3 600) -2 100 -2 800

-15500 -15 500 -15 700 - 15 700 - 15 900 -15600 - 16 200 - 14 500

- 14 200

-17 100

B. acetonitrile

MeJNI 5.64 4 -2 300 +5.4 -4000 -8 700 KI 3.52 4 +4 100t t 13 .4 t t 8 0 -7100 KC104 3.70 4 +1 800 $10.5 -1 400 -8400

* Calculated from ref. (5) in the range +5”C < 0 < + 35°C. 7 Calculated from the initial slope.

d = (a + s; 4). These results have been obtained by applying eqn (16) and setting I = s. In both cases eqn (16) yields h , - and derived enthalpy and entropy values (table 3, in parenthesis) which are comparable with AG:, AH: and AS: as obtained by eqn (14). The contribution of the second type of ion-pairs which are defined by a distance a - s < r < q is small [-lo% of (1 - E)/C for KI and -4% for LiCl].

A treatment based on Fuoss’s association concept or a treatment on the basis of a Born process in conjunction with an appropriate introduction of a residual energy term provides the same information about the sign and the relative order of AHA- values as does table 3.2*7

Solutions of LiCl in propanol show special properties : AH:-values as determined with the help of eqn (14) or (16) and with a = 2.49 A are positive, but small. If, however, we postulate solvent-separated ion-pairs by setting a = 5.30 A, values are obtained which are comparable with those of the other alkali salts [cf. table 3, fig. 21. The distance parameter a = 5.30 A is calculated from Pauling’s radii of Li+, C1- and the van der Waals volume of -O-H.14

In propylene carbonate solutions association occurs only to a small extent. The &-values show large fluctuations and thus make an accurate evaluation of the thermo- dynamic data impossible. Suffice it to note that an evaluation for LiClO, solutions with a = 3.5 A yields positive AH:- and AS:-values.

To sum up, the above model, that is, eqn (14) with d = q, allows us to account for short range forces by means of their overall contributions to the residual chemical potentials of ions and ion-pairs. This account is approximate as a result of the assumptions p(r) = 1 and ~ ( r ) = U* = const. which are applied to U(r), eqn (13).

294 C O N T R I B U T I O N S O F N O N COULOMBIC FORCES

An appropriate choice of the lower limit of the integral, eqn (14), may be used to distinguish solvent-separated and contact ion-pairs. The knowledge of AG; as a function of temperature in a sufficiently large temperature range allows an unambigu- ous differentiation between types of interaction forces.

Thanks are due to the Deutsche Forschungsgemeinschaft for a grant enabling us to conduct these investigations.

Publication in preparation. J. Barthel, Ionen in nichtwuj3rigen Losungen (Dr. Dietrich Steinkopff Verlag, Darmstadt, 1976). J. E. Prue, in Chemical Physics of Ionic solutions, ed. B. E. Conway and R. G. Barradas (Wiley, New York, 1966), p. 163; J. E. Prue and P. J. Sherrington, Trans. Faraday SOC., 1961, 57, 1795; R. Fernlndez-Prini and J. E. Prue, Trans. Faraday SOC., 1966,62, 1257. J.-C. Justice, Electrochim. Acta, 1971,16, 701; J. Phys. Chem., 1975,79,454. J. Barthel, J . 4 . Justice and R. Wachter, Z. phys. Chem. (N.F.), 1973, 84, 100. M.-C. Justice and J.-C. Justice, Colloques internationaux du C.N.R.S., 1975,246, 241. R. Wachter, Habilitationsschrift (Regensburg, 1973).

R. Fernlndez-Prini, Trans. Faraday SOC., 1969, 65, 331 1. * R. M. Fuoss and K.-L. Hsia, Proc. Nut. Acad. Sci. USA, 1967, 57, 1550.

lo E. Pitts, Proc. Roy. SOC. A , 1953, 217, 43. l1 R. Fernlndez-Prini and J. E. Prue, Z. phys. Chem. (Leipzig), 1965, 228,373. l2 L. Pauling, Die Nafur der chemischell Bindung (Transl.) (Verlag Chemie, Weinheim, 1968).

R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 2nd edn, 1970).

l4 Calculated from A. Bondi, J . Phys. Chem., 1964,68,441. l5 H. Falkenhagen and W. Ebeling in Ionic Interactions, ed. S . Petrucci (Academic Press, New

York, 1970), vol. 1, p. 1. l6 J. Barthel, R. Wachter and H.-J. Gores, Vth International Conference on Non-Aqueous Solutions

(Leeds, 1976). l7 G. Kelbg, Z. phys. Chem. (Leipzig), 1960,214, 8.

J. C. Rasaiah and H. L. Friedman, J. Phys. Chem., 1968, 72, 3352; J. C. Rasaiah, J . Chem. Phys., 1970, 52,704.