SERGIOPETRUCCI AND GORDON ATKINSON
2550
Ultrasonic Absorption in Solutions of Tetra-n-butylammonium Bromide in Two Isodielectric Solvent Mixtures
by Sergio Petrucci and Gordon Atkinson’ Department of Chemistry, University of Maryland, College Park, Maryland
80740 (Received F e h r y $1, 1966)
The ultrasonic absorption of Bu4NBr solutions in CC14-CHsOH and C6H5N02-CC14mixtures has been measured at 2.5’ in the frequency range 25 to 250 MHz. In each case a single, concentration-dependent relaxation is observed. This relaxation is interpreted in terms of a diffusion-controlled ion association process, and the rate constants and equilibrium constants are derived. A comparison of the ultrasonic equilibrium constants with conductance association constants indicates that the association is a single-step process in the nitrobenzene mixture but a two-step process in the methanol mixture. The magnitude of the diffusion rate constants and the AVO values for the association processes are discussed.
aqueous systems is a necessary step in the establishment of a general theory of the effect of solvent characRelaxation methods and, in particular, ultrasonic ter on the ion association process. Water is a particular absorption have been used to study the kinetics of ion and peculiar medium. Because of its very strong association in a variety of 2-2 electrolytes in ~ a t e r . ~ , ~ tendency to coordinate to both anions and cations, it In the cases where a rather complete study would be can obscure differences between ions that should be obmadel4t5it could be shown that association in this type served. However, its importance in biological systems of electrolyte took place in three kinetically distinct and in common chemical work has focused most of the steps. This was originally postulated by Eiged and fast kinetic work on it. This situation is similar to applied with great success to a number of systems.’ that in electrical conductivity work in the era around The stepwise association picture has also been applied 1920. to a number of other charge-type electrolytess (2-1, The specific problem of ion association is such an 3-1, 4-1), but in most of these cases insufficient data important one in many areas of chemistry that the are available for a complete analysis. In general, 1-1 electrolytes do not show any chemical relaxation but only increase or decrease the absorption (1) To whom all correspondence should be addressed. coefficient of the water. This is most probably a struc(2) G. Kurtre and K. Tamm, Acustica, 3, 33 (1953). tural relaxation phenomenon. The lack of chemical (3) K.Tamm, G. Kurtze, and R. Kaiser, ibid., 4,380 (1954). relaxation in aqueous 1-1 electrolytes, except for weak (4) G. Atkinson and 8. Petrucci, J . Phys. Chem., in press. acids and bases, is primarily due to the rather small as(5) M. Eigen and K. Tamm, Z . Eledrochem., 66, 107 (1962). sociation typical of such systems. (6) M. Eigen, G. Kurtre, and K. Tamm, ibid., 57, 103 (1953). No work has been reported on 1-1 salts in nonaqueous (7) M. Eigen and L. De Maeyer in “Investigations of Rates and Mechanlsms of Reactions,” Part 11, Interscience Publishers, Inc., solvent systems. The only nonaqueous work has been New York, N. Y., 1963. Chapter XVIII. on 2-2 salts in mixed water-organic systems of rela(8) J. Stuehr and E. Yeager in “Physical Acoustics,” Vol. 11, Part A, W. P. Mason, Ed., Academic Press Inc., New York, N. Y.,1965, tively high dielectric constant. 9-11 This was underChapter 6. taken as an extension of the aqueous work to examine (9) J. R. Smithson and T. A. Litovits, J. Acoust. Sac. Am., 28, 462 the role of the bulk dielectric constant in the stepwise (1956). association. (10) 9.K. Kor and G. 9. Verma, J. Chem. Phys., 29, 9 (1958). The extension of the relaxation techniques to non(11) G.Atkinson and 9. K. Kor, J. Phya. Chem., 69, 128 (1965).
Introduction
The Journal of Physical Chemiatry
ULTRASONIC ABSORPTION IN TETRA-TI-BUTYLAMMONIUM BROMIDE
failures of the classical continuum solvent theories to explain it have been a particular embarrassment to the solution chemist. The stepwise association model of Eigen based on relaxation techniques offers a powerful tool for the detailed analysis of the mechanism of association. This need for a new approach is illustrated by the increasing complexities and ambiguities of the conductance theory which has served as a base line for the determination of so many association constants. 12-15 These association constants are obtained in conductance work16 from the difference between the experimental data and a theoretical curve. Any attempts to correlate the derived association constants with parameters such as dielectric constant or ion size again demand some choice between a F ~ o s s or ’ ~Bjerrum’* association model. Even more basic problems arise when we examine in detail the validity of such parameters as the bulk dielectric constant. We find many cases where the same electrolyte in isodielectric mixtures gives drastically different association constant^.'^ In these cases neither classical theory is able to explain the results, and specific solvent effects must be invoked in an ex post facto rationalization.20 For an initial assay into nonaqueous systems, we chose a system where the above problem prevailed. In 1954 Fuoss and Sadek21published conductance results for Bu4NBr in CHSOH-CC14, C&,N02-CC14, and CH30H-C6HsNO2solvent mixtures. Then in 1959 the same authors recalculated the conductance parameters Ao, U J , and K A using the Fuoss-Onsager theory.22 The main problem in interpretation was the greatly different association constants ( K A ) for isodielectric mixtures. The authors discussed this in terms of the empirical ion-solvent interaction parameter, E,, of G i l k e r ~ o n . ~ ~ For a specific example, at D = 16.0, K A for Bu4NBr in CH30H-CC14 (68.8% w/w CC14) was 537, but a t the same D the K A was 1820 in the CaH5N02-CC14 mixture (55.4% w/w CCl,). We decided to examine this pair of systems by ultrasonic absorption in an attempt to obtain a more detailed picture of the association process.
Experimental Section The apparatus and experimental method have been described in detail in recent publi~ations.~J~ The CHSOH was purified by a double distillation from A1 amalgam.24 The CeH5N02was distilled three times a t 1 mm with only the central portion being collected each time.26 The CC14 was purified by fractional distillation from P206.26Bu4NBr2?was dried at 1 mm and 50” for 3 days. The solutions were made up by weight using glove-bag techniques to maintain dry conditions.
2551
Results The ultrasonic absorption coefficient is defined by
I , = Ioe-2ax (1) where I , = sound intensity a t x cm, Io = sound intensity at x = 0, and x = distance in cm. In the case of electrolytes we are concerned with the excess absorption defined by cy‘
= ffsolution
-
(2)
%solvent
and in the absorption per wavelength Ir,
= ff’h =
(3)
.I(;)
where v = ultrasonic velocity and f = ultrasonic frequency. Since velocity dispersion is small for these systems, we can use v in the solvent in our calculations. The solvent parameters measured are given in Table I together with other useful solvent data.
Table I: Solvent Parameters at 25’ Mixture
CHsOH-CCII
CsHsNOrCCh
Composition, W/W % CCla
68.80
54.81
16.0
16.2 0.0125 125.0 X lo-” 1.220 x 106
D 7, poise a/?, cm-1 sect
v, cm sec-l
0.00779
6 0 . 3 x 10-17 1.035 X loK
Figure 1 shows the relaxation spectrum of the BudNBr in the CC14-C6H5N02mixture. In the frequency (12) R. M. Fuoss and L. Onsager, J. Phys. Chem., 67, 621 (1963). (13) D. J. Karl and J. L. Dye, ibid., 66, 477 (1962). (14) 9. Petrucci, Acta Chem. Scad., 16, 760 (1962). (15) G. Atkinson and C. J. Hallada, J. Am. Chem. SOC.,84, 721 (1962). (16) C. B. Monk, “Electrolytic Dissociation,” Academic Press Inc., New York, N. Yo,1961. (17) R. M. Fuoss, J . Am. Chem. SOC.,80, 5059 (1958). (18) N. Bjerrum, KgZ. Danske Videnekab. Selakab, 7 , No. 9 (1926). (19) G.Atkinson and S. Petrucci, J. Am. Chem. SOC.,86, 7 (1964). (20) A. D’Aprano and R. M. Fuoss, J. Phys. Chem., 67, 1704, 1722, 1871 (1963). (21) H. Sadek and R. M. Fuoss, J. Am. Chem. Soc., 76, 5897, 5905 (1954). (22) H. Sadek and R. M. Fuoss, ibid., 81, 4507 (1959). (23) W.R.Gilkeraon, J . Chem. Phys., 25, 1199 (1956). (24) H. Hartley and H. R.Raikes, J. Chem. SOC.,524 (1925). (25) K.B. McAlpine and C. P. Smyth, J. Chem. Phye., 3,55 (1935). (26) “Organic Solvents,” Interscience Publishers Inc., New York, N. Y.,1955. (27) Eastman Organic Chemicals, Item 7377.
Volume 70,Number 8 August 1966
SERGIO PETRUCCI AND GORDON ATKINSON
2552
-WZ-
2VW
.
0
A
0.01 c
0.05C
CI
2 1
1 30
1 5 x )
1
I
1 1 1 1 1 1 50 7090 LOG f (MH)
1
I
15020OxK)
1
1
!DO
Figure 1.
I
I
1 I I Ill
(V,Z -
v02)
+ (Urn2-1 Vo2)T
(4)
where pmaxis a constant for a given salt-solvent curve. The parameters p,,, and r are varied to obtain the best fit of the experimental curve over the frequency region. The relaxation parameters derived by this process are tabulated in Table 11.
I
~
Table 11: Relaxation Parameters of BuaNBr
8
6ok
W2T
where w = angular frequency = 2nf, vm = high-frequency limit of sound velocity, vo = low-frequency limit of sound velocity, T = relaxation time = (2TfR)-l, and fR = relaxation frequency. In the Mikhailov technique (wZ/2v3a’)is plotted against u2,and the slope and intercept are determined. Then the ratio of slope to intercept gives r 2 from which we can evaluate f R . This technique is very sensitive to errors in CY’ and is useful only for very accurate data. A more generally useful approach is to use the equation for a single relaxation processz9
0.10 c
1
-
Bu4NRr in CC14 -CH,OH
104pmu,
Mc
nepers/ wavelength
0.030 0.050 0.100 0.200
170 173 175 180 183
7.0 7.8 8.9 12.6 16.5
0.010 0.050 0 * 100
46 60 65
5.2 8.8 17.8
Solvent system
Salt concn
CCGCHsOH
0.010
CCGCeHsN02
fR9
0 0.01c
-
0 0.05C A 0.20~
-
The high frequency a t which the relaxation occurs and its concentration dependence indicate the most logical first approach. In this we consider the equilibrium leading to the relaxation to be kn
Bu4N+
Figure 2.
region measured (25-170 Mc) only a single relaxation is observed. Figure 2 gives the analogous results in the CC14-CH30H mixture. Again a single relaxation fits the curves over the frequency range measured (25-250 Mc). Two methods were employed in the data analysis to obtain the frequency of maximum absorption. The first technique is that of Mikhailov who has shownz8that The Journal of Physical Chemistry
+ Br- 1_ Bu4N+Brkni
(6)
For such an equilibrium the relaxation time is related to the rate constants by30 T-’
=
k21
+ klz@(C)
where (28) I. G . Mikhailov, Dokl. A M . Nauk SSSR, 89,991 (1953). (29) J. Lamb, ref 8, Chapter 4. (30) M. Eigen and K. Tamm, 2. Elektrochem., 66, 93 (1962).
(7 )
ULTRASONIC ABSORPTION IN TETRA-WBUTYLAMMONIUM BROMIDE
@(C) = ~Cy*'[2
+ 81
-sIz+Z,I(~C)'/~
+ Ba0(aC)'/2
where S and B = Debye-Hiickel parameters and uo = mean distance of closest approach. The calculational procedure is as follows: (1) estimate a K12 and calculate a a; (2) calculate @(C)for each C using eq 9; (3) plot eq 7 and find kZ1and klz; (4)calculate a new kzl and klz and calculate an ao from the Bjerrum theory;18 (5) recycle steps 1, 2, and 3 using eq 10 in step 2; and (6) repeat the cycle until Klz(out) and K12(in) agree. In the cases analyzed here three cycles were sufficient to ensure agreement in step 6. Table I11 gives the final results.
Table I11 : Bu4NBr Kinetic Results Solvent system
CCla-CHaOH CC14-Ce.H6N02
kiz, M-1
sec-1
13.3 X 10" 1 3 . 1 X 10"
8ec-1
Kn-1, M-1
KA," M-I
8.0 X 10' 7.9 X 10'
166 1650
1700
kri,
+ Br-(MeOH), 1kzi
0
[Bu4N+(?tleOH)Br-] [Bu4N+Br- J
0 where state @ is a solvent-separated ion pair and state @ a contact ion pair. For this process the over-all association constant is related to the step constants by
-S[Z+Z_[(UC) 1
Bu4N+(MeOH),
kiz
(9)
or In yi =
I
0
(8)
and u = degree of dissociation, C = analytical concentration of Bu4NBr, yi = mean ionic activity coefficient, 8 = [ ( bIn ri2)>l(b In u) lo, and KIZ = (k21/k12) = a2Cyi2/(1 - a). The terms involving yA are calculated using the Debye-Hiickel theory in the form In yi =
2553
537
' Conductance results from ref 22, interpolating when necessary from the reported data, written as an association constant.
Discussion of Results In the CC14-CeHsN02system the agreement between the conductance KA value of 1?00 and the ultrasonic XI2-' value of 1650 is very good. This agreement suggests that the association mechanism is diffusion controlled and occurs in a single step. By analogy with the stepwise process found for the 2-2 sulfates, this indicates that the rate of exchange of the polar solvent component in the coordination spheres of the ions is fast compared to the diffusional movement of the ions. The CCL-CH30H mixture results seem to demand a more complicated picture. Here the ultrasonic K12-l of 166 is substantially lower than the conductance KA of 537. This suggests a multistep association process of which we are examining only step I. The postulated mechanism would be
KA =
+
1 K23 K12K23
~
Taking KA = 537 and K1z-l = 166, we find K23 = k32/ k23 = 0.45, which is of the same size as analogous steps in the 2-2 electrolyte cases. It is also useful to examine the apparent Bjerrum distances in the two cases. Here we calculate aB,
CClrCeH6N02 CClrCH30H
Kiz-1
A
1650 166
3.4 9.3
The C6H6No2result is a little lower than would be expected from the sum of the ion radii, while the CHZOH result is close to the sum of the ion radii plus the size of one methanol molecule. Unfortunately, the existence of the second step in the CH30H case has not been demonstrated experimentally as yet because of the experimental difficulties encountered in the frequency range below our present measurements. It is useful to examine further the curious equality of the k12 rate constants in the two systems. The Debye equation can be approximated by the following equation.
where q = solvent viscosity and b' = I&Z2jeo2/r~DkT. In the approximation we have used the Stokes-Einstein equation to approximate the diffusion coefficient. The comparison of the calculated and experimental values then becomes System
CHaOH-CCla COHsNOt-CCla
klz(exptl), M-' sec-l
13.3 X 1010 13.1 X 10"
kn(calcd), M-' sec-'
3.3 3.7
x x
10'0 1010
The calculated values are lower by about a factor of 4. It is not fruitful to speculate on this discrepancy at this time. However, the equality of k12 in the two systems Volume 70, Number 8 August 1966
SERGIO PETRUCCI AND GORDON ATKINSON
2554
can be explained by the above equation. Let M represent the methanol mixture and N the nitrobenzene.
1-1 association reaction. However, the equation assumes AHo = 0 for the process which is undoubtedly incorrect. Further explication of this result must await more extensive measurements on this type of system.
Conclusion
= 0.9 II 1
That is, the increased viscosity of the nitrobenzene mixture is off set by the decreased “diffusion distance,” r ~ . Another interesting calculation involves the calculation of the approximate AVO for the reaction from the measured excess absorption. Herea1 (Avo)2 =
where pmax = a‘X = excess absorption per wavelength a t relaxation frequency and Po = compressibility of solvent. Using known values for Po and the measured values of pcc,a, and u, we calculate AVO = 1 2 2 cmg/mole for the nitrobenzene system and 15 cms/mole for the methanol system. These values appear quite high for a
The Jourmal of Physical C h m k t r g
The experimental results indicate but do not prove that the discrepancy between the association constants in the two solvent systems is due to a basic difference in the association mechanism. I n the nitrobenzene solvent system the association takes place in a single step and, consequently, the system behaves in a classical fashion. However, in the methanol system, a two-step process would seem to be involved, with the second step being substantially slower than the first. The reason for this mechanism is presumably a “slow” release of CHaOH molecules from the first coordination sphere of one of the ions. Such a two-step process is not describable in terms of the continuum solvent model basic to the bulk of modern electrolyte theories.
Acknowledgments. The authors acknowledge the support for the U. S. Atomic Energy Commission under Grant AT- [40-11-2983. They also express their appreciation to Dr. S. K. Kor for his invaluable help. (31) Reference 8, p 387.
