COMPROPORTIONATION KINETICS
701
be found for carbanions when protonated in ethereal solvents by water or alcohols, although the studies of such reactions are likely to be complicated by the aggregation of the resulting hydroxides or alcoholates in the low polarity media.
Acknowledgment. The finanical support of this research by the National Science Foundation (GP 26350) and by the Petroleum Research Fund, administered by the American Chemical Society, is graterully acknowledged.
Cornproportionation Kinetics of Stable Violene Radical Ions by Bruce C. Bennion, James J. Auborn, and Edward M. Eyring* Department of Chemistry, University of Utah, Salt Lake City, Utah 8.4112 (Received May 20, 1971) Publication costs assisted by the U.S. Air Force Ofice of Scientific Research
Violene radical ion systems contain highly colored oxidized, reduced, and semireduced species, all existing in simultaneous equilibrium in solution. Kinetic measurements by the stopped-flow method have enabled calculation of a rate constant for the rapid combination of the reduced and oxidized forms (comproportionation) of 1,1’,2,2‘-tetramethyl-(cis-+ truns-)vinylene-3,3’-diindolizine:k = (6.5 It 2.0) X 108 M-1 sec-’ in acetonitrile ( p 5 loF4M , 25’). The kinetics of a second violene system are just beyond the range of accessibility of the stopped-flow apparatus. The comproportionation reaction appears to be close to diffusion-controlled in acetonitrile.
A significant collection of radical ion systems, whose suggested name is the ‘Lviolenes,”l are known to exist as part of a two-step redox system represented by
verse rate constants for formation of the semireduced form. Two systems were prepared
-0
X+CH=CHjX reduced
CH fB
x+CH=CHjX semireduced
I
2
-e
II
Jr
-e
CH
I
fB
e3
X=+CH--CH+=X
(1)
oxidized
and
The three forms are each isolable and can exist in simultaneous equilibrium in solution as
+ oxidized 1_ 2 semireduced lo1
reduced
lo -1
(2)
[serniredu~ed]~ = K > 100 (3) [reduced][oxidized] Because the extra electron of the semireduced form is delocalized in a r-electron system, this form is especially stable and absorbs light of longer wavelengths. Although Hunig and c~-workers’-~have reported equilibrium constants for many of these systems, no attempts to measure the related rate constants have been reported. We report here the preparation of two violene systems and measurements of the forward and re-
CH,
Iv
The Journal of Phgaical Chemistry, Vol. 76, No. 6,1972
B. C. BENNION, J. J. AUBORN,AND E. M. EYRING
702
+
1,1',2,2 '-t etramethyl- (cistrans- )vinylene-3,3'diindolizine and its semireduced and oxidized forms (I, 11, and 111) were prepared as described by Fraser and Reid.5 We isolated a sample of the trans isomer of I by chromatographing the cis-trans mixture on alumina, but the trans isomer gave no different kinetic results than did the original mixture of isomers. Therefore, we made no further efforts to separate isomers in other syntheses. We prepared 1,2-bis-(3'-methylbenzothiazol-2'-ylidene)ethane and its oxidized form (IV and VI) by the method of Kiprianov and Kornilov.6 The semireduced form (V) was prepared by dissolving equimolar quantities of (IV) and (VI) in acetonitrile and allowing them to react. We checked the purity of each compound by comparison with melting point and spectral data from the published reports of those who first prepared them.6v6 Agreement was excellent in all cases, with the exception that the reported spectrum for species (IV) in ethanol5 does not represent that species. We dissolved a sample of (IV) in alcohol and observed that the solution changed from yellow to rose within a few minutes. This latter solution gave a visible spectrum which corresponded exactly with the published but we found that this solution would not react with (VI) to give the distinctly red colored intermediate (V). Compound (VI) was stable in acetonitrile only under a I\Tz atmosphere. Kiprianov and Kornilov reported no melting point for the diperchlorate salt of (VI), but we found mp 208-209'. All kinetic experiments were carried out in acetonitrile because this solvent afforded the best stability. Hiinig' suggests that the ideal solvent for violene radical ion systems should be aprotic and exhibit neither nucleophilic nor reducing power, especially towards the oxidized forms. The indolizine system (I, 11, and 111) remains stable for several hours in acetonitrile, which appears to be a nearly ideal solvent. The other violene system (IV, V, and VI) is less stable in either acetonitrile deoxygenated by bubbling with Nz, or in dimethyl formamide, another good violene solvent. To ensure that instability would be no problem, all experiments were conducted within minutes after preparation of stock solutions. Immediately after each experiment, solutions were checked for decomposition by measuring optical absorbances at the maxima for each of the three species in each system. Only species (VI) decomposed appreciably during an experiment. Since for other __ reasons we were not able to measure a rate constant for the system of which (VI) is a part, no corrections for concentration changes were attempted. Reagent grade acetonitrile (J. T. Baker and Eastman) containing less than 0.1% water was used in all M each experiments. Stock solutions of 1.00 X of both the reduced and oxidized forms were prepared to IJg accuracy by weighing the respective with a Mettler microbalance. The Journal of Physical Chemistry, Vol. 76,N o . 6,1972
Kinetic experiments were conducted with a DurrumGibson Stopped-Flow Spectrophotometer equipped with a 2-mm optical-path-length Kel-F absorbance cuvette. The instrument was thermostated at 25 i 0.05" by means of a Lauda K-2 circulator. The flow deadtime was determined to be less than 1 msec using SCN- reaction and the extrapolation the Fea+ method recommended by the manufacturer. The triggering mechanism normally used with the temperature-jump accessory to the instrument was used in these stopped flow experiments and was set to exclude extraneous effects seen during mixing. Equal concentrations of the freshly prepared oxidized and reduced forms of the compounds in acetonitrile were mixed in the stopped-flow apparatus and the rate of formation of the semireduced form was followed spectrophotometrically with 2-mm slits at 643 nm for (11) and 594 nm for (V). The results for the indolizine system could be checked with less sensitivity by following the rate of dissappearance of either of the reactants at the wavelengths of their absorption maxima, (I) at 412 nm or (111) at 512 nm. The reaction was too rapid to permit the approximation of pseudo-first-order kinetics by increasing the concentration of one reactant significantly above that of the other. The reactants were unstable at concentrations below -10-6 M in acetonitrile through which Nz had been bubbled. Only the last few percent (-1-5%) of a relatively large transmittance change (up to -80%) that occurred upon mixing could be reliably observed. With kinetic data obtained so close to equilibrium, the forward and reverse rates are nearly equal. The most obvious way t o treat such data is by means of relaxation kinetics. A characteristic relaxation time was determined from each oscilloscope photograph of transmittance vs. time. We developed a useful kinetic expression in the following manner. The relaxation time for reaction 2 is found by standard procedures to be
+
7-l
= 4kl [semireduced]
+
kl ([reduced]
+ [oxidized])
(4)
Because we always mixed equal concentrations of reduced and oxidized forms in our experiments, we can write, using equation 3 [reduced] = [oxidized]
=
K - '/'Cc, 1
+ 2K-'/'
(5)
(1) 5. HQnig in "Free Radicals in solution," Plenary lectures presented at the International Symposium on Free Radicals in Solution, Ann Arbor, Michigan, August 21-24, 1966, pp 109-122, Butterworths, London, 1967. (2) s. HClnig and J. Gross, Tetrahedron Lett., 2599 (1968). (3) 8. Hunig, H. Schlaf, G. Kiesslich, and D. Scheutzow, Tetrahedron
Lett.i 2271 (1969)* (4) S. HBnig, Angew. Chem., Int. Ed. Engl., 8, 286 (1969). ( 5 ) M. Fraser and D. H. Reid, J. Chem. Soc., 1421 (1963). (6) A. I. Kiprianov and M. Yu. Kornilov, Zh. Obshch. Khim., 31, 1699 (1961).
703
COMPROPORTIONATION KINETICS
and
I [semireduced] =
co
1
+ 2K-'l2
where C, represents the total violene concentration, including all three species. Substitution of eq 5 and 6 into eq 4 leads to the simplified expression = 2k1K-'/'CO
(7) A plot of 7-l us. C, will yield a slope from which kl can be readily calculated from the known equilibrium constant. These data are presented in Table I for the (I, 11, 111)indolizine system. A plot for this system is shown in Figure 1. 7-l
Table I : Comproportionation Kinetic Data for Indolieine Radical Ions in Acetonitrile a t 25" Co,O 10-6 M
2.5 3.0 5.0 10.0
7-1:
108 880-1
1.33 1.75 1.64 2.08 2.27 4.35 4.45
kl,c
108 M - 1
880-1
7.5 8.2 4.6 5.9 6.4 6.1 6.3
a Total concentration of indolieine in all forms. b Observed relaxation time from stopped-flow experiments. Calculated cornproportionation rate constant.
Taking K = 8 X lo2from a published value' for the same solvent, we calculate kl = 6.5 X los M-' sec-'. For the reverse rate constant we calculate k-1 = kl/K = 8.1 X 105 M-' sec-l. Considering the scatter of points in Figure 1, our calculated rate constant is accurate to about *30%. Attempts to measure relaxation times for the second violene system (IV, V, and VI) were not successful. This reaction is apparently more rapid than the first, and is nearly completed within the mixing time of the stopped-flow instrument. Therefore, it can only be determined that kl for this system is within the same order of magnitude, but more rapid than for the indolizine system. The rate constant, ICl = 6.5 X lo8 M-l sec-l, lies near the limit of accessibility of the stopped-flow method. We had attempted to measure the same kinetics using a temperature-jump relaxation method, but found that the equilibrium is quite temperature insensitive, even to a 15" perturbation. This implies a relatively low heat of reaction. The Stokes-Einstein equation for the diffusion coefficients of the reacting species taken with the Smoluchowski relation for the rate of a diffusion-controlled reaction between molecules of equal radii7 predicts a limiting rate constant of 1.8 X 1O'O M-' sec-' in acetonitrile a t 25". Our ob-
Figure 1. Plot of reciprocral relaxation time, 7-1, vs. total indolizine concentration, CO,in acetonitrile a t 25". Circles denote experimental data points of Table I. Vertical error bars correspond to the estimated &30% imprecision in measured 7 values. The diagonal theoretical line is the best fit of the data subject to the constraints imposed by eq 7 that it be linear and that it pass through the origin of coordinates.
served comproportionation rate constant for the indolizine system is slightly more than one order of magnitude slower than the diffusion-controlled rate predicted by this approximate theoretical equation. This is consistent with measured rates8 for other presumably diff usion-controlled reactions. Our results also compare favorably with those of Diebler, Eigen, and Matthies, who investigated the cornproportionation reaction between benzoquinone and hydroquinone anion to form the semiquinone radical ion in basic aqueous solution.9 They reported a comproportionation rate constant k1 = 2.6 X lo8 M-' sec-l and a disproportionation rate constant IC-I = 7 X lo7 M-l sec-I at 11' in aqueous solution with p H >10 and ionic strength p = 0.1. If we correct their kl for the viscosity of acetonitrile and a temperature of 25" we would predict a comproportionation rate of 7.1 X los M-' sec-l for the benzoquinone system under the conditions of our experiments, This predicted rate is very close to that measured for the violene system considered in this paper and lies within the range of experimental error. We might expect comproportionation electron transfer reactions of other violenes and quinone-like systems to exhibit similar behavior in solvent systems where they remain stable.
Acknowledgment. This work was supported by AFOSR (SRC)-OAR, USAF, Grant No. 69-1717-F. (7) E. F. Caldin, "Fast Reactions in Solution," Blackwell, Oxford, 1964. (8) P. Warrick, Jr., J. J. Auborn, a n d E . M. Eyring, J. Phys. Chem., in press. (9) H. Diebler, M. Eigen, and P. Matthies, 2. Naturforsch., B, 16, 629 (1962).
The Journal of Physical Chemistry, Vol. 76, No. 6, 1078
