J . Phys. Chem. 1988, 92, 6574-6579
6574
TABLE 111: Ion Product Distributions for the Reactions of N+ with the Isomers of C2HzC12 ion product distributions for the
C,H,Cl, isomers. % products C2HCI++ HCI C2H2CIC+ Cl C2H2C12'
trans- 1,2-
cis-1,28 42
1,l-
12 38
50
50
38
6 56
singly charged ions with the isomers of C2H2CI2using an ion cyclotron resonance apparatus ostensibly at room temperature. They observed that the polar isomers always reacted more rapidly than the nonpolar isomer but surprisingly that their experimental rate coefficients were appreciably larger than the calculated collisional rate coefficients for all of the reactions studied. We also studied the H3+reactions with all three isomers, since we anticipated that such reactions would proceed via proton transfer (these are more intimate interactions that are generally considered to be better tests of collision theories than charge transfer such as occurs in the N+ reactions; for example, see the review paper ref 16 and also see below). In the event, the reaction probabilites for these reactions were indistinguishable from those for the N+ reactions (see Table 11). Why then are the reaction probabilities for the reactions of the polar molecules so obviously less than unity? We tentatively suggest that the favored angle of approach of the ion for the most efficient charge transfer to occur is not collinear with the dipole, which would maximize the k,, but rather the best angle of approach for charge transfer is (15) Su, T.; Bowers, M. T. J . Chem. Phys. 1973, 58, 3027. (16) Adams, N. G.;Smith, D. In Reactions of Small Transient Species; Fontijn, A,, Clyne, M. A. A,, Eds.; Academic: London, 1983; p 311.
out of the plane of the molecule when the electron jumps out of the a bond onto the ion. Clearly, at this angle of approach the ion senses a much smaller (even zero) dipole, and thus the rate coefficient will fall below the expected kc. For the nonpolar trans- 1,2-C2H2CI2isomer, the theoretical k, do not depend on the angle of approach of the ion. However, it should be pointed out that since the nonpolar isomer is shown to have a Langevin rate coefficient in the experiments, the point on the potential energy surface at which electron transfer occurs must be inside the Langevin capture radius. It is instructive to consider, briefly, the products of these reactions. The products were obtained only in the SIFT experiment at 300 K and are shown in Table 111. For the N+ reactions, about half of the N+/C2H2CI2collisions result in nondissociative charge transfer and half in dissociative charge transfer. An interesting point is that the efficiency of elimination of HCI molecules is seen to be related to the proximity of the H and C1 atoms in the molecule; this favors HC1 elimination in the trans- 1,2-C2H2C12 isomer relative to the other isomers (see Table 111). The H3+ reactions result in the same single product ion mass for all these isomers, Le., C2H2C1+. The reaction therefore presumably proceeds via proton transfer producing the transient C2H3CI2+,which immediately dissociates to C2H2CI+and HC1. The proton transfer (by analogy with the electron transfer discussed above) presumably involves a transient weak bonding to the a orbital followed by the rapid formation of an H-C1 bond and rapid HCI elimination.
Acknowledgment. The work at Birmingham was supported by the SERC and the USAF. The work at Cambridge was supported by the SERC and the EEC. C.C. and D.C.C. thank Dr. R. A. Amos for advice in using his CADPAC program. Registry No. N', 14158-23-7;H,', 28132-48-1;truns-1,2-C2H2C12, 156-60-5; 1,l-C2H,CI2, 75-35-4;~is-1,2-CzH2C12,156-59-2.
Proton-Electron Transfer: Kinetics and Mechanism in the Ketone-Ketyl Redox System Yousry M. A. Naguib, Colin Steel,* and Saul G. Cohen Department of Chemistry, Brandeis University, Waltham, Massachusetts 02254 (Received: January 29, 1988; In Final Form: April 13, 1988)
-
Rate constants for the two ketyl-ketone redox systems AH' + K A + KH' (7) and K*H' + K K* + KH' (14), where AH', K*H', KH', K, and A are dimethylketyl (Me2COH), 4-tert-butyldiphenylketyl,diphenylketyl (Ph2COH), benzophenone, and acetone, are k7 = (3.5 i 1.5) X lo4 M-l s-l and k I 4= (1.5 & 0.2) X lo4 M-I s-I at 298 K. The value for k7 is significantly lower than previous literature reports for this number. However, the current values for both k7 and k14 are consistent with considerable chemical evidence from other sources. It is shown that these reactions, although formally hydrogen transfers, cannot occur by a "normal" H atom transfer. They also do not occur by sequential transfer of a proton followed by an electron, or vice versa. Instead it is proposed that the carbonyl acts as a dual-site receptor for proton and electron transfer from the dual-site donor, the reducing ketyl radical. -+
Introduction The photoreduction of benzophenone (K) by alcohols (AH2) is an archetypical photochemical reaction.'" One of the important steps is hydrogen transfer from the alcohol-derived radical (AH') to K (reaction 7). It is therefore surprising to find that the literature references to rate constants for hydrogen transfer between ketyl radicals and aromatic carbonyls are sparse and that the reported value^^-^ differ substantially for the same reaction (1) Turro, N. J. Modern Molecular Photochemistry; Cummings: Menlo Park, CA, 1978. (2) Cowan, D.0.; Drisko, R. L. EIements of. OrRanic Photochemistry; Plenum: New York, 1976. (3) Calvert, J. G.;Pitts, J. N. Photochemistry; Wiley: New York, 1966. (4) Thurnauer, M. C.;Meisel, D. Chem. Phys. Lett. 1982, 92, 343-348. (5) den Hollander, J. A,; Hartel, A. J.; Schippers, P. H. Tetrahedron 1977, 23, 211-215. (6) Simic, M.; Neta, P.; Hayon, E. J . Phys. Chem. 1969, 73, 3794-3800. ( 7 ) Nelson, D. A.; Hayon, E. J . Phys. Chem. 1972, 76, 3200-3207.
SCHEME I K 3K
+
3K
AH2
1 0 b8
(1)
3K
-K
+
KH'
AH'
(2) (3)
(4a) KH'
+
KH.
AH'
+
AH*
K2H2
KH2
AH. K
+
+
-
A
KH.
AH*
+
+
K
(4b)
AH2
(5) (6a)
KAH2
-
KH:! KH'
+
+
A A
(6b) (7)
and are not consistent with the chemical e v i d e n ~ e . ~ J ~ The basic scheme for reduction is given in eq 1-7 (Scheme I).
0022-365418812092-6574$01.5010 0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6575
Proton-Electron Transfer
Triplet benzophenone (3K) is formed with unity quantum yield." Reaction 2 represents all first-order or pseudo-first-order decay channels of 3K.In the presence of an alcohol (AH2) 3K may abstract a hydrogen, forming diphenylketyl radical (KH') and the alcohol-derived radical AH'. For example, in the case of 2-propanol we have dimethylketyl, Le., AH' = (CH&COH. These radicals are then consumed by radical-molecule and/or radical-radical reactions (reactions 7 and 4-6, respectively). Reaction 7 is important in explaining how the quantum yield of benzopinacol (K2H2) formation can approach unity at high benzophenone concentration^.^^^^-^^ It also explains why W. D. Cohen observed no cross-coupled pinacols (reaction 6a) in the photoreduction of benzophenone by substituted benzhydrolI8 and why small concentrations of mercaptans can be so efficient in retarding the photoreduction of benzophenone by a l c o h ~ l s . ' ~ * ' ~ An early pulse radiolysis study6p7yielded k7 C lo7 M-' for AH' = dimethylketyl, but a later pulse radiolysis experiment4 gave k7 = 1.9 X lo9 M-' s-l. In a CIDNP studyS of the same reaction, the rate constant was reported as 2.8 X lo8 M-' s-l while a flash photolysis study yielded 1.0 X lo7 M-' As we shall see in the Discussion, high values for this rate constant (>lo7M-' s-l ) are not consistent with considerable chemical evidencegJOfor this and related reactions. We therefore decided to redetermine the rate constant for hydrogen transfer from dimethylketyl radical to benzophenone (reaction 7) and also to determine the rate constant for the related hydrogen transfer from diphenylketyl radical to benzophenone (reaction 1 4 ) , since this is also an important reaction in the photoreduction of benzophenone.
TABLE I: Quantum Yields for Benzopinacol (K,H,), Benzhydrol (KH2), and Mixed Pinacol (KAH,) Formation as a Function of Benzophenone Concentration (IK1)"
Results The basic set of reactions is shown in Scheme I, and before discussing the redetermination of k7, we shall make some comments on the scheme. At room temperature in acetonitrile, the solvent used in this study, values as long as 1 5 0 ps have been obtained20for the lifetime of 3K although under routine conditions 70 ps is more typicalz1and so we shall set k2 = 1.4 X lo4 s-l. For AH2 = 2-propanol, k3 = 2 X lo6 M-' s-1.22 The value for k4 in and it is known that disproacetonitrile is 1.05 X lo8 M-' portination of KH' is minor so that a is In contrast, for AH' radicals disproportionation is dominantsz6 Since the mode by which AH' is consumed is not important in this study, we only display the disproportionation step ( k , = 2 X lo9 M-' s-I 27a) in Scheme I. WeinerZ8has studied reaction 6 and obtained k6a = 1.0 X lo8 M-' s-' and p = 0.44 f 0.06. On the basis of therK modynamic arguments he also discounted AH' KH' AH2 as a major channel. As we shall see, under our conditions
Figure 1. Ratio of quantum yields for benzhydrol (KH2) to benzopinacol (K,H,) formation as a function of the ratio of mixed pinacol (KAH,)to benzopinacol (K,K,) quantum yields (primary data in Table I).
+
-
+
~
(8) Laszlo, B.; Demeter, A. Zf I-Mitt. 1984, 97, 147-152; Chem. Abstr. 1985, 103, 4 5 6 5 0 ~ . (9) Beckett, A.; Porter, G. Trans. Faraday SOC.1963, 59, 2038-2050. (10) Cohen, S. G.; Rose, A. W.; Stone, P. G.; Ehret, A. J. Am. Chem. SOC. 1979, 101, 1827-1832. (1 1) Murov, S. L. Handbook of Photochemistry; Marcel Dekker: New York, 1973; p 49. (12) Pitts, J. N . ; Letsinger, R. L.; Taylor, R. P.; Patterson, J. M.; Recktenwald, G.; Martin, R. B. J . Am. Chem. SOC.1959, 81, 1068-1077. (13) Moore, W. M.; Hammond, G. S.; Foss, R. P. J . Am. Chem. SOC. 1961,83, 2789-2794. (14) Moore, W. M.; Ketchum, M. D. J . Phys. Chem. 1964,68, 214-217. (1 5) Yang, N. C.; Murov, S. L. J . Am. Chem. Soc. 1966,88, 2852-2854. (16) Cohen, S . G.; Cohen, J. I. Tetrahedron Lett. 1968, 4823-4826. (17) Cohen, S.G.; Cohen, J. I. Isr. J . Chem. 1968, 6, 757-767. (18) Cohen, W. D. Red. Trav. Chim. Pays-Bas 1920, 39, 243-279. (19) Stone, P. G.; Cohen, S. G . J . Phys. Chem. 1981, 85, 1719-1728. (20) Chilton, J.; Giering, L.; Steel, C. J . Am. Chem. SOC.1976, 98, 1865-1870. (21) Naguib, Y . M. A,; Steel, C.; Cohen, S. G.: Young, M. A. J . Phys. Chem. 1987, 91, 3033-3036. (22) Cohen, S.G.; Litt, A. D. Tetrahedron Letr. 1970, 837-840. (23) Naguib, Y . M. A,; Cohen, S. G.; Steel, C. J. Am. Chem. SOC.1985, 108, 128-133. (24) Schenck, G. 0.;Koltzenburg, G.; RoseLius, E. Z.Naturforsch. 1969, 24, 222-224. (25) Schuster, D. I.; Karp, P. B. J. Photochem. 1980, 12, 333-344. (26) Larof, G. P.; Fischer, H. Helv. Chim. Acta 1973, 56, 2011-2020. (27) (a) Paul, H.; Segaud, C. Int. J . Chem. Kinet. 1980,12,637-647. (b) A similar value for k5 is given in: Lehni, M.; Fischer, H. Int. J. Chem. Kinet. 1983, 15, 733-757. (28) Weiner, S. A. J . Am. Chem. Soc. 1971, 93, 425-429.
4K2H2
6KH2
k4H2
[KI, M
0.97 0.98 0.95 0.80 0.58 0.60 0.62
0.022 0.026 0.036 0.060 0.095 0.08 1
0.013 0.014 0.027 0.077 0.100 0.108 0.150
1.0 x 10-1 1.0 x 10-1 1.0 x 10-2 1.0 x 10-3
0.130
3.0 X lo4 3.0 X lo4 1.0 x 10-4
aSolvent C H 3 C N , [AH,] = 1.3 M, sample volumes 3 mL, tin = 1 min, Io at 366 nm = 1.0 X einstein/s. 25r
r
0
I
10
lo2' +,AH,
20
I 30
/+K2H2
reaction 6 is a fairly minor channel and "wastage" by this reaction would not significantly affect our analysis. As we shall see in the Discussion, a value of k7 can be estimated from a knowledge of the falloff in the quantum yield of benzophenone consumption as [K] decreases in the photoreduction of benzophenone by 2-propanol. However, the earlier schemes did not include all the reactions now known to occur (Scheme I). Moreover, in order to obtain yields in terms of benzophenone consumption, considerable reactions has to take place, and this always results in the formation of LAT's (light-absorbing transients) which complicate the system not only because of their masking effect but also because they are good triplet quenchers.20,29-34 For such reasons we decided to only go to small amounts of photolysis (51%) and to follow the reaction by monitoring product buildup using HPLC. Disproportionation versus Coupling of Ketyl Radicals. In terms of Scheme I and under steady-state conditions
where KH2, K2H2,and KAH2refer to benzhydrol, benzopinacol, and the mixed pinacol 1,l -diphenyl-2-methylpropane- 1,2-diol, respectively. The dependence of quantum yields of these products on benzophenone concentration is given in Table I and plotted in Figure 1 . The slope and intercept yield /3/( 1 - 8) = 0.79 f 0.06 and a / ( l - a) = (1.2 f 0.8) X respectively. Thus p = 0.44 f 0.02, in excellent agreement with Wienersz8 A disproportionation-to-coupling ratio of 0.01 for KH' radicals is also in agreement with previous qualitative observations. Schenck e t (29) Backstrom, H. L. J.; Appelgren, K. L.; Niklasson, R. J. V. Acta Chem. Scand. 1965, 19, 1555-1565. (30) Backstrom, H . L. J.; Niklasson, R. J. V. Acta Chem. Scand. 1966, 20, 2617-2626. (31) Schenck, G. 0.;Cziesla, M.; Eppinger, K.; Matthias, G.; Pape, M. Tetrahedron Lett. 1967, 193-198. (32) Filipescu, N.; Minn, F. L. J . Am. Chem. SOC.1968, 90, 1544-1547. (33) Wagner, P. J. Mol. Photochem. 1969, I, 71-87. (34) Scaiano, J. C.; Abuin, E. B.; Stewart, L. C. J. Am. Chem. SOC.1982, 104, 5673-5619.
6576 The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
Naguib et al.
\ ~.,(M-Is-~) I 2
3 0
2
3 104 5 x io4 2 104
4
6
[ benzophenone]
/
a
o 01 001
o
=
k,(M-ls-')-
I
n
I 108
IO
[benzophenone]/-
al.24 and Schuster and KarpZ5 found that photoreduction of deuterium-labeled benzophenone by unlabeled hydrol resulted in a minute amount of labeled benzhydrol and concluded that disproportionation of diphenylketyl radicals is very minor. It is worthwhile noting that the corresponding ratio for dimethylketyl radicals is 7.8 f 1.5.35 The finding that coupling predominates for KH' while for AH' disproportionation dominates has been attributed to a lack of 0-hydrogen in KH' and a transfer of 0-hydrogen between AH' radicals to give the enol, CH?=C(OH)CH3, and 2-propan01.~~ The enol can then tautomerize to A. Rate Constant for Hydrogen Transfer from Dimethylketyl to Benzophenone. (a) From Benzopinacol Yields. In order to get a simple analytical expression, it is helpful at first to make some approximations. If for the moment we neglect reaction 6 and, because of the small value of cy, drop reaction 4b compared to 4a, then with reaction 3 as the dominant fate of 3K, it may be shown that at steady state 4
- 1~ = -~-k7 ~ [KI ~
(1 - 4K2H2)'/'
3 x 104
I x 108 0
Figure 2. Benzopinacol quantum yields as a function of benzophenone concentration: (0) experimental points. For model curves 1 and 2 k3 = 2 X lo6,k4 = 1.05 x lo8, ks = 2 log9k6 = 1.0 lo8 in M-' s-l), 1, = 1.8 X lo* einstein/(cm2S), 6 = 56 M-' cm-' at A t r = 365 nm, [AH,] = 1.3 M. Line 3 is obtained from eq 9 with k5 = 2 X lo9 and k7 = 2 X lo4 (both in M-' d).
2
2
kS'/' IabS1I2
(9)
where Iab is the rate of light absorption (einstein/(L s)) by benzophenone. However, we do not have to introduce the above approximations if we are willing to solve the equations numerically. From the steady-state conditions for [KH'] and [AH'], we have
+
k3[3K][AH2] k7[K]y - 2k4xz - k6xy = 0
(10)
and k3[jK] [AH21 - kT[K]y - 2 k g 2 - k6Xy = 0
(1 1) where x = [KH'] and y = [AH']. Values for x and y are conveniently obtained by the Newton-Raphson method36and hence $K2H2 (= (1 - cy)k4[KH*I2/Zab)obtained for a series of ketone concentrations. It is still convenient to plot the data by using coordinates suggested by the approximmate equation (9). Such a procedure yields the model curves 1 and 2 shown in Figure 2. For these curves we used the literature values for k3, ..., k6 and set cy at our experimental value of 0.01. By comparing the model curves with the experimental data, we see that k7 must lie between 3 X lo4 and 5 X lo4 M-' s-'. The straight line 3 is what we would obtain if eq 9 was valid. Using the literature value k5 = 2 X lo9 M-I s-l, we get k7 = 2 X lo4 M-' s-I, which is not too different from the value of k7 obtained by the detailed modeling. Basically, this comes about because neglect of reaction 6 does not have too serious an effect on the steady-state concentration of KH' and hence on 6K2H2. ( b ) From Benzopinacol and Mixed Pinacol Yields. In the previous section we used the variation in 4K2H2 with benzophenone concentration to get a value of k7. We can also obtain this rate (35) Henne, A,; Fischer, H. J . Am. Chem. SOC.1977, 99, 300-302. (36) McCracken, D. D.; Dorn, W. S . Numerical Methods and Fortran Programming; Wiley: New York, 1964; pp 144-145.
~i~~~~ 3. ~ ~(K,H,) and ~mixed pinawl~ ( K A H ~ )quantum ~ yields as a function of benzophenone (K) concentration: (0) experi-
, mental data from Table I; model curves have same k&r L, r ~ and [AH,] values as for Figure 2; also a! = 0.01 and P = 0.44. The values for k7 are as indicated on the graph,
constant from the simultaneous variation in both hKIHZ and 4KAH2, where the latter is the quantum yield of the mixed pinacol. As before, because of the high concentration of 2-propanol, reaction 3 is the dominant fate of 3K and we shall first omit (4b), (6a), and (6b) in arriving at steady-state expressions for [KH'] and [AH']. Under these conditions we obtain ( 2 4 -~ ~ ~ ~ 4KAH2
=-- k7k41/2 [K] k6(1 - P )
(12)
If we do not employ the above approximations, there is no simple analytical expression, but, as before, by numerical methods we can obtain values of $K2H2 and +KAH2 at various ketone concentrations using the literature values of k2-k6, cy = 0.01, P = 0.44, and trial k7's. Curves for two such k7's are displayed in Figure 3. Once again we have chosen to use the expressions suggested by the approximmate analytical equation (12) for the ordinate and abscissa. In this case the range k7 = (2.5 f 0.5) X lo4 M-I s-l encompasses the data. Thus, both methods are consistent and indicate that k7 lies in the range (3.5 f 1.5) X lo4 M-'s-I a t 298 K. Of course, this value of k, does depend upon k6 which we have taken from Weiner (1.0 X lo8 M-I 8).He studied the reaction in acetone, a solvent of comparable viscosity to acetonitrile. However it is possible that k6 should be somewhat larger. For example, since k4 is 1 X lo8 M-' s-I a nd k5 is 2 X lo9 M-' s-I, an intermediate value for k6 i= 5 X lo8 M-' s-I would certainly not be unreasonable. Such a 5-fold increase in k6 results in an increase in k7 from 2.5 X lo4 to 6.3 X lo4 M-I s-l. Rate Constant for Hydrogen Transfer from 4-tert-Butyldiphenylketyl Radical to Benzophenone. 4-tert-Butylbenzhydrol (K*H2) was chosen as a hydrogen donor since abstraction by triplet benzophenone (3K) from the tert-butyl group (=lo4 M-' s-' 37-39) is much slower than abstraction of a hydrol hydrogen (%io7 M-1 s-i 1 ). The mechanism of photoreduction is 3K K*H2 KH' K*H' (13)
-
+ + K + K*H' KH' + K* KH' + KH' KzHz K*H' + KH' KK*H2 K*H' + K*H' K2*H2 +
+
(14) (4a) (4b)
(4c) In the above scheme we only show pinacol formation (reactions 4a-4c) since disproportionation of KH' is quite minor (see above). Furthermore, because percentage conversions were kept low, the effect of LAT's (light-absorbing transients) on yields and kinetics can be neglected. The low conversions also mean that K* formed in (14) is small and does not compete with K for the absorption -+
(37) Giering, L.; Berger, M.; Steel, C. J . Am. Chem. SOC. 1974, 96, 953-958. (38) Berger, M.; Camp, R. N.; Demetrescu, I.; Giering, L.; Steel, C. Isr. J. Chem. 1977, 16, 311-317. (39) Gramain, J.-C.; Remuson, R. J . Org. Chem. 1985, 50, 1120-1122.
~
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6577
Proton-Electron Transfer of light at the photolysis wavelength (A = 365 nm) and that back-reaction (-14) can be neglected (see below). The rate constant k13 (=(1.2 f 0.2) X lo7 M-l s-I) for the interaction of 3K with K*H2 was determined from measurement of the variation of 3K lifetimea on addition of K*H2 I/. = 1/70 kl3[K*H2] (15)
+
where 70and 7 are the lifetimes of 3K in the absence and presence of K*H2, respectively. The value of k13 compares well with the corresponding rate constant for unsubstituted benzhydrol (= 1 X lo7 M-' s-l'). Thus, as in the case of the AH2/3K system, pseudo-first-order decay processes, including hydrogen abstraction from the solvent acetonitrile, can be neglected if we use sufficiently high concentrations (20.1 M) of K*H2 to intercept all 3K formed. Using the above reaction scheme, including the reverse reaction (-14), we obtain
=
[KI [Rf(K2*H2)11/2(1- 6(Rf(K2H2)/Rf(K2*H2))1/2) (16a)
where 6 = [K*]/[K] and Rf(K*) represents the rate of formation of K*, etc. Since 6 was kept very small, we immediately obtain the more tractable equation Rf(K*)k4,'12 k14
=
[KI [Rf(K2*H2)I'12
(16)
(Rf(K2H2) - Rf(K2*H2)1k4c1/2 [KI [Rf(K2*H2)1
(17)
Degassed samples (3 mL) of K (7.7 X IO4 M) and K*H2 (0.1 1 M) in acetonitrile were irradiated at 365 nm (Iab= 3.7 X lo-' einstein/(L s)) for 2 min and products analyzed by HPLC. Averaged over several runs photolysates yielded Rf(K2*H2)= (3.6 f 0.2) X 10" M s-l and Rf(K*) = (1.9 f 0.3) X M s-l. Rate constant kk can be estimated from the Hammett equation log (k,/k,) = pup, where p = -1.06 and up = -0.14 for the tert-butyl This gives kk = 1.4k4,, and with k4a = 1 X lo8 M-' s-l eq 16 yields k14 = 1.5 X lo4 M-' s-l. Unfortunately, the rate of formation of K2H2 could not be determined since the K2H2 peak on our chromatographs was masked by that for K*H2. However, an upper limit for Rf(K2H2) can be estimated. From the above scheme, Iabstirr = [K2H2] [K2*H2] [KK*H2], and so Rf(K2H2)= [K2H2]/tirr< Iabs[K2*H2]/ti,,. This yields Rf(K2H2) < 3.4 X M s-I, and so from eq 17 we obtain k14 < 2 X lo4 M-' 8, which is consistent with the value found from (16). Thus at 298 K, k14 = (1.3 f 0.2) x 104 M-1 s-1, Temperature Dependence of k7 and k14. Since the activation energy of reaction 3 is very 10w,38342we can use a high enough concentration of 2-propanol (2.6 M) to ensure that (3) is still the predominant fate of 3K even at the lowest temperatures (233 K). In terms of Scheme I we then obtain for the rate of formation of the mixed pinacol (KAH)2
+
+
0.018
0.018 0.022 0.022 0.0 18 0.018
T, K
295 297 297 296 296 276 276 235 235
4.8
10*Rt(KAH2), M s-I 6.2 7.8
5.1 5.0 5.3 4.9 5.4 3.5 4.8
10.8 13.0 11.4 12.9 14.0 23.0
106RdK2H2), M s-' 2.2
8.8
i-, 0.19 0.16 0.16 0.17 0.19 0.23 0.22 0.39 0.39
'Solvent CH3CN, [AH2] = 2.6 M, sample volumes = 1 mL, ti, = 2 min, 1, at 366 nm = 7 X einstein/s.
T, K
107Rr(K*), M s-l
295.0 294.4 293.7 273.3 233.0 233.0
1.88 1.74 3.20 2.34 3.10 3.50
1O8R~(K2*H2), M s-I
s-1/2
3.60 2.73 4.50 4.12 8.30 7.60
Y,
M-112
1.3 1.4 2.0 1.5 1.4 1.6
'Solvent CH,CN, [K] = 7.7 X lo4 M, [K*H,] = 0.11 M (contains as an impurity 0.065% K*), tin = 3 min.
and thus k14 =
[KI, M 0.010 0.022 0.022
TABLE 111 Temperature Dependence of Rates of Formation of K* and K2*HZ'
Rf(K*) ksc1I2 k14
TABLE 11: Temperature Dependence of Rates of Formation of K2H1 and KAH2'
Rf(KAH)2 = ( 1 - @)k6[KH'][AH']
(40) (a) Steel, C.; Thomas, T. F. J . Chem. SOC.,Chern. Commun. 1966, 900-902. (b) Solomon, B.S.;Thomas, T. F.; Steel, C. J . Am. Chem. SOC. 1966, 90, 2249-2258. (41) (a) Hammond, G. S.; Weiner, S. A. Intra-Sci. Chem. Rep. 1969, 3, 241-245. (b) Wells, P . R. Linear Free EnergV Relationships, Academic: New York, 1968; p 14. (42) Topp, M. R. Chem. Phys. Left. 1975, 32, 144-149.
We chose our experimental conditions so that [4k5Rf(K2H2)]/ [(k7[K])2(l - a ) ] I 0.15 and so immediately obtain RfWH2) Rf(K2H2)3/2 (1
I-@ k6 - 1 1 - a)3/2 k41/2k7 [Kl
t 19)
Experimental data are given in Table 11. Notice how little Rf(K2H2)varies with temperature, a qualitative clue that reaction 7 must be quite temperature insensitive. This can be confirmed quantitatively. Defining f = [K]Rf(KAH)2/R~(K2H2)3/2,E' is obtained from E ' = -R 8 In l/a(l/T), where E' = E6 - '/2E4 E7. Taking the literature activation energy for E428and making correction for solvent viscosity, we get E4 = 1 kcal/mol in acetonitrile. Then assuming E6 = E4, we find E7 = 2.3 f 0.1 kcal/mol. We also used computer modeling to obtain this quantity, Le., none of the approximations used in obtaining eq 19 are made, and obtained very similar values for E7.In this full treatment E5 is also required (= 2.1 kcal/mol in acetonitrile), and so we have over our temperature range k7 (M-l s-l) = 2.0 X IO6 exp(-2300/ RT). The absence of significant temperature dependence in k14 was also noted, and pertinent data are given in Table 111. In this case, using eq 16 as our guide, we define = Rf(K*)/([K]Rf(K2*H2)1/2) and obtain E'= -R a In r/a(l/T) where E'= E14 - 1/2E,. Again taking Eb = 1 kcal/mol, least-squares analysis gives E14 = 0.5 f 0.3 kcal/mol and so k14 (M-* s-') = 3.0 X lo4 exp(-SOO/RT).
r
Discussion Comparisons with the Literature. There are several sources in the literature that allow us to make a rough estimate of k7. Beckett and Porter's early studies9 established that, for the photoreduction of benzophenone in neat 2-propanol, the quantum yield of benzophenone consumption (&K) tended toward 2 as the benzophenone concentration increased. Cohen and C0henl~3'~ also found that C # L ~ was close to 2 when the photoreduction was carried out in benzene, indicating that the hydrogen transfer from AH' to K does not occur only in a polar environment. Beckett and Porter discussed their results in terms of the set of reactions 1, 3, 4a, 5, and 7 of Scheme I. They did not analyze their data quantitatively because of inhomogeneity effects. Also, although values of the incident light intensity, Io, are given, there is not enough experimental information to calculate I,, exactly (eq 1). Nevertheless, an order of magnitude calculation is in order. They
6518
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988
M &K had dropped to =1.5. In found that at [K] = 2 X terms of reactions 1, 3, 4a, 5 , and 7, when I # L ~ has fallen off from 2.0 to 1.5, then k7 = (k5Za,)'/2/[K]. Taking a reasonable cell volume (1 cm3) and realizing that at the concentrations and wavelength (254 nm) employed the transmittance is small, we calculate Iab = 1 x 1 0 - ~einstein/(L s) for Io = 1 x einstein/(cm s). Now k5 = 2 X lo9 M-' s-' a nd so k7 = 1 X lo4 M-' s-l, in nice agreement with our studies. Mercaptans (RSH) in small amounts (=lod3 M) can effectively inhibit the photoreduction of K by AH2 by catalyzing the KH' and AH' formed in step 3 back to starting material
+ RSH KH' + RS'
AH'
-
-
AH2 K
+ RS'
+ RSH
(20) (21)
For RSH = 2-mercaptomesitylene, AH2 = 2-propanol, and K = benzophenone, Cohen et al. estimated k2o/k7 = 150.1° Although k2, is not known, since the A factor for a typical hydrogen abits value is expected to be C-0-H O=C< >C=O H-0-C< an even electron ground state is formally the abstracting moiety, and so "normal" hydrogen transfer might be expected to have a significant energy barrier. However, the small temperature dependence for the rate constants of the two reactions studied shows that in fact any energy barriers are minimal. Simple electron or proton transfer is also energetically unfavorable. Notice that either yields similar ionic species. For example, in the case of KH'
-
KH- + K
PhCHO
+ Me2COH
-
PhCHOH
+ Me2C0
(23)
They fit their overall kinetics with an assumed log k23 (M-' s-l) = 8.5 - 6.9/0 where 0 = 2.303RT (kcal/mol). This yields k23 = 2.6 X lo3 M-' s-' a t room temperature. We conclude that both kinetic and chemical evidence favor low values for the rate con(43) Benson, s. W. Thermochemical Kinetics; Wiley: New York, 1968. (44) Ingold, K. U . Free Radicals; Kochi, J. K., Ed.; Wiley: New York, 1973; Vol. I . (45) Kaptein, R. In Aduances in Free Radical Chemistry; Williams, G . H . , Ed.; Academic: New York, 1975; Vol. 5, pp 319-376. (46) Closs, G. L.; Paulson, D.R. J . Am. Chem. SOC.1970,92,7229-7231. (47) Malwitz. D.;Metzger, J . 0. Chem. Ber. 1986, 119, 3558-3575.
L..KH+ +
H+
+
+
KO-
+
KH' K KO- KH+ It is interesting to make an estimate of the energetics of forming such an ion pair. The gas-phase ionization potential for dimethylkety121and the gas-phase electron affinity of b e n z ~ p h e n o n eare ~ ~ known (all energies in kcal) AH'(g) K(g)
-
AH+(g) + e-
+ e-
-
K'-(g)
AE = 147.6 AE = -14.7
The energy released in bringing the two ions to a separation distance, r (=5 A), and then solvating the dipole so formed in a solvent with dielectric constant, e (=37.5 for CH3CN), can be obtained from standard formulas50
--
AH+(g) + K'-(g)
[AH+,K'-],
PE = -98.7
Finally, we estimate the internal energy in taking K and AH' from solution into the gas phase AE = 13.3 K(s) K(g)
+
-
-
+
AH'(s)
AH'(g)
AE = 8.2
Here we have simply assumed an ideal solution so that AE = AHvap.However, by Trouton's rule AHvap = 0.023Tb. For benzophenone the boiling point ( Tb) is 579 K and we shall assume AH' has a similar Tb to AH2 (=355.3 K). So finally AH'(s)
+ K(s)
-
[AH', K'-],
AE = +55.7
However, ketyl radicals generally act as reducing species by losing not only an electron but also a proton, undoubtedly a significant part of the driving force being the formation of the carbonyl double bond. KH' K H+ + eSo the question arises whether the reaction of ketyl radicals with carbonyl can involve some form of coupled proton-electron transfer. Because the reaction also apparently occurs in the gas phase, we cannot think of the proton as being released into the solvent. However, ketones may act as acceptors for both protons and electrons with the transfers reinforcing each other. This can
-
+
(48) Trotman-Dickenson, A . F. In Aduances in Free Radical Chemistry; Williams, G. H., Ed.; Academic: New York, 1965; Vol. I , pp 1-38. (49) Caldwell, G.; Kebarle, P. J . Chem. Phys. 1984, 80, 577-579. (50) Weller, A. Z. Phys. Chem. (Munich) 1982, 133, 93-98.
Proton-Electron Transfer
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6579
be readily seen if we write the ketone in its dipolar form and postulate a hydrogen-bonded complex >F-O)
(
+
\
‘,
H -
*A
>c-g:-
>Lo:-
>$-0
7
In this sense the sites of electron and proton transfer are distinct in contrast to “normal” hydrogen transfer in which the loci of the moving proton and electron coincide. The incipient bonding between the proton and the carbonyl oxygen makes the carbonyl carbon more positive and the ketyl carbon more negative, aiding electron transfer which might be facilitated by tunneling of the light electron through substantial barriers and over a distance of several angstroms. Experimental Section Photochemical. Room-temperature samples (3 mL) were degassed by freeze-thaw cycles at Torr and irradiated in rectangular 1-cm path length cells with stirring at 365 nm using a conventional optical train?’ with the collimated beam essentially filling the solution volume. For the temperature dependence studies samples were irradiated in 1-cm-diameter tubular cells contained in a thermostated Dewar. The rate constant for the interaction of triplet benzophenone with 4-tert-butylbenzhydrol was determined by using a lifetime apparatus described previously.@ Analysis. Product analyses were carried out by HPLC using a Waters 440 detector equipped with a wavelength extender (214 nm) and a 5-rm reverse-phase column (Waters Nova-Pak CIS). Compounds were identified by co-injection with authentic samples. Absolute yields of the various components in the photolysate were calculated from standard calibration curves of these components. The photolysates of photoreduction of K by AH2 were analyzed for K2H2,KH2 and KAH2 by using 50% aqueous acetonitrile with a flow rate 1 mL/min at 1000 psi; the order of elution was KH2, KAH2, K, and K2H2. The photolysates of photoreduction of K by K*H2 were analyzed by using 20% aqueous acetonitrile for K2*H2and 40% aqueous acetonitrile for K*; the order of elution was K, K*H2, K2H2, K*, and K2*H2 (two diastereoisomers). Compounds. Acetonitrile and 2-propanol (Fisher spectrograde) were purified as previously des~ribed.~,Benzophenone (Aldrich) was recrystallized from ethanol; 4-tert-butylbenzophenone (Lancaster Synthesis Ltd.) was distilled at 0.03 mm, bp 122 OC nm (e in M-’ cm-I), in CH3CN: (lit.S1bp 189 OC at 4 mm). , A, (51) Fischer, A.; Grigor, B. A.; Packer, J.; Vaughan, J. J. Am. Chem. Soc 1961,83,
4208-4210.
260 (1.77 X lo4), 335 (174); at 365 nm, = 80 M-’ cm-’ (lite5, 259 (1.69 X lo4), 325 (230) in ethanol). 4-tert-Butylbenzhydrol was synthesized in a straightforward manner by sodium hydride reduction of the corresponding ketone. The hydro1 (K*H2) was recrystallized from hexane-benzene (3: 1 V/V)to give white crystals, mp 79-81 “C (lit.5382 “C). ‘HN M R (CDCl,) 6 1.30 (s, 9 H), 2.23 (d, 1 H), 5.71 (d, 1 H), 7.27 (m, 9 H). HPLC analysis of K*H2 showed it to contain 0.06% K*. l,l-Diphenyl-2-methylpropane 1,2-diol (KAH,) was synthesized as described by Weiner,28mp 89-91 OC: ’H N M R (CDCl,) 6 1.33 (s, 6 H), 2.18 (s, 1 H), 2.76 (s, 1 H), 7.23 (m, 6 H), 7.6 (m, 6 H ) (lit. mp 92-93.5 OC; N M R (CC14) 6 1.35 (s, 6 H), 1.95 (s, 0.7 H), 2.53 (s, 0.7 H), 7.23 (m, 6.5 H), 7.68 (m, 3.3 H)). 1,2-Bis(4-tert-butylphenyl)-1,Zdiphenylethane-1,2-diol (K2*H2) was prepared by irradiation at 365 nm in a degassed solution (3 mL) of 4-tert-butylbenzophenone(0.13 M) and 2-propanol (0.65 M) in acetonitrile for 7 h. The solvents were evaporated on a rotovapor to give a white solid. The solid was washed several times with hexane, to remove unreacted ketone, to yield the pinacol, K2*H2(Found: C, 85.69; H, 8.1 1. C34H3802 requires C, 85.31; H, 8.00). ’H N M R (CDC1,) 6 1.27 (d, 18 H), 2.95 (s, 2 H), 7.12 (m, 18 H). Photoreduction of Benzophenone by 4-tert-Butylbenzhydrol. A degassed solution (3 mL) of benzophenone (0.018 M) and 4-tert-butylbenzhydrol (0.114 M) in acetonitrile was irradiated at 365 nm for 2 min. The quantum yield for the appearance of 4-tert-butylbenzophenone,as determined by HPLC (monitored at 214 nm, 40% aqueous acetonitrile as solvent), was found to be 0.95 f 0.03 averaged over three runs. HPLC analysis of the photolysate showed no K2*H2but an unidentified additional peak, presumably the mixed pinacol KK*H2, absent in the zero-time samples, with a retention time between those for samples of K2H2 and K2*H2. On the other hand, photolysis of a much lower M) with 4-tert-b~concentration of benzophenone (7.7 X tylbenzhydrol(O.11 M) resulted in the formation of K2*H2which gave rise to two closely spaced peaks in a ca. 1:l ratio due to the two stereoisomers (monitored at 214 nm with 20% aqueous acetonitrile as solvent). Acknowledgment. We thank the Polaroid Foundation for financial support. Registry No. Benzophenone, 119-61-9; dirnethylketyl, 5131-95-3; 4-?ert-butyldiphenylketyl,1 16597-10-5; 4-tert-butylbenzophenone, 22679-54-5; 1,2-bis(4-tert-butylphenyl)-1,2-diphenyl-l,2-ethanediol, 1 16597-11-6; 4-tert-butylbenzhydrol, 22543-74-4. (52) Rekker, R. F.; Nauta, W. Th. Red. Trao. Chim.Pays-Bus 1961,80, 164-714. (53) Hughes, E. D.; Ingold, C. K.; Taher, N. A. J . Chem. SOC.1940, 949-956.
