1970
The Journal of Physical Chemistry, Vol. 83, No. 15, 1979
(22) D. P. L. Satchel1and J. Secemski, J. Chem. SOC.8 , 130 (1969). (23) 0.B.Nagy, V. Reullaux, and J. B.Nagy, to be published. (24) D. R. Robinson and W. D. Jencks, J . Am. Chem. SOC., 89, 7088 (1967). (25) In the present case the reaction rate is too high to measure in pure amine solution but this has been done for 4-amineN-n-butylphthalimide and the results conflrm the points discussed here (to be published).
(28) A. K. Colter and S. S. Wang, J . Am. Chem. Soc., 85, 114 (1964). (27) 0.B.Nagy and J. B.Nagy in "Environmental Effects on Molecular Structure and Properties", B. Pullman, Ed., Reidel Publishing, Dordrecht, Holland, 1976. (28) We thank Professor G. Germain for having carried out the computations. (29) M. Muanda, J. B.Nagy, and 0. B.Nagy, Tetrahedron Lett., No. 38,
3421 (1974). (30) For a more complete kinetic analysis see S. Dupire, J. B.Nagy, 0. B.Nagy, and A. Bruyhnts, J. Chem. Soc., Perkin Trans. 2,478(1974). (31) J. B.Nagy, 0.B.Nagy, and A. Bruyhnts, J. Chem. Soc., Perkin Trans. 2,2084 (1972). (32) 0.B.Nagy, J. B.Nagy, and A. Bruyhnts, J. Chem. Soc., Perkin Trans. 2,968 (1972). (33) S. Dupire, J. M. Mulindabyuma, J. B.Nagy, and 0. B.Nagy, Tetrahedron, 31, 135 (1975). (34) J. B.Nagy, A. Bruylants, and 0. B.Nagy, Tetrahedron Lett ., No. 54, 4825 (1969). (35) V. Reuliaux, PhD. Thesis, Universite Catholique de Louvain, Louvain-la-Neuve, 1973. (36) G. Briegleb, "Elektronen-Donator-Acceptor-Komplexe", Springer, Berlin, 1961.
J. F. Evans and H. N. Biount
(37) T. C. Bruice and S. J. Benkovic, J. Am. Chem. Soc., 86, 418 (1964). (38) W. P. Jencks, "Catalysls in Chemistry and Enzymology", McGraw-Hill, New York, 1969. (39) D. Mukana, J. B.Naav, 0. B.Naav, -. and A. Brwhnts. Boll. SOC.Chlm. Belg., 83, 201 (1974). (40) V. D. Kiselev and J. G. Miller, J. Am. Chem. SOC.,97, 4036 (1975). (41) Manuscrlpt in preparation. (42) V. I. Vedeneyev, L. V. Gurvich, V. N. Kondrat'yev, V. A. Medvedev, and Ye. L. Frankevich, "Bond Energies, Ionization Potentials and Electron Affinities", Edward Arnold, London, 1966. (43) L. J. Andrews and R. M. Keefer, J. Am. Chem. Soc., 74, 4500 (1952). (44) E. M. Arnett, W. G. Bentrude, J. J. Burke, and P. McC. Duggleby, J . Am. Chem. Soc., 87, 1541 (1965). (45) E. Grunwald, G. Baughman, and G. Kohnstam, J. Am. Chem. Soc., 82, 5801 (1960). (46) A. K. Covington and K. E. Newman, J. Chem. Soc., Faraday Trans. 7 , 69, 973 (1973). (47) E. Grunwald, K. CH. Pan, and A. Effio, J. Phys. Chem., 80, 2937
(1976). (48) A. H. Falnberg and S. Winstein, J. Am. Chem. Soc., 78, 2770 (1955). (49) J. B. Hyne, R. Wills, and R. E. Wonkka, J . Am. Chem. SOC.,84, 2914 (1962). (50) E. Grunwald and A. Effio, J . Am. Chem. SOC., 96, 423 (1974). (51) M. W. Hanna and D. G. Rose, J. Am. Chem. SOC.,94, 2801 (1972). (52)R. L. Scott, Red. Trav. Chim., Pays-Bas, 75, 787 (1956). (53) 0.B.Nagy, M. wa Muanda, and J. B.Nagy, J. Chem. SOC.,Faraday Trans. 1 , 74, 2210 (1978). (54)L. Hevesi, E. Wolfson-Davidson, J. B.Nagy, 0. B.Nagy, and A. Bruyiants, J . Am. Chem. SOC., 94, 4715 (1972).
Reactions of Cation Radicals of EE Systems. 8. Effects of Initial Cation Radical Concentration on the Rate-Determining Step in the Half-Regeneration Mechanism' John
F. Evans
Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455
and Henry N. Blount* Brown Chemical Laboratory, The University of Delaware, Newark, Delaware 1971 1 (Received October 6, 1978; Revised Manuscript Received March 28, 1979) Publication costs assisted by the University of Minnesota
The reactions of the cation radical derived from 9,lO-diphenylanthracene with the nucleophiles pyridine and 4-cyanopyridine in acetonitrile have been studied by three kinetic techniques: single potential step spectroelectrochemistry,open circuit relaxation spectroelectrochemistry, and stopped-flow kinetic spectrophotometry. The half-regeneration mechanism is shown to account for the observed reaction dynamics for both reaction systems. Under conditions of high initial cation radical concentration, the experimental rate law is found to be first order in both cation radical and nucleophile concentration and independent of the concentration of the neutral precursor, while at low initial concentration of cation radical, second-order dependence on cation radical concentration is found with a first-order dependence on nucleophile concentration and an absence of precursor concentration dependence. In the former case adduct formation from the initial reaction of nucleophile and cation radical is rate determining. A shift in kinetic control to the monoelectronic oxidation of reversibly formed adduct by free cation radical is found under the latter reaction conditions.
Introduction In a recent investigation it was found that the reaction of the cation radical of 9,lO-diphenylanthracene (DPA'.) with chloride ion in acetonitrile followed a rate law which is given by2 -d [DPA+*]/ d t = k,,,[DPA+*] 2[ C1-] (1) The mechanism for this reaction was found to adhere to a half-regeneration scheme3 of the general form A+.
k +N5 A(N)+. k-2
(2)
0022-3654/79/2083-1970$01 .OO/O
A(N)+. + A+.
k-a
A(N)2++ A
(3)
(4) where N represents a nucleophile and A, A+-,and A2+are the neutral, cation radical, and dication forms of the substrate. That C1- reacted with DPA+. with a secondorder dependence on [DPA'.] indicating kinetic control by k3 (eq 3) was unexpected in light of the previous report concerning the analogous reaction of DPA+. with pyridine 0 1979 American Chemical Society
Reactions of Cation Radicals of EE Systems
( P Y ) . ~Although the reaction with Py, a “stronger” nucleophile1 than C1-, proceeded by the same general mechanism, the rate of radical ion disappearance was found to be first order in both [DPA+.] and [Py] indicating kinetic control by k 2 (eq 2). The reaction of DPA+- with Py was characterized by using t h e technique of single potential s t e p spectroelectrochemistrf (SPS/SE) while the reaction with C1- was investigated with stopped flow kinetic spectrophotometry2 (SF). In the spectroelectrochemical experiment, the reactants are nonhomogeneously distributed in solution whereas in SF, homogeneous distribution prevails. That this nonhomogeneous spatial distribution of reactants and resulting intermediates may have influenced the observed kinetics of the pyridination reaction led to the examination of this system with SF. Characterization of the reaction kinetics by this technique afforded a rate law which, like the C1- reaction, was second order in [DPA+.] and prompted consideration of either the possible insensitivity of SPS/SE to second-order processes or the possibility of direct electrode participation in the reaction scheme (ECE).4 This report details the comparative evaluation of the kinetics of the reactions of Py and 4-cyanopyridine (CNPy) with DPA+. determined by SPS/SE, SF, and open circuit relaxation spectroelectrochemical (OCR/SE) techniques under a wide variety of reaction conditions.
The Journal of Physical Chemistry, Vol. 83, No. 15, 1979
1971
TABLE I: Stopped-Flow Kinetic Data for the Reaction of DPA+. with Pva [DPA’.],, [pyl,, replik,k,lk-,,* [DPA],, x l o 4 x l o 5 X l o 4 cates M-, s-’ x l o - * 3.8 65.0 5 7.34(*0.35)c 5.65 4.1 6.50 5 7.50(*0.20) 5.62 4.0 3.96 8 6.92(+0.82) 4.50 3.2 0.40 7 7.84(*0.15) 4.60 7 6.51(?0.35) 0.28 2.1 0.40 av 32 7.19(*0.66) ~~
a All concentrations in M. k , k , / k - , = k , /2 from eq 5. Data fitted for 75% of reaction via rnethocfof least squares with coefficient of correlation of at least 0.9990 for all cases. Parentheses contain one standard deviation. I
45.5
I
39 .o
32.5
36.0 %I
m ‘0
Experimental Section Reagents. The sources of and purification procedures for acetonitrile, tetrabutylammonium perchlorate (TBAP), tetraethylammonium perchlorate (TEAP), 9,lO-diphenylanthracene (DPA), and Py have been reported e 1 ~ e w h e r e . l ~CNPy ~ ~ ~ (Aldrich) was twice recrystallized from benzene, mp 79.0-79.5 “C. All other chemicals were reagent grade or equivalent. Concentrations of DPA were determined spectrophotometrically (log €392.5 = 4.072). CNPy solutions were prepared by direct weighings. Concentrations of Py in acetonitrile stock solutions were determined by titration with HCIOl in acetic acid (potentiometric end point detection).s Electrochemical Apparatus. All electrode potentials are reported relative to the aqueous saturated calomel electrode and were controlled by a potentiostat equipped with iR compen~ation.~ A mercury wetted relay was used for connection and disconnection of the working electrode in OCR/SE experiments.1° Kinetic Spectrophotometry. SF determinations were carried out with a Durrum D-11OB spectrophotometer equipped with a 2.00-cm cuvet. DPA+- was electrogenerated external to the SF spectrophotometer as previously described.2 For spectroelectrochemical kinetic studies, platinum optically transparent electrodes (Pt-OTE), prepared by vapor deposition,ll were used as working electrodes. These Pt-OTE’s were incorporated into cells similar to those already reported.12 All kinetic determinations were carried out at 25.0 (f0.2) “C. The analytical wavelength employed for all kinetic experiments was the A,, of DPA+. in acetonitrile (653.0 nm, e = 8700 M-l cm-l).12 The value of € D p ~ + . f ) D p ~of~ l30.8 ~ M-’ s-’I2 had been previously determined in the 0.20 M TEAP/acetonitrile medium.13 Digital simulations were after the manner of Feldberg.14 A dedicated minicomputer system (Data General Corporation Nova 1200) was used to control both S F and SE kinetic spectrophotometers and to acquire and reduce kinetic data.
; 19.5
le
13.0
6.5
0 .o 000
165
330
495
660
t,s
Figure 1. Secondorder plot for the reaction of DPA’. and Py observed via SF. Conditions: rDPAIn = 4.58 X M, [DPA+.],, = 3.20 X
Results and Discussion SF kinetic determinations for the DPA+./Py reaction were conducted over a broad range of concentrations of DPA, DPAt-, and Py. Results of these measurements, summarized in Table I, indicate the validity of a rate expression of the form -d [DPA+.]/dt = kapp[DPA+.]2[P~] (5) From this table it can be seen that the kinetics of this reaction are independent of [DPA]. Typical of these determinations are the data shown in Figure 1. Clearly, a mechanism of the form given by eq 2-4, wherein a rapid adduction equilibrium (eq 2) is maintained prior to rate-determining electron transfer (k3,eq 3), can account for these observations. The dicationic product of this oxidation step, DPA(PY)~+, is rapidly consumed through reaction with a second Py molecule (eq 4) to form the disubstituted product,15 D P A ( P Y ) ~ ~These + . observed kinetics (eq 5) are inconsistent with the previous SPS/SE studies in which the data were shown to fit the half-regeneration mechanism (see ref 4, Figure 1)but follow a rate law of the form -d[DPA+*]/dt = kaPp[DPA+*][Py]
(6)
1972
The Journal of Physical Chernistty, Vol. 83, No. 75, 1979
O2
F. Evans and H. N. Blount
which rearranges to
lot 0.8
J.
IIn this general formulation, A+. and N correspond to DPA+. and Py, respectively, and the rate constants are from eq 2-4. That the rate of the back-reaction of eq 3 is insignificant is supported by the independence of the observed kinetics on [DPA] (Table I). In the limit of high concentration of cation radical, eq 8 assumes the form
t
1
-d[A+*]/dt = 2k,[A+*][N]
0020
-15
-10
-05
00
05
10
I5
LOG(k2t[P~]o)
Figure 2. SPSlSE data for the reaction of DPA’. with Py compared to computer simulated responses. Conditions: [DPA] = 1.05 X M, [Py] = 1.07 X M. Solid lines are simulated responses for (A) half-regeneration mechanism, (B) ECE mechanism with “nuan~e”,~~’’ and (C) ECE with k2 = 1.86 X lo4 M-’ s-’ . Solid squares are from ref 4, open circles, this study.
which indicates that the adduction reaction (k2, eq 2) is rate determining. This apparent discrepancy prompted repetition of the previous work4 with the self-same materials employed in the SF determinations. SPS/SE data obtained in this present study are in exact agreement with those originally r e p ~ r t e d .A~ composite of data from these two studies is shown in Figure 2. The working curve to which these data are fit (curve A) arises from simulation of the half-regeneration mechanism (eq 2-4) wherein k2 (eq 2) is rate determining. This is identical with curve E in Figure 1 of ref 4. Simulation of the involvement of the electrode in the oxidation of the Py adduct of DPA+. either singularly (ECE) or in concert with oxidation by a nonadducted cation radical (ECE “nuance”)16 gives rise to working curves B and C, respectively. The goodness of fit of the SPS/SE data to curve A further substantiates the form of eq 6 as a valid description of the kinetics of the DPA+.Py system under these reaction conditions. We are confronted with two differing kinetic views of the same system. The fundamental differences in the two kinetic techniques used are (1)the presence of the electrode in SPS/SE affords an alternative means of oxidation of intermediates during the course of the reaction, and (2) the grossly different spatial distribution of concentrations of reactants and intermediates in the two methods. The lack of fit of the SPS/SE data to either curve B or curve C in Figure 2 indicates the electroinactivity of the adducted cation radical [DPA(Py)+.] a t the applied electrode potential. Consideration of the effects of the nonhomogeneous distributions of reactants present in SPS/SE on the observed kinetic demeanor of the half-regeneration mechanism (eq 2-4) affords an understanding of these apparently divergent results. A rate law describing eq 2-4 was derived under conditions of a rapid adduction equilibrium (eq 2) followed by rate-determining homogeneous oxidation of the adducted cation radical (k3, eq 3). These constraints are those which gave rise to the form2 of eq 5. However, an application of steady state kinetic arguments to the concentration of adducted cation radical [DPA(Py)+.] affords the general rate law given by d [A+.] = 2k2k3[A+*] [N] dt k-2 + k,[A+-]
--
(7)
(9)
which is identical with the form of eq 6. In the limit of low concentration of cation radical, eq 8 reduces to d[A+*] k2k3 - 2-[A+*l2[N] dt k-2
which is identical in form with eq 5. In the SE experiments, the cation radical is nonhomogeneously distributed and its concentration in the vicinity of the electrode surface is held approximately equal to the bulk concentration of precursor, ca. M, throughout the experiment. In the SF experiments, the cation radical is homogeneously M. distributed with an initial concentration of ca. That the concentration of cation radical in the SE experiments was two orders of magnitude greater than that present in the SF case accounts for the manifestation of the rate law (eq 8) in two different forms, eq 6 and 9 and eq 5 and 10, respectively. While the arguments presented above may serve to explain the discrepancies between reaction dynamics observed from SF and SPS/SE measurements, these do not completely resolve this issue. Questions may be raised as to the possible insensitivity of SPS/SE to reaction dynamics in which the concentration of the absorbing reactant appears as a second-order term in the rate law describing its consumption (e.g., eq 1 or eq 5). It is therefore appropriate to demonstrate both extremes of kinetic demeanor (as well as intermediate behavior) as observed by a single kinetic technique. There are several appproaches which can be taken. The first involves conducting SF determinations at high initial cation radical concentrations. DPA+. must be externally electrogenerated for S F experimenk2 During the time required to prepare M DPA+. from solutions of high DPA concentration,21 side reactions of DPA+ with solvent and nucleophilic impurities in the solvent-supporting electrolyte system consume significant quantities of the cation radical, even when solvent and supporting electrolyte are rigorously purified. Our inability to completely exclude trace nucleophilic impurities resulted in the preparation of solutions which gave spectral e ~ i d e n c e l ~ ~ ’ ~ of intermediates arising from the partial hydrolysis of DPA+.. The presence of these species therefore precluded the acquisition of reliable SF data a t high initial DPA+. concentrations. A second approach involves conducting SPS/SE in the concentration regime of the aforementioned SF determinations (i.e., with [DPA+.Iq = M). Under these conditions, extremely poor signal-to-noise ratios were observed in the absorbance transients. (This was also found when less reactive pyridines were selected as nucleophiles.) Consequently, the integrity of this data, and, in turn, the large errors associated with fitting it to SPS/SE working curve^,^ were such that unambiguous
Reactions of Cation Radicals of
EE Systems
The Journal of Physical Chemistry, Vol. 83, No. 15, 1979
1973
TABLE 11: S t o p p e d - F l o w K i n e t i c D a t a for t h e R e a c t i o n of D P A + " w i t h CNPya [DPA],,
lo4
x
x lo5
[DPA"],,
5.09 0.28 5.12 5.05
k,k,lk-,,b
[CNPy], x l o 2 5.16 5.16 2.07 0.52
3.2 2.6 2.9 3.6
M-*S - 1 x
replicates
6 6 7 6 av 25
105
2.44(+0.07)c 2.66( i 0.06) 2.48(+0.05) 2.82(+ 0.29) 2.55(i 0.13)
All concentrations are M. A c c o r d i n g to eq 10. D a t a f i t t e d for 75% o f reaction via m e t h o d o f least squares w i t h Parentheses c o n t a i n one standard deviation. coefficient o f correlation of at least 0.9985 for a l l cases. I
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