Ion Pair Formation
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Ion Pair Formation as PDF for free.
More details
- Words: 4,507
- Pages: 10
Contribution of Non Coulombic Forces to Ion-pair Formation in some Non-aqueous Polar Solvents BY J. BARTHEL,R. WACHTERAND 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
Conductance data on the investigated electrolyte solutions have been evaluated with the help of the set of equations
A
= .[Ao
- SVZ f EUClog EC f Jl(Rl)xc + J@2)t13’2~3’2]
(la)
In y A = 0. (Id) 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 appropriate 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 KA is independent of the theoretical constructure of the coefficients J,(R,) and J2(R2), 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
CONTRIBUTION OF NON COULOMBIC FORCES
EXPERIMENTAL 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 prepared 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 t e c h n o l ~ g y . ' ~ ~ 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 estimate to what extent KA values are conditioned by conductance theory. Some representative examples are listed in table 1.
TABLE 1.-COMPARISON electrolyte
eqn
OF CONDUCTANCE DATA FROM DIFFERENT EVALUATIONS
Ao /W cmz mol-'
R1 18,
KA
51
Jz
A. propanol (25'C); q LiCl
FHFP4 FJ 4 FJ 3
20.007 2032 20.003 1692 20.038 (2046)
Pr4NI
FHFP4 FJ 4 FJ 3
26.282 26.279 26.274
(mol-' dm3 =
fJA
13.68 8,
-6733 -5780 -9 677
265 276 309
10.1 10.6 (13.7)
10.0 10.2 13.1
0.001 0.001 0.005
3 266 -14 751 2905 -13 663 (2765) -11 729
516 525 516
14.1 14.7 (13.7)
12.3 13.8 12.9
0.005 0.005 0.005
B. acetonitrile (25°C); q = 7.77 A KI
PFPP 3 FJ 3
186.69 186.64
(4 209) -14 388 (3072) -8952
19.5 17.5
(7.8) (7.8)
6.5 8.2
0.026 0.018
Me4NI
PFPP 3 FJ 3
196.51 196.48
(4 399) -14 387 (3 241) -7 844
32.3 32.7
(7.8) (7.8)
6.3 7.6
0.013 0.010
4.9 5.5
0.004 0.004
C. propylene carbonate (25°C); q LiC104
PFPP 3 FJ 3
26.751 26.75
(100)
(69)
- 257 - 154
1.4 1.3
=
4.28 8, (4.3) (4.3)
The first column of table 1 indicates the equation on which the data analysis is based a n d its underlying conditions. FHFP means an evaluation according to the
J . B A R T H E L . R . W ' A C H T E R 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,, J2and KA by a least squares method without making use of eqn (2). The values R, and R2 were then calculated 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 suggestion of Justice,, data analysis is conducted with fixed S, E and R1 values to determine 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 corresponding 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 parametric fit FJ 3, therefore, yields cornperable results for all salts. The significance of this investigation becomes evident when we review the conductance 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 condition, 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 T a r e listed in table 2. From a chemical point of view the hypothesis R = q is not always quite satisfactory. 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 identified with the centre-to-centre distance of hard spheres, e.g., KI, R,NI. For nonsymmetric 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 approach, 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. aParameters 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
CONTRIBUTION OF NON COULOMBIC FORCES
&/A
CONSTANTS K,/mol-' dm3 AND DISTANCE PARAMETERS VARIOUS SALTS IN PROPANOL, ACETONITRILE AND PROPYLENE CARBONATE FROM CONDUCTANCE MEASUREMENTS
TABLE 2.-ASSOCIATION
OF
A. propanol (s = 6.90 .&)la
temperature
-30°C
-40°C 31.28
&rl
KA
R,
4
Bu.NI 7.10 8,
KA
a =
Rz
i-Am4NI a = 7.10 8,
KA
RP
-Am,BuNI 7.10 8,
KA
a =
Rn
MeBu,NI
KA
a = 5.64 A
R,
-1OT
27.52
0°C
25.86
11.99
24.19
12.28
+lO°C
+25"C
22.66
20.48
11.45
11.71
475 f 1 12.5 2.2
457 f 1 12.2 2.3
447 f 1 12.0 2.4
445 i 1 12.1 2.5
452 & 1 12.2 2.7
469 i 1 12.5 2.8
516 f 1 12.9 3.0
471 f 7 16.1
456 & 8 15.3
448 i 8 14.7
447 f 7 14.4
456 i 8 14.1
471 f 13 14.3
514 f 8 14.4
554 3 14.3
529 f 3 14.0
516 i 3 13.7
510 i 3 13.6
514 f 3 13.6
527 f 3 13.6
570 f 3 13.9
537 + 2 13.5
516 i 1 13.1
504 & 1 12.8
500 f 1 12.7
506 i. 1 12.8
521 i 1 12.9
565 f 1 13.2
563 & 1 13.0
539 f 1 12.8
528 1 2 12.6
527 11 12.4
536 f 1 12.6
558 5 1 12.6
615 i 2 13.1
q/A [eqn (311
Pr,NI a = 6.68 A
-2O'C
29.35
12.64
13.02
13.68
EtBu,NI = 6.17 A
KA
u
RZ
492 rt 5 12.9
476 f 5 12.5
468 i 4 12.4
466 i 4 12.4
473 f 3 12.5
495 f 3 12.5
543 f 3 12.9
a =
Me2BuzNI 5.64 8,
KA RI
590 i 4 12.9
571 13 12.4
563 f 3 12.2
564 i 2 12.0
578 i 2 12.1
603 i 2 12.3
673 f 2 12.7
KI
KA
89i2 13.3
107i2 13.4
128i2 13.5
156i3 13.6
192f3 13.9
239f3 14.1
343i5 14.5
74 i 1 11.3
87 f 1 11.5
106 f 1 11.7
129 i 1 11.9
162 f 1 12.2
206 f 1 12.5
309 & 2 13.1
~
a = 3.52 8,
Rz
LiCl
KA
a = 2.49 8,
R,
B. acetonitrile (s temperature
q/A [ e m (311
-40°C
-35T
-25T
48.21
47.11
45.00
7.43
7.45
7.48
=
5.12
-15T
-5°C
+5"C
+15T
+25"c
43.03
41.15
39.38
37.69
36.07
7.52
7.57
7.63
7.69
7.77
~~
a::
31.4 10.3 31.4 i 0.2 30.9 10.1 30.7 5 0 2 ZC.8 5 0.2 31.1 ii 0.2 31.7 6.9 7.1 7.3 7.2 7.4 7.6 7.6 2.2 2.3 2.4 2.4 2.4 2.4 2.2
a = 3.52A
KA Rt
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 7.9 7.9 8.0 8.1 8.1
KC104 a = 3.70 8,
KA Rt
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 6.8 7.0 7.0 7.0 7.0 7.4 7.5 7.5
Me,NI
KA
a = 5.64 8,
R,
KI
C. propylene carbonate (s temperature Er'
q/A [ e m ( 3 1
LiClO. a = 3.66 8,
KA R,
KPF6 a = 3.08,
KA
R,
-49.2
-35°C
-25°C
-15°C
85.89
82.59
79.41
4.26
4.25
4.24
8.1
0.2 i 0.3 7.3
0 9.3
0.5i0.1 7.1
0
=
0.2
3 2 . 7 1 0.2 7.6 2.4
14.3 i 0.3 15.7 f 0.3 17.5 f 0.2 8.2 8.3 8.2
5.40 -5'C
+5"C
+15T
+25T
76.36
73.48
70.65
67.99
65.42
4.24
4.24
4.25
4.26
4.28
0.4 i 0.2 7.2
0.9 f 0.2 6.1
1.0 f 0.1 6.1
1.1
0.6iO1 6.8
0.750.2 6.7
0.8f0.1 6.6
1.3i0.1 5.8
i 0.1
5.8
1.4 i 0.2 4.8
1.3 i 0.1
1.2fO.l 6.1
1.3i0.1 6.0
5.5
J . B A R T H E L , R . W A C H T E R A N D H.-J. GORES
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 - PC' - P A - =
PCC'A-I
(5)
leads to eqn (lb) with -RTln
K A = pUOCc+A-l
- &+
-pi-.
(6)
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;
(8)
leading to a formal separation of these contributions in the association constant
K,
=
KiKP: = KZ exp [-AGJRT].
(9)
As y ; +1 and yA-+ 1 with vanishing electrolyte concentration,
KA = lim c-0
-.1--o! 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 lSinitially derived for purely coulombic interaction forces in a more general context16 1-x-
--
C
4000
N L m r'w(r) exp [- U(r)/kT] dr.
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 considered bound in the sense of ion-pairs. Different assumptions have been made
290
about
C O N T R I B U T I O N OF N O N COULOMBIC FORCES
For our purpose we choose w(r) to be a step function
w(r).'j
w(r) =
r
1 i f r, d.
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 contributions of ion-ion, ion-dipole, induction-, dispersion- and repulsion forces as tabulated 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 e2 U ( r ) = - -4+) 4mO~,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.' 4000 R N exp (-AG;/RT)[
-= I-u C
r 2 exp
because the quantity NU* may be regarded as AG;.
[4neoc,rkT e2 ]dr
Thus
K: = 4000 R N [ r2 exp [4nEoerrkT] e2 dr. Eqn (15 ) 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 framework 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 association 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 ~and k ) 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. G O R E S
29 1
of conductance data. On the other hand d = q means satisfying a chemical assumption 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-alkylammonium 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 noncoulombic interactions.
+
+
0.7
0.6
0 .3
3.5
40
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) and acetonitrile (a). (a) i-AmaN+I-, (b) i-Am,BuN+I-, (c)BudN+I-, (d)Pr4N+I-, ( e ) Me2Bu2N+I-,(f)MeBu,N+I-; EtBu,N+I-, ( g ) Me4N+I-.
292
CONTRIBUTION OF N O N COULOMBIC FORCES
1.0
0.9
-Yo !=
0.8
4
0.7
0.6
3.5
4.0
4.5
IO~KIT
FIG.2.-Plot of B ( T ) against T-' according to eqn (17) for alkali salts in propanol (0)and acetonitrile(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 discussion 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 For alkali salts AH: > 0, but this heat required for ion-pair formation is comAG:. 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-alkylammonium 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 investigation, only their relative values can provide information. In table 3 we have added for the salts KI and LiCl values indicated by the symbol
293
J . B A R T H E L , R . W A C H T E R A N D H.-J. GORES
TABLE3.-THERMODYNAMIC
DATA O F ION-PAIR FORMATION
-40°C < 6’
4
electrolyte
AH: /J mol-’
d
e=2
< +25”C
AS; AG; /J mol-l K-l /J mol-l
5
~
AG; /J mol-‘
A. propanol ~~
Pr4NI BLI~NI i-Am4NI i-Am,BuNI MeBu N I EtBuSNI Me2Bu2NI KI
6.68 7.10 7.10 7.10 5.64 6.17 5.64 3.52 3.52 2.49 2.49 5.30 3.20
LiCl CsOPr *
4 4 4 4 4 4 4 4 a t s; 4 4 a s; 4
+
-6 800 -6 900 -7 500 -7 300 -6 200 -6 200 -6 000 +3 500 (f3900) >O (>O)
4
+7 400t
4
+8 300
~~
-8.0 -8.0 -8.4 - 8.4 -6.7 - 6.7 -5.0 t13.4 (+14.7)
900 900 100 100 400 -460 (- 500) +3 300 (+3 600) -2 100 -2 800
+5.4 t13.4t $10.5
-4000 t80 -1 400
+-
-4 -4 -4 -4 -4 -4 -4
400
500
-15500 -15 500 -15 700 - 15 700 - 15 900 -15600 - 16 200 - 14 500
- 14 200 -17 100
B. acetonitrile
MeJNI KI
5.64 3.52 3.70
KC104
4 4 4
-2 300 +4 100t +1 800
* Calculated from ref. (5) in the range +5”C slope. d = (a
+ s;
4).
< 0 < + 35°C. 7 Calculated
-8 700 -7100 -8400 from the initial
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 K I 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 AHAvalues 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 thermodynamic 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
CONTRIBUTIONS OF NON 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 unambiguous 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. M. Fuoss and K.-L. Hsia, Proc. Nut. Acad. Sci. USA, 1967,57, 1550. R. Fernlndez-Prini, Trans. Faraday SOC.,1969,65, 331 1. 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.
Conductance data on the investigated electrolyte solutions have been evaluated with the help of the set of equations
A
= .[Ao
- SVZ f EUClog EC f Jl(Rl)xc + J@2)t13’2~3’2]
(la)
In y A = 0. (Id) 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 appropriate 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 KA is independent of the theoretical constructure of the coefficients J,(R,) and J2(R2), 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
CONTRIBUTION OF NON COULOMBIC FORCES
EXPERIMENTAL 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 prepared 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 t e c h n o l ~ g y . ' ~ ~ 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 estimate to what extent KA values are conditioned by conductance theory. Some representative examples are listed in table 1.
TABLE 1.-COMPARISON electrolyte
eqn
OF CONDUCTANCE DATA FROM DIFFERENT EVALUATIONS
Ao /W cmz mol-'
R1 18,
KA
51
Jz
A. propanol (25'C); q LiCl
FHFP4 FJ 4 FJ 3
20.007 2032 20.003 1692 20.038 (2046)
Pr4NI
FHFP4 FJ 4 FJ 3
26.282 26.279 26.274
(mol-' dm3 =
fJA
13.68 8,
-6733 -5780 -9 677
265 276 309
10.1 10.6 (13.7)
10.0 10.2 13.1
0.001 0.001 0.005
3 266 -14 751 2905 -13 663 (2765) -11 729
516 525 516
14.1 14.7 (13.7)
12.3 13.8 12.9
0.005 0.005 0.005
B. acetonitrile (25°C); q = 7.77 A KI
PFPP 3 FJ 3
186.69 186.64
(4 209) -14 388 (3072) -8952
19.5 17.5
(7.8) (7.8)
6.5 8.2
0.026 0.018
Me4NI
PFPP 3 FJ 3
196.51 196.48
(4 399) -14 387 (3 241) -7 844
32.3 32.7
(7.8) (7.8)
6.3 7.6
0.013 0.010
4.9 5.5
0.004 0.004
C. propylene carbonate (25°C); q LiC104
PFPP 3 FJ 3
26.751 26.75
(100)
(69)
- 257 - 154
1.4 1.3
=
4.28 8, (4.3) (4.3)
The first column of table 1 indicates the equation on which the data analysis is based a n d its underlying conditions. FHFP means an evaluation according to the
J . B A R T H E L . R . W ' A C H T E R 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,, J2and KA by a least squares method without making use of eqn (2). The values R, and R2 were then calculated 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 suggestion of Justice,, data analysis is conducted with fixed S, E and R1 values to determine 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 corresponding 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 parametric fit FJ 3, therefore, yields cornperable results for all salts. The significance of this investigation becomes evident when we review the conductance 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 condition, 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 T a r e listed in table 2. From a chemical point of view the hypothesis R = q is not always quite satisfactory. 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 identified with the centre-to-centre distance of hard spheres, e.g., KI, R,NI. For nonsymmetric 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 approach, 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. aParameters 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
CONTRIBUTION OF NON COULOMBIC FORCES
&/A
CONSTANTS K,/mol-' dm3 AND DISTANCE PARAMETERS VARIOUS SALTS IN PROPANOL, ACETONITRILE AND PROPYLENE CARBONATE FROM CONDUCTANCE MEASUREMENTS
TABLE 2.-ASSOCIATION
OF
A. propanol (s = 6.90 .&)la
temperature
-30°C
-40°C 31.28
&rl
KA
R,
4
Bu.NI 7.10 8,
KA
a =
Rz
i-Am4NI a = 7.10 8,
KA
RP
-Am,BuNI 7.10 8,
KA
a =
Rn
MeBu,NI
KA
a = 5.64 A
R,
-1OT
27.52
0°C
25.86
11.99
24.19
12.28
+lO°C
+25"C
22.66
20.48
11.45
11.71
475 f 1 12.5 2.2
457 f 1 12.2 2.3
447 f 1 12.0 2.4
445 i 1 12.1 2.5
452 & 1 12.2 2.7
469 i 1 12.5 2.8
516 f 1 12.9 3.0
471 f 7 16.1
456 & 8 15.3
448 i 8 14.7
447 f 7 14.4
456 i 8 14.1
471 f 13 14.3
514 f 8 14.4
554 3 14.3
529 f 3 14.0
516 i 3 13.7
510 i 3 13.6
514 f 3 13.6
527 f 3 13.6
570 f 3 13.9
537 + 2 13.5
516 i 1 13.1
504 & 1 12.8
500 f 1 12.7
506 i. 1 12.8
521 i 1 12.9
565 f 1 13.2
563 & 1 13.0
539 f 1 12.8
528 1 2 12.6
527 11 12.4
536 f 1 12.6
558 5 1 12.6
615 i 2 13.1
q/A [eqn (311
Pr,NI a = 6.68 A
-2O'C
29.35
12.64
13.02
13.68
EtBu,NI = 6.17 A
KA
u
RZ
492 rt 5 12.9
476 f 5 12.5
468 i 4 12.4
466 i 4 12.4
473 f 3 12.5
495 f 3 12.5
543 f 3 12.9
a =
Me2BuzNI 5.64 8,
KA RI
590 i 4 12.9
571 13 12.4
563 f 3 12.2
564 i 2 12.0
578 i 2 12.1
603 i 2 12.3
673 f 2 12.7
KI
KA
89i2 13.3
107i2 13.4
128i2 13.5
156i3 13.6
192f3 13.9
239f3 14.1
343i5 14.5
74 i 1 11.3
87 f 1 11.5
106 f 1 11.7
129 i 1 11.9
162 f 1 12.2
206 f 1 12.5
309 & 2 13.1
~
a = 3.52 8,
Rz
LiCl
KA
a = 2.49 8,
R,
B. acetonitrile (s temperature
q/A [ e m (311
-40°C
-35T
-25T
48.21
47.11
45.00
7.43
7.45
7.48
=
5.12
-15T
-5°C
+5"C
+15T
+25"c
43.03
41.15
39.38
37.69
36.07
7.52
7.57
7.63
7.69
7.77
~~
a::
31.4 10.3 31.4 i 0.2 30.9 10.1 30.7 5 0 2 ZC.8 5 0.2 31.1 ii 0.2 31.7 6.9 7.1 7.3 7.2 7.4 7.6 7.6 2.2 2.3 2.4 2.4 2.4 2.4 2.2
a = 3.52A
KA Rt
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 7.9 7.9 8.0 8.1 8.1
KC104 a = 3.70 8,
KA Rt
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 6.8 7.0 7.0 7.0 7.0 7.4 7.5 7.5
Me,NI
KA
a = 5.64 8,
R,
KI
C. propylene carbonate (s temperature Er'
q/A [ e m ( 3 1
LiClO. a = 3.66 8,
KA R,
KPF6 a = 3.08,
KA
R,
-49.2
-35°C
-25°C
-15°C
85.89
82.59
79.41
4.26
4.25
4.24
8.1
0.2 i 0.3 7.3
0 9.3
0.5i0.1 7.1
0
=
0.2
3 2 . 7 1 0.2 7.6 2.4
14.3 i 0.3 15.7 f 0.3 17.5 f 0.2 8.2 8.3 8.2
5.40 -5'C
+5"C
+15T
+25T
76.36
73.48
70.65
67.99
65.42
4.24
4.24
4.25
4.26
4.28
0.4 i 0.2 7.2
0.9 f 0.2 6.1
1.0 f 0.1 6.1
1.1
0.6iO1 6.8
0.750.2 6.7
0.8f0.1 6.6
1.3i0.1 5.8
i 0.1
5.8
1.4 i 0.2 4.8
1.3 i 0.1
1.2fO.l 6.1
1.3i0.1 6.0
5.5
J . B A R T H E L , R . W A C H T E R A N D H.-J. GORES
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 - PC' - P A - =
PCC'A-I
(5)
leads to eqn (lb) with -RTln
K A = pUOCc+A-l
- &+
-pi-.
(6)
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;
(8)
leading to a formal separation of these contributions in the association constant
K,
=
KiKP: = KZ exp [-AGJRT].
(9)
As y ; +1 and yA-+ 1 with vanishing electrolyte concentration,
KA = lim c-0
-.1--o! 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 lSinitially derived for purely coulombic interaction forces in a more general context16 1-x-
--
C
4000
N L m r'w(r) exp [- U(r)/kT] dr.
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 considered bound in the sense of ion-pairs. Different assumptions have been made
290
about
C O N T R I B U T I O N OF N O N COULOMBIC FORCES
For our purpose we choose w(r) to be a step function
w(r).'j
w(r) =
r
1 i f 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 contributions of ion-ion, ion-dipole, induction-, dispersion- and repulsion forces as tabulated 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 e2 U ( r ) = - -4+) 4mO~,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.' 4000 R N exp (-AG;/RT)[
-= I-u C
r 2 exp
because the quantity NU* may be regarded as AG;.
[4neoc,rkT e2 ]dr
Thus
K: = 4000 R N [ r2 exp [4nEoerrkT] e2 dr. Eqn (15 ) 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 framework 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 association 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 ~and k ) 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. G O R E S
29 1
of conductance data. On the other hand d = q means satisfying a chemical assumption 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-alkylammonium 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 noncoulombic interactions.
+
+
0.7
0.6
0 .3
3.5
40
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) and acetonitrile (a). (a) i-AmaN+I-, (b) i-Am,BuN+I-, (c)BudN+I-, (d)Pr4N+I-, ( e ) Me2Bu2N+I-,(f)MeBu,N+I-; EtBu,N+I-, ( g ) Me4N+I-.
292
CONTRIBUTION OF N O N COULOMBIC FORCES
1.0
0.9
-Yo !=
0.8
4
0.7
0.6
3.5
4.0
4.5
IO~KIT
FIG.2.-Plot of B ( T ) against T-' according to eqn (17) for alkali salts in propanol (0)and acetonitrile(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 discussion 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 For alkali salts AH: > 0, but this heat required for ion-pair formation is comAG:. 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-alkylammonium 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 investigation, only their relative values can provide information. In table 3 we have added for the salts KI and LiCl values indicated by the symbol
293
J . B A R T H E L , R . W A C H T E R A N D H.-J. GORES
TABLE3.-THERMODYNAMIC
DATA O F ION-PAIR FORMATION
-40°C < 6’
4
electrolyte
AH: /J mol-’
d
e=2
< +25”C
AS; AG; /J mol-l K-l /J mol-l
5
~
AG; /J mol-‘
A. propanol ~~
Pr4NI BLI~NI i-Am4NI i-Am,BuNI MeBu N I EtBuSNI Me2Bu2NI KI
6.68 7.10 7.10 7.10 5.64 6.17 5.64 3.52 3.52 2.49 2.49 5.30 3.20
LiCl CsOPr *
4 4 4 4 4 4 4 4 a t s; 4 4 a s; 4
+
-6 800 -6 900 -7 500 -7 300 -6 200 -6 200 -6 000 +3 500 (f3900) >O (>O)
4
+7 400t
4
+8 300
~~
-8.0 -8.0 -8.4 - 8.4 -6.7 - 6.7 -5.0 t13.4 (+14.7)
900 900 100 100 400 -460 (- 500) +3 300 (+3 600) -2 100 -2 800
+5.4 t13.4t $10.5
-4000 t80 -1 400
+-
-4 -4 -4 -4 -4 -4 -4
400
500
-15500 -15 500 -15 700 - 15 700 - 15 900 -15600 - 16 200 - 14 500
- 14 200 -17 100
B. acetonitrile
MeJNI KI
5.64 3.52 3.70
KC104
4 4 4
-2 300 +4 100t +1 800
* Calculated from ref. (5) in the range +5”C slope. d = (a
+ s;
4).
< 0 < + 35°C. 7 Calculated
-8 700 -7100 -8400 from the initial
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 K I 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 AHAvalues 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 thermodynamic 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
CONTRIBUTIONS OF NON 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 unambiguous 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. M. Fuoss and K.-L. Hsia, Proc. Nut. Acad. Sci. USA, 1967,57, 1550. R. Fernlndez-Prini, Trans. Faraday SOC.,1969,65, 331 1. 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.
Related Documents
Ion Pair Formation
April 2020 11
Pair
May 2020 20
Twisted Pair
November 2019 18
Formation
June 2020 25
Tmk Pair
June 2020 24
Pair Performance
November 2019 15More Documents from ""
Abschied Von Der Gluehbirne Sz05092009
June 2020 9
Dissertation Alina Voinescu
May 2020 4
Thesis Nina Vlachy
May 2020 1
Elektrolyte Fuer Lithium Ionen Zellen
May 2020 7
Szmagazin 49 2008. Der Staat Als Retter
April 2020 5