G. S. DARBARI AND S. PETRUCCI
268 this reflects a =t27yO uncertainty in the position of the , 1/T plot. It seems, howrate constants on a log k ~8s. ever, that the differences of the values of kb of the various series are not due to the experimental inability of determining U1 more accurately. We cannot give at the moment a satisfactory explanation for these differences in kb. We can merely state that this phenomenon was also observed in our recent studies of the HtS DZ8and NH3 D213exchange reactions. It clearly indicates that this behavior is typical of the technique rather than the specific reaction studied. When the high- and the low-temperature rate constants are compared on the basis of an Arrhenius extrapolation, the agreement obtained is very satisfactory considering the long extrapolation. The most encouraging result obtained from these data is the negligible effect of argon. As mentioned before, no effect of argon on the rate of this reaction is expected according to the “vibrational excitation mechanism.” Since translation --F vibration energy exchange in No2 is very efficient, the atom transfer step
+
+
should be rate controlling, and this is what is being found. The 0.1 order with respect to the argon might result from some slight error in the Nz04 2N02 equilibrium calculations, which might cause a slight error in the composition. Another source for the slight argon dependence may result from some contribution of the reactions Ar
+ NO2 -+Ar + NO + 0
Ar+CO+O+Ar+COz although extrapolation of the dissociation rate of NO2 to the temperature range covered in this study shows a negligible contribution of the latter to the observed rate. l4 The reason for obtaining a reaction order higher than unity for CO is unclear. It should be mentioned however that Thomas and Woodman have also reported no0 = 1.05in their low-temperature data.a
I
(13) P. Schechner, A. Burcat, and A. Lifshitz, J . Chem. Phys., in press. (14) H. Hiroyuki and R. Hardwick, ibid., 39, 2361 (1963).
Ultrasonic Relaxation of Some Tetraalkylammonium Salts in Acetone at 25”
by G. S. Darbari and S. Petrucci Department of Chemistry, Polytechnic Institute of Brooklyn, Brooklyn, New York 11901 (Received April 8, 1869)
Ultrasonic absorption measurements of 0.1 M solutions of Me4NPi, EtdNPi, BudNPi, and BudNNO, and of solutions of AmdNBr, BurNBr, and BudNCl in the concentration range 0.05-0.20 M at 25” in acetone are reported. (Pi = picrate, Me = methyl, Et = ethyl, Bu = butyl, Am = amyl). After evaluation of possible C-C isomeric relaxation, the results are interpreted by the hypothesis of ionic,association. The conclusion is that the forward rate constant is diffusion controlled but the reverse rate constant is not. This conclusion is corroborated by analysis of previous conductance results indicating the presence of two types of ion pairs for similar systems.
Introduction Classical mass transport experiments and theories like electrical conductance’ have been extensively applied to alkylammonium salts in aqueous and nonaqueous solvents.2 These systems were originally chosen so as to have the closest resemblance to the features of the assumed model’ (ions taken as spheres in a continuum, lack of ion solvent interactions and Stokes hydrodynamics). Surprisingly enough, very often even these systems offered effects that could not be explained by the. classical theories. They were rather rationalized in terms of a posteriori invoked ion-solvent interaction^.^ The reliability of such effects has been The Journal of Physical Chemistry
proven by independent tools4 on the same systems, denying any claims of calculation ambiguities of the conductance theory but rather confirming the presence of real effects. On the other hand, ion-solvent interactions in these systems should represent the weakest form possible out of other comparable interactions that (1) R. M. Fuoss and F. Accascina, “Electrolytic Conductance,” Interscience Publishers, New York, N. Y., 1959. (2) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed, rev., Butterworth and Co., Ltd., London, 1969 p, 550. (3) H. Sadek, E. Hirsch, and R. M. Fuoss in “Electrolytes,” B. Peace, Ed., Pergammon Press Ltd., London, 1962. (4) 8. Petrucci and M. Battistini, J . Phys. Chem., 71, 1181 (1967); S. Petrucci and F. Fittipaldi, ibid., 71,3087 (1967).
ULTRASONIC RELAXATION OF SOME TETRAALKYLAMMONIUM SALTS
269
Table I": Sound Absorption Coefficients a t Different Frequencies for the Various Systems Investigated MaNPi, c /, MHz
5
EtrNPi, c
0.10 M
15 21 25 27 33 35 45 55 65 75 85 105
3
a,om-1
25 35 45 55 65 85 105 115 125 155
0.0870 0.159 0.231 0.254 0.367 0.426 0.671 1.006 1 337 1.768 2.198 3.309 I
0.225 0.449 0.702 1.11 1.39 2.44 3.57 4.20 5.24 7.83
a,om-1
f, MH5
a,cm-1
15 25 35 45 55 85 90 105 115 125 135 150 190 210
0.072 0.213 0.403 0.670 0.969 2.37 2.63 3.61 4.34 4.99 6.19 7.55 12.25 13.63
15 25 35 45 55 65 90 95 110 115 125 130 150 170
0.093 0.249 0.507 0.802 1.22 1.73 3.27 3.74 4.84 5.41 6.23 6.85 9.06 12.0
AmrNBr, c = 0.20 M f , MHz a,cm-1
10 30 50 70 90 110 130 150 170 190 210
0.0633 0.547 1.485 2.763 4.317 6.620 8.635 11.51 14.39 17.50 20.03
c = 0.10 M a,om-1
f. MHz
10 30 50 70 85 95 105 110 130 170 190 210 230 250
BurNI, c = 0.20
M
f, MHz
a,om-1
10 30 50 70 90 110
0.0461 0.403 1.140 2.187 3.569 5.296
c = 0.20 M j,MHz a,om-'
130 150 170 190 210
5.756 7.483 9.440 11.51 13.82
BurNNOa, c = 0.10 M
BurNPi, c = 0.10 M
f , MHz
c
-
f, MHz
10 15 25 30 35 45
0.0480 0.417 1.162 2199 3.273 4.079 4.714 5.276 7.023 11.40 14.52 17.10 19.57 23.03 0.10 M a,om-1
0.0410 0.0892 0.249 0.345 0.4605 0.794
c = 0.05 M a,cm-1
f, MHz
10 30 50 70 90 110 130 150 170 190 210 230
0.0421 0.380 0.979 1.888 3.016 4.605 6.102 8.347 10.25 12.44 15.02 17.46
c = 0.05 M f , MHz a,om-'
10 30 50 70 90 110
0.0353 0.322 0.852 1.669 2.832 4.029
-
ButNI
0.10 M
f, MHz
a,om-1
c 0.1OM f, MHz a,cm-1
50 55 65 70 75 85 95 105 110 115 130 150 170 190
c = 0.05 M f, MHz a,om-1
0.952 1.174 1.586 1.796 2.072 2.697 3.399 4.202 4.375 4.778 5.987 8.289 9.556 12.43
130 150 170 190 210 230
7.023 9.671 12.09 14.97 16.81 20.26
BurNBr, c = 0.20 M f, MHz a,cm-1
15 25 30 35 50 55 65 70 75 85 95 105 115 125 145 155 185 195 205
0.1235 0.328 0.4835 0.6505 1.266 1.612 2.257 2.533 2.798 3.569 4.398 5.484 6.102 7.276 9.556 10.36 14.05 14.97 16.58
c = 0.10 M f , MHz a,om-1
15 25 35 45 50 70 75 85 95 105 115 125
f,
0.108 0.282 0.530 0.9095 1.082 2.026 2.360 2.878 3.534 4.202 4.778 5.641
c = 0.05 M MHz a,cm-1
15 21 27 33 39 45 57 69 75 81 87 95 99
0.0892 0.176 0.282 0.4145 0.587 0.800 1.220 1.727 1.946 2.234 2.556 3.051 3.316
BurNC1, c = 0.20 M
c = 0.10 M a,cm-1
f , MHz
a,om-1
f , MHz
10 30 50 70 90 110 130 150 170 190 210 230 250
0.0691 0.581 1.589 2.878 4.835 6.965 9.786 12.43 15.43 18.305 21.41 25.10 28.21
10 25 30 35 55 65 75 85 95 130 135 145 150 155 170 190 230
c = 0.05
M
f , MHz
a,cm-1
10 15 25 30 35 45 50 55 70 75 85 90 105 110 150
0.0437 0.0921 0.265 0.368 0.501 0.840 1.013 1.186 1.957 2.164 2.648 3.051 3.851 4.087 7.483
0.0653 0.372 0.535 0.608 1.700 2.266 2.856 3.626 4.433 7.555 7.977 9.337 9.745 10.20 11.90 13.94 19.83
" At least one figure in excess with respect to the sensitivity of the method is reported for the absorption coefficient a. This has been done in order to avoid rounding off errors during possible calculations from these data by others. Volume 74,Number I
Januarg 99,lQ70
270 are rather well understood for the intermediate cases of transition metalsb and for the extreme cases. of the solution chemistry of square planar Pt(I1) and octahedral Co(II1) complexes.6 From a kinetic point of view, (considering the solvent molecules associated with the ions in solution as ligands) the solvent substitution by the associating ionic partner should occur in these systems with a rate comparable to the rate of attack by the incoming ion, namely with rates comparable to diffusion-controlled reactions. It has been with these preambles in mind and in an effort to understand the mechanism of ionic association in nonaqueous solvents that it was decided in this laboratory to study with a modern kinetic tool a series of systems already investigated by electrical conductance. Kraus, et al.,' in a series of papers reported the electrical canductance of several alkylammonium halides, nitrates, and picrates in acetone at 25'. These excellent data have recently been reanalyzeds by the 1959 version of the Fuoss-Onsager conductance theory for associated electrolytes' providing useful parameters such as association constants and minimum approach distance between free ions.
G . S.DARBARI AND S. PETRUCCI ;AikylI, N Picrates in ac8'tone at 25OC
501
t
' "1
@
M e 4 N Picrate 0.1 M
V
Bu4
b
I
I
20
50
A bsorpi ion
m-
N
Picrate 0.1 M
io
Oi
I
I
I
zoo
100
500
-
f (MH21
Figure 1. Plot of acetone a t 25'.
60
(ly/f2)
vs. f for MerNPi and BuhNPi in
1 BuqNBr IN ACETONE AT 25%
Experimental Section Materials. Acetone (Baker, reagent grade) was distilled over anhydrous Gus04 in a 3-ft Vigreux all-Pyrex distillation assembly. Only the middle portion was collected. All the salts were Eastman Kodak reagent grade. They were dried at 40-50" under vacuum at 1 mm up to constancy of weight ( f1 mg) before use. This proved to be important especially for Bu4YC1 which is extremely hygroscopic. The solutions were prepared by dissolving weighed amounts of dry salts in freshly purified acetone and diluting to volume in volumetric flasks. Equipment. A Matec 560 Ultrasonic Pulser-Receiver was used in conjunction with a 531 A oscilloscope and a 608D Hewlett-Packard Standard Signal Generator. The cell assembly and the method of measurements have already been de~cribed.~Many runs were repeated by changing the piezoelectric crystal from 3 to 5 and to 10 MHz (fundamental frequency) and scanning the sound absorption in all the frequency ranges observable in order to ensure reproducibility after several days with the same solution. The values of the measured frequencies were checked by a crystal calibrated frequency standard. The temperature was maintained within f 0.05" during the measurements by means of a Forma Junior refrigerated bath.
Results I n Table I the absorption coefficients CY (nepers cm-') and the corresponding frequencies f (MHz) for the various electrolytes investigated are reported. In Figures 1 and 2, representative plots of the quantity ( a / f z )us. The Journal of Physical Chemistry
'Or
70
I 20
I
I
50
100
I 200
I 500
f(MHz) --P
Figure 2. Plot of ( q ' f a ) us. f for BurNBr in acetone a t 25".
f are presented. The data in Figures 1 and 2 are analyzed using a function for a single relaxationlo
(5) T. R. Stengle and C. H. Langford, Coordination Chem. Rev., 2 , 349 (1967). (6) C.H.Langford and H. B. Gray, "Ligand Substitution Processes," W. A. Benjamin, New York, N. Y.,1965. (7) M.B. Reynolds and C. A. Kraus, J . Amer. Chem. Soo., 7 0 , 1709 (1948);M.J. McDowell and C . A. Kraus, ibid., 73,3293 (1951). (8) D.F. Evans, C . Zawoyski, and R. L. Kay, J . Phys. Chem., 69, 3878 (1965). (9) S. Petrucci, ibid., 71, 1174 (1967). (10) J. Lamb in "Physical Acoustics," Vol. 11, part A, Ed., W. P. Mason, Academic Press, New York, N. Y.,1965.
ULTRASONIC RELAXATION OF SOMETETRAALKYLAMMONIUM SALTS where A is a constant at each concentration and temperature, f r is the relaxation frequency, and B is solvent absorption which at 25" was found to be a~/$= (30 f 2) lo-'' cm-' sec2in the range of frequency 10210 MHz. The individual determinations at the frequencies investigated are reported in Table 11. No evidence of solvent relaxation is visible in this frequency range. Additional measurements down to -5" do not show any relaxation in the same frequency range. All the systems showing a relaxation could be interpreted by the single relaxation function (1). The values of A and f r for the electrolyte solutions investigated are reported in Table 111. The parameters A and f r are precise to about h 10%. The system 0.1 M Bu4NBr in acetone already i n ~ e s t i g a t e dgave ~ ~ a relaxation frequency of fr = 66 MHz. These data combined with the ones of the present work (Figure 2) give a more reliable value off, = 90 f 15 MHz. The reason of the lower (previously) calculated relaxation frequency is due to a point a t 15 MHz (Figure 2) that is clearly too high.
Table I1 : Sound Absorption Coefficient LY and Ratio (Q) Acetone a t 25'
30 50 70 90 110 150 170 190 210
0 273 0.702 1.50 2.39 3.80 7.02 8.23 12.1 12.8 I
for
30.4 28.1 30.6 29.5 31.4 31.2 28.5 33.5 29.0
In this regard one should notice that the overall excess absorptions (./$ - a0/f2)with respect to the solvent are rather small. Because of the sensitivity of the method (i2%) and of the small excess absorption, a complete analysis by the excess function aeyexcX vs. f is not feasible with the present data. Indeed the scatter of the individual points is too high especially for the more dilute solutions. For MerNPi, measurements at higher concentration than 0.1 M are not possible because of solubility limitations. (For Me4NBrthe solubility is so low that it is impractical to make any attempt to measure its sound absorption). Therefore, for the picrates this study has been limited to the single concentration 0.1 M in order to allow for a qualitative comparison between different alkylammonium picrates; 0.1 fM Bu4NN03 has also been studied to demonstrate the effect of an anion (other than halides or picrate) on the ultrasonic absorption.
27 1
Table 111: Parameters from Equation 1 for the Various Systems Investigated
c, M
A x 1017, om-1 sees
MerNPi EtrNPi Bu4NPi BU~NNO~
0.10 0.10 0.10 0.10
9 7 3 10.5
AmrNBr
0.20 0.10 0.05 0.20 0.10 0.05 0.20 0.10 0.05 0.20 0.10 0.05
32 18 11
Salt
BurNI
BurNBr BurNCl
17 9.5 6.0 26 19 10 38 31 13
fr,
MHz
* *
35 5 10 85 Relaxation frequency above the range of measured frequencies if present 210 rt 20 180 4 20 160 f 20 240 4 25 180 4 20 150 f 15 150 rt 15 90 4 15 80 f 10 190 f 20 130 f 15 95 rt 10
Discussion The Hypothesis of Isomeric Relaxation. Symons, et al.," measured the ultrasonic relaxation of pure 3,3diethlypentane and of its solutions in n-hexane. These authors attributed the observed relaxation to an internal rotation about a C-C bond. They also suggested that all or part of t4heultrasonic absorption of alkylammonium ions in so1ution12 is caused by a comparable rotational isomerism. The present authors, although finding this hypothesis very interesting, do not share with this view as applicable to the present data. The following considerations lead to the above conclusion. Inspection of Figure 1 and Table I11 shows that a relaxation process is present for Me4NPi where no internal rotation is possible. Et4NPi still shows a relaxation a t higher frequency than MeeNPi. For Bu4NPi if a relaxation is existing (in view of A being statistically larger than B ) it is above the range of our measurements. See Figure 1 and Table 111. The trend in the ultrasonic absorption going from NIedNPi to Et4NPi and to BurNPi might be due to the decreasing association constants the values being K (A) = 67 =!= 1, 45 f 2, and 17 5, respectively.8 Further, on comparing the observed relaxation effects for BurNNOa, Bu4NPi, B u ~ N I Bu4NBr, , and Bu4NCI, one may conclude that the relaxation frequency is dependent on the anion for the same cation (Table I11 and Figure 3). (11) M. J. Blandamer, M. J. Foster, N. J. Hidden, and M. C. R. Symons, J . Phys. Chem., 72,2268 (1968). (12) 8.Petrucci and G. Atkinson, ibid., 70,2550 (1966).
Volume 74, Number 2 January 22, 1970
272
G. S. DARBARI AND 8.PETRUCCI 70
I
O.IM Bu&+SALTS
IN ACETONE AT 2 5 O C
2
I
N -
\ Y Ci
30
"I 0
SOLVENT ABSORPTION
0
Bu4NCI
@
Q
Bu4NBr(Ref. 4b) Bu4NI
D
Bu4NPi
20
50
100
200
I
lo 102
5
1 -
I
I
I
500
f(MHz)-
Figure 3. Plot of (a/f2)us. f for 0.1 M Bu4NCIJBurNBrJ BudNI, BurNNOs, and Bu;NPi in acetone a t 25'.
Finally, for the same electrolyte, the relaxation frequency is concentration dependent (Table 111, Figure 2) indicating a bimolecular (or more complex) process but not a first-order isomeric transformation. The above rules out rotational isomerism to be the only source of excess sound absorption. It remains to discuss the possibility of a contribution to the sound absorption due to isomeric relaxation. This cannot be ruled out in principle; however, our interest is focused on the observed relaxation region and, in particular, on the relaxation frequency of the process observed. Apart from the unlikelihood of having two kinetic processes of different order and nature occurring with the same reIaxation time, the data show a single relaxation process varying with the nature of the anion for the same cation. Therefore, even if for a particular electrolyte the overlapping of the two processes exists, the shifting of the frequency with the nature of the anion should reveal the overlapping. Further, the data can be interpreted with the value of B equal to the sound absorption of the solvent. It means, therefore, that if isomeric relaxation has an observable relaxation, this should show up a t frequencies below the investigated region. Finally, it should be remembered that the electrolytes are not heavily associated. Therefore, most of the ions are free. This eliminates the most unlikely possibility, namely of the anion being associated to the cation and influencing with its proximity and nature the internal rotation about C-C bonds. The Hypothesis of Ionic Association. The hypothesis is advanced, therefore, that the observed relaxation processes are due to ionic association. According to The Journal of Physical Chemistry
Figure 4. Plot of T - I vs. e for the tetraalkylammonium halides investigated in acetone at 25'.
Eigen,13the relaxation time T = [2rjr]-I is correlated to the forward and reverse rate constants kf and k~ of the chemical equilibrium by the relation 7-1
=
kre
+
kR
(2)
where the quantity e is a function of the concentrationla of the electrolyte of the type (3)
with u the degree of ionization, c the stoichiometric concentration, and y+ the ionic mean activity coeficient. The quantity 0 has been estimated by combining the expression for the association constant as determined by electrical conductance and the Debye-Hiickel expression for yA retaining the quantity UJ from conductance results as the minimum approach distance between the free ions. 1 - u
K(A) = u2cy*2
-log
y*2
=
(4)
2Srl/ca
1
+AuJ~/&
Combination of expressions 4 and 5 gives u and y*2 and therefore 0 from expression 3. The plots of 7-1 us. e are shown in Figure 4. The results for kr and k ~ are t reported in Table IV. In the same table the rates of a diffusion-controlled process (1s) M. Eigen and L. DeMayer in "Investigation of Rates and Mechanisms of Reactions," Vol. VIII, part 2, Ed., A. Weissberger, John Wiley and Sons, New York, N. Y., 1963.
ULTRASONIC RELAXATION OF SOMETETRAALKYLAMMONIUM SALTS
273
Table IV : Association Constants, UJ Parameters, Fuoss Association Constants, Calculated Forward and Reverse Diffusion-Controlled Rate Constants, and Experimental Forward and Reverse Rates for the Tetraalkylammonium Halides Investigated in Acetone Electrolyte
K ( A ) , M-1
aj X
AmrNBr BurNI BurNBr BurNCl
220 f 20 143 f 6 264 f 5 430 f S b
7 f 1 6 . 1 f 0.3 5 . 4 f 0.2 5.7 f O . l b
Wcm
KF‘ M-1
38 42 64 55
kD X 10-10 ’, M-1 sec-1
8.5
9.7 11.1 10.3
k-D X 10-9 a sec-1
k f X 10-10, M -1 sec -1
k u X 10-8, sec-1
2.2 2.3 1.7 1.9
7 f 5 11 f 3 10 f 2 13 f 2
0 . 5 f 0.5 0.25 f 0.25 Not measurable
The values of UJ from the conductance calculations have been used for the present calculations. b The authors are indebted to Dr. Fennel1 Evans of Case Western Reserve University, Cleveland, Ohio, for having furnished these data as a private communication.
of ionic recombination k~ and ion pair dissociation k - ~ the calculated 8 values are completely unreliable, the conclusion k - ~> k~ remains valid. are also reported. These quantities have been calculated by means of the relations of Smolu~howski-Debye~~ In regard to the accuracy of 8, the use of the DebyeHuckel theory to calculate yk2 is one of the major for kD and EigenI6for k - ~ ,respectively, modified by the sources of error. I n order to try t o get an assessment use of the Stokes-Einstein equation on the reliability of the above conclusions ( k = ~ kr) a calculation has been performed using only the data at the lowest concentration 0.05 M . For these systems, the ionic strength is around 0.02-0.03, that is still in a range where eq 5 may apply with some accuracy. From eq 2 considering K(A) = kf/kR the following expression for kfis derived where k is the Boltzmann constant, T the absolute temIr 1 1 perature, N Avogadro’s number, q the viscosity of the solvent, and b the Bjerrum parameter; a has been set equal to UJ. One can see from Table IV that the exI n Table V, the calculated kt values are reported toperimental kf and kD are comparable. Considering the gether with the values of e used for this concentration. drastic approximations involved (e.g., (1) the use of the It may be seen that the values of kf are rather lower Debye-Huckel expression for the activity coefficients at than in Table IV (having imposed the condition (kf/K(A) the present concentrations in the calculation of 8, (2) = k ~ but ) still close enough to the calculated diffusionthe use of the Debye-Ruckel potential in the calculacontrolled rates k~ not to invalidate the above conclution of the electrostatic factor in eq 6 and 7 (- b/ebB- l), sions ( k =~ kf). and (- b/l - e”, ( 3 ) the use of the Stokes-Einstein equaIndependent Support. The reverse rate constants not tion to calculate the diffusion coefficients of the ions being diffusion controlled corresponds to saying that the through the viscosity of the solvent, and finally (4) the association process cannot be expressed through a conunknown effects of the use of the static activity coeffitinuum model, or in mathematical terms through the cients for the dynamical process in question where the rate of ionic recombination is comparable to the rate of rearrangement of the ionic atmosphere) the Table V : Calculated Forward Rate Constant kf agreement is good enough to conclude that the forfrom the Relation ward process of ionic recombination to form an ion pair is diffusion controlled or at least close to diffusion controlled. The same cannot be said, however, for the (e + --i_) x io*, reverse rate constant k ~ .Inspection of Table IV K(A) r - I x 10-8, k f X 10-10, shows that k~ is smaller than k - ~by about one order of Eleatrolyte e X 102, M m a -1 M M-1 @ea-1 magnitude. For Bu4NC1 and Bu4NBr, k~ cannot be AmrNBr 0.72 10 f 1 1.17 9A 1 even read on a 7-l vs. 0 plot, the intercept being about BurNI 0.69 9.4 f 1 1.39 7 f1 zero (Figure 4). BurNBr 0.57 5.0 A 0.7 0.95 5 3~ 1 Some words must be spent oh the reliability of the BurNCl 0.57 6 . 0 f 0.6 0.80 8 rt 1 above conclusions in view of the approximations involved. It is clear from Figure 4 that the intercept of the r--l vs. 0 plots cannot ever give a k~ = L-D since this (14) M. Von Smoluchowski, Phusik. Z . , 17, 657 (1916), P. Debye, would imply an ordinate larger than the observed 7-l a t Trans. Electrochem. SOC.,82, 265 (1942). the highest concentration studied. Therefore, even if (15) M. Eigen, Z . Phys. Chem., (Frankfurt am Main), 1, 176 (1954). Volume 74,Number 8 January 22, 1070
G. S.DARBARIAND S. PETRUCCI
274
Fuoss expression of ionic association,16that is the ratio between eq 6 and 7 4rNa3 KF
=
3ooo
exp(b) =
47rNa3
exp
-
3000
( z z L (9) ) le2
aDkT
This, on the other hand, was self-evident from the conductance results themselves. Indeed in Table IV, the association constants K ( h ) obtained through conductance and the parameters aJ are reported. The value of K F from eq 9 using UJ are also reported. It can be seen that KF = 38-64 J 4 - I while the experimental data LD for K ( h ) vary between 140 and 430. [Since kf this corresponds to saying that k~ < k - ~ ] . Notice also that in order to force the Fuoss function to reproduce K ( h ) one should impose a value of a in formula 9 much smaller than the parameters U J . One could speculate therefore from conductance alone that two minimum approach distances can be calculated from conductance data, a collision diameter between free ions UJ and a minimum distance between the same ions from K ( h ) much smaller than U J . Indeed for Bu4NIJ Sears, et al.," have calculated the association constant from conductance data from -55 to 25". If one plots the log K ( A ) os. (DT)-' according to eq 9 one obtains a straight line up to -30" while the last two points at -40 and -50" are somewhat below. From the slope of the straight line one can calculate the parameter a = 2.2 8,much smaller again than UJ = 6.1 f 0.3 8 at 25". Also, Adams and Laidler'* in a series of recent papers on association and mass transport of alkylammonium salts in acetone have rationalized the
-
The Journal of Phvsical Chemistry
data with the assumption of at least two species of ion pairs, "solvent-separated" and "solvent-shared" ion pairs. The presence of contact ion pairs was postulated at lower dielectric conp+mt than 20. Also, Taylor and Kuntz'g in a study of ionic association by nmr of [Me(Bu)~]N-B(C6H6)4 in several solvents have concluded from limiting shifts that a large fraction of ion pairs in acetone must be solvent-separated ion pairs.
Conclusions The systems investigated seem to represent a case where rates of diffusion-controlled approach between ions and rates of desolvation are almost comparable. For the reverse rate constants, however, a substantial difference exists between the diff usion-controlled rates of separation of the less "tight" ion pairs and the rates of separation of the more "tight" ion pairs, having assumed their existence on the basis of independent evidences.
Acknowledgments. The authors wish to express their thanks to machinist Richard Parla and his apprentice, Marvin Charles, for having constructed the ultrasonic cell used in this work. (16) R. M. Fuoss, J . Amer. Chem. Soc., 80,5059 (1958). (17) P. G. Sears, E. D. Wilhoit, and L. R. Dawson, J . Phys. Chem., 60,169 (1956). (18) W. A. Adams and K. J. Laidler, Can. J . Chem., 46, 1977, 1989, 2006 (1968). (19) R. P. Taylor and I. D. Kuntz, Jr., J . Amer. Chem. Hoc., 91, 4006 (1969).
