432
RUDOLPH J. MARCUS, BRUNO J. ZWOLINSICIAND HENRY EYRING
the hydrocarbon is converted to the deuterocarbon. A like statement may be made for the cyclohexane. The relationshipg is apparently due to a fortunate 2.45AE,,,
AF&
(3)
cancellation of a number of opposing effects. The ratios of viscosity of deuterocarbon to viscosity of precursor hydrocarbon, a t three temperatures, appear in Table 111. It is surprising that, for a given temperature, the ratios are the same for two very different structures, benzene and cyclohexane. Before embarking on a speculative flight it would be most desirable to see whether this relationship would hold for other hydrocarbon structures. TABLE I11 RATIOSOF VISCOSITIES OF DEUTEROCARBONSAND HYDROCARBONS Temp.,
Coin pounds
CtiDdCeHs
CsDdCaHi2
CaHidCeHe CBHI~CBHII
O K .
?D/~E
293.18 310.96 333.18 293.18 310.96 333.18 293.18 293.18
1.065 1.062 1.058 1.064 1.062 1,060 1.506 3.192
MD/MH'/~
1.038
1.070
Vol. 58
tion of the measurements and is believed to be real. Due to the number of simplifying assumptions involved in deriving presently available viscosity equation^^.^'.'^ and also because two important parameters of most such equations energy of vapori ~ a t i o n ~and ~ . ' ~"energy of activation for viscous f10w1'14appear to be sensitive to isotope replacement it is felt that comparison of the data here reported with predictions of the equations may not be meaningful. However, as predicted by most of the theories the viscosity does appear to be a function of a fractional power of the molecular weight. Included in Table I11 are the ratios of the viscosities of cyclohexane to benzene, and of cyclohexane to n-hexane. These data point up an observation previously reported,15 that the effect of molecular weight on viscosity is very small in comparison with the effects of other structural parameters. The infrared spectra of cyclohexane-d12has been included because the only previously published spectrogram was obtainedle on material whose purity and isotopic composition is not obvious. Acknowledgment.-The authors express their appreciation to the American Petroleum Institute for the grant which made this research possible. (11) J. Frenkel, "Kinetic Theory of Liquids," Clarendon Press, Oxford, 1946.
Although the decrease with temperature of the ratio of the viscosities is small it exceeds the devia-
(12) M. Telang, J . Chem. Phya., 17, 536 (1949). (13) F. E. Condon, J . A m . Chem. Soc., '78, 4676 (1951). (14) See values of Euiain Table 11. (15) R. W . Schiessler, el al., Proc. A.P.I., 24, 111, 49 (1943); 2 6 111, 254 (1946). (16) A. Langseth and B. Bak, J . Chem. Phys., 8 , 1103 (1940).
THE ELECTRON TUNNELLING HYPOTHESIS FOR ELECTRON EXCHANGE REACTIONS1 BY RUDOLPH J. MARC US,^ BRUNO J. ZWOLINSKIAND HENRY EYRING Departmenl of Chemistry, University of Utah, Salt Lake City, Utah Received January $3, 1964
The available data pertaining to electron-exchange reactions in aqueous solutions are collected and classified on the basis of the entropy of activation. An electron tunnelling mechanism is developed and discussed in relation to the FranckCondon principle. The extrema1 value for the specific rate constant as a function of the distance of approach is used to determine the most stable activated complex. This maximization is necessary to find the best distance of ap roach for the interacting ions, leading to largest values for the probability of electron penetration consistent with the s m d e s t energy of activation. An approximate expression for the closest distance of approach is derived and related to variables such as temperature, dielectric constant, and also to the nature of the reacting ionic species. Calculated values agree satisfactorily with the available experimental data.
Introduction Whereas any oxidation-reduction reaction may be termed an electron-exchange reaction, this name is more usually applied to a group of ionic reactions for which the standard free energy change is zero, i.e., the reacting species are identical with the products. I n such systems, radioactive tracers are usually employed to follow the course of the reaction. It appears that this technique was first inI
(1) Presented in part a t the 123rd National Meeting of the American Chemical Society, Los Angeles. California, March, 1953. This work was supported by the University of Utah Research Fund and by the U. 8. Atomic Energy Commission. (2) This material is taken in part from a thesis submitted by Rudolph J. Marcus to the faculty of the Gradnate School, University of Utah, in partial frMlinent of the requirements for the degree of Doctor of Philosophy.
troduced by Hevesy and Zechmeister3 in 1920. The availability of radioactive tracer materials in recent years has greatly expanded work in this field. This particular class of reactions can be given a more quantitative formulation a t the present time. The pertinent experimental data are presented in Tables I and 11, based on recently published information on electron-exchange reactions. The tabulated data refer only t o the rate-determining step in each case except for reactions 1, 3 and 4 of Table 11, for which the mechanism of the over-all reaction is less certain. All of these rate studies were carried out in perchlorate salt media where the (3) G. Hevesy and (1920).
L. Zechmeister, Z . Elelclrochem., 26, 151
May, 1Y54
ELECl'ROh' T U N N E L L I N G
HYPOTHESIS FOR ELECTRON-EXCHANGE h.4CTIONS
433
TABLE I SUMMARY OF DATA Rate constants measured at 25" for all reactions except the ones involving Fe+2, where the temperature was 20". All reactions are first order in each of the two reactants. The electronic transmission coefficient ( K ~ ) was evaluated from the relation AS* = R In K ~ . Reaction
C O ( E ~ ) ~ + " C O (+3 E~)~ T1+-TIOH +2 VOH +"VO +a Fe +Z-Fe +3 Fe +Z-FeOH -1-2 Fe +"FeCl +2 Fe +2-FeCl2 +
AS*, e.u.
AEexp.
koal./mole
AF* lical./idole
- 33 -33
14.3 14.7 10.7 9.9 7.4 8.8 9.7
-24 -25 - 18 -24 -20
Reference
K0
7 x 107 x 10-8 6X 4 x 10-6 1 x 10-4 ti x 10-6 5 x 10-6
23.5 23.9 17.2 16.7 12.2 15.3 15.1
9
10 11 12 12 12 12
TABLE I1 SUMMARY OF DATA Rate constants measured a t 25" for all reactions except the ones involving Ce+3where the temperature was 0". actions are first order in each of the two reactants except U+4-U+6, which is second order in Uf4. AEexp,
Reaction
kcal./mole
Fe+3-Y +I i P Fe +3-hydroquinone ion
35.0 20.2 33.4 23.7 7.7 24.0
u feu +e
Sn +"Sn Ce +"Ce
+4
(abs. alc.) (1) (2)
AS*, e.u.
+51 53 +31 16 40 $25
+ + -
AF*, kcal /mole
19.2 3.8 23.6 18.3 18.0 16.6
Other orders
K0
[H+]-3 [H+]-3 2 IH +I
-9
x
10-9
All re-
Reference
13 14 15 16 17 17
effects of complexing are negligible. This question action may proceed by either path; for all other reof participation of foreign anions in these reactions actions, one or the other of these possible paths is has been examined thoroughly and the results are definitely favored. A consideration of the current theories and models based on media effects such as available elsewhere. Among inorganic systems only positive ions have dielectric constant, ionic strength, electrostatic been observed to react with measurable rates. Some charge effects, the effects of solvation and desolvapreliminary studies have been made by Adamsons tion of the activated complex, fail to yield a consistand co-workers on electron-exchange reactions in- ent explanation of the above facts.4 An approach volving negative ions; in general, these proceed including, in addition, the hypothesis of electron with immeasurably fast rates. Other workersa-s tunnelling explains these anomalous experimental have obtained similar results with negative ion re- results satisfact orily actions. The reason for this is that the reorganizaApplication of the Franck-Condon Principle tion free energy of activation, AF?, of the hydraI n the oxidation-reduction reactions under contion shell is so small for negative ions that the elecsideration, the polyatomic ions modify their structron transfer becomes immeasurably fast. ture in such a way that transfer of the electron An examination of the data in Tables I and II leaves the total energy unchanged. During the indicates that there are two possible reaction paths approach of the reactive ionic species leading to the for electron-exchange reactions: one with a low en- transition state, ionic repulsion forces are overcome ergy of activation and a negative entropy of activa- and the coordination and hydration shells of both tion (Le., low frequency constant), and the other ions rearranged until their electronic states are with a higher energy of activation and a positive symmetrical, thus permitting a rapid transition to entropy of activation (i.e., high frequency con- take place. Those configurations which give the stant). It is interesting to see that the cerium re- fastest reaction will be the ones measured. (4) R. J. Marcus, Thesis, University of Utah, 1954. Such configurations will be the best compromise 66, 858 (1952). (5) A. A. Adamson, THISJOURNAL, giving frequent electronic transitions without too (6) F. P. Dwyer and E. C. Gyarfas, N a t w e , 166, 481 (1950). high a free energy of activation. Thus any measur(7) J. C. Hornig, G. L. Ziinmermanand W. F. Libby, J . Am. Chem. soc., 7a, 3808 (1950). able rate for an oxidation-reduction reaction nec( 8 ) R. L. Wolfgang, ibid., 74, 6114 (1952). essarily involves a transmission coefficient less than (9). W. B. Lewis, C. D. Coryell and J. W. Irvine, J. Chsm. Sac., unity since it is arrived a t as this best compromise. SUPPI.Issue No. 2, S 386 (1949). To a first approximation, its magnitude will be (10) G. Harbottle and R. W. Dodson. J. A m . Chem. Sac., 73, 2442 (1951). determined by the height and thickness of the (11) S. C. Furman and C. S. Garner, ibid., 74,2333 (1952). electronic barrier for this transition. The variation (12) J. Silverman and R. W. Dodson, THISJOURNAL, 66, 846 in the thickness of the electronic barrier with the (1952). (13) J. R. Huizenga and L. B. Magnusson, J. Am. Chem. Sac., 73, relative distance of approach of the two ions is 3202 (1951). shown schematically in Fig. l b and is related to the (14) J. H.Baxendale, H. R. Hardy and L. H. Sutcliffe, Trans. Faratotal molecular electronic energy of the reaction day Sac., 47, 963 (1951). system in Fig. l a for three values of the atomic reac(15) E. Rona, J. Am. Chem. Soc., 73, 4339 (1950). tion coordinate.. (16) E. G . Meyer and M . Kahn, ibid., 73, 4950 (1951). (17) J. W.Gryder and R. W. Dodson, ibid., 73, 2890 (1951). It is to be expected that cases will exist where
.
434
RUDOLPH J. MARCUS, BRUNOJ. ZWOLINSKIAND HENRYEYRING
r, w
rg
2
r*
ATOMIC REACTION COORDINATE ( r ) Fig. la, I 1I
I ’
I 1 1 ! I
I
> w
rz
I I I I
ELECTRONIC COORDINATE Fig. Ib.
tions for the two cations. The approximations that have to be made with respect to the nuclear coordinates of complex systems to make these calculations possible have been pointed out recently in a paper by Melvin Lax.20 In our particular approach to the problem, the probability of an electronic transition is considered as a transmission coefficient ( K ~in ) the expression for the specific rate constant and, in addition, the free energy of activation for the electron exchange reaction is considered to be made up of the free energy for rearrangement of the hydration and coordination shells of the two cations plus the electrostatic repulsive energy. The exchange repulsions of inner shells have been assumed to make a negligible contribution because of the comparatively large interionic distances of electron transfer. Similarly, the free energy change due to coordination and hydration changes seem largely unaffected by the approach of the ions toward each other a t the large distance a t which electron transfer occurs. The contributions considered will be discussed in turn. For convenience, the electronic transmission coefficient is assumed to be represented by the approximate expression which can be derived for the case of a triangular potential barrier.21 This can be expressed in the following form K~
the electronic barrier is quite thin a t the transition point with the probability of transition, i.c., the transmission coefficient, being near unity. This extreme case is demonstrated by the class of reactions with positive entropies of activation and large energies of activation, the latter being due to the closeness of approach of the reacting cations. The positive entropies of activation can, in turn, be ascribed to dehydration and change in coordination in the activated states. The entropy of fusion for water is 5.3 e.u. per mole. The number of water molecules lost in the dehydration process is actually greater than that indicated by the apparent positive entropy of activation by the amount necessary to compensate for the transmission coefficient being less than unity. The reactions characterized by apparent negative entropies of activation (calculated by taking K = l), according to the proposed model, are those with appreciable electron barrier widths a t the activated state, consistent with smaller energies of activation a t larger critical distances of ion approach. Thus, as previously stated, a reaction occurs a t a maximum velocity for the particular activated state defined in terms of the maximum value for the product of the electronic transmission coefficient and the factor exp ( - A F * / R T ) . Qualitatively, somewhat similar considerations have been discussed by Franck and more recently by Libby.ls,lg Theoretical Analysis In a complete solution to the problem of an electron-exchanging positions between two polyatomic cations, it is necessary to calculate the probabillty of electronic transitions from the known eigenfunc(18) W. F. Libby, THISJOURNAL, 116, 863 (1952). (19) R. J. Marcus, B. J. Zwolinski end H. Eyring, to be published.
Vol. 58
= exp
[- a r,b(%n(V - W))’/z] ST
I
(1)
where V = height of the electron barrier W’
kinetic energy of the tunnelling electron tunnelling distance m = electron mass h = Planck’s constant =
Tab =
The choice of the expression for a triangular barrier was dictated by the ease of algebraic manipulation in the analysis which follows. It is recognized that the characteristics of the actual barrier \vi11 be intermediate between the two extremes of triangular and rectangular barriers. At a point where V = -2W and V , = 0, where the electron tunnelling distances through the two kinds of barriers are equal, the ratio of transmission coefficients is found to be 4n Kreot./Ktri. = 4 exp - (mv>Liz Tab] (2)
[ a
For values of Tab of 3, 6 and 9 i., the ratio in equation 2 has the values 0.63, 0.10 and 0.025, respectively, when a value of V = 6.7 e.v., corresponding to the Fe+2-Fe+3system is used. I n estimating the height of the electronic barrier, however, a smoothed potential function is actually used, based on the simple one-dimensional electrostatic model that is diagrammed in Fig. 2. The height of the potential barrier is then given by V = v, - Vi3 (3) where Vo is the zero-point energy of the electron and Vm is the maximum potential energy for the system consisting of the exchanging electron interacting with the two cations of charges n, and nb, respectively. (20) M. Lax, J . Chem. Phys., 20, 1752 (1952). (21) N. F. Mott and I. N. Sneddon, “Wave Mechanics and Its Applications,” Clsrendon Press, Oxford, 1948.
*
May, 1954
ELECTRON TUNNELLING HYPOTHESIS F’OR ELECTRON-EXCHBNGE
REACTIONS
435
Using Coulomb’s law for point charges, and assuming the cations to be fixed at some distance Tab, the potential energy is expressed by
where D is the dielectric constant of the medium and x is the distance of the interacting electron from the cation of smaller ionization potential (n,). Maximizing with respect to x, one obtains
where
y2 =
nb/na and in turn V,
=
EL €C TRON COORDIN.4TE. Fig. 2.
e2
--f(n) Drab
where f(n) = nJ(1
+ rI2- nbl
An expression is needed for the zero-point energy of the exchanging electron to permit one to calculate the height of the barrier by use of equation 3. It is assumed that the zero-point energy is given by
organization of the coordination and hydration shells of the two reacting ions. The specific rate constant for the electron-exchange reaction is, therefore
(7)
where Z* is the positive charge on the central atom of the complex ion and ro is the radius of the classical orbit for the exchanging electron. Equation 7 applies to the complex cation whose central coordinated atom or ion has the smallest ionization potential. When all the coordinating groups about the central ion are neutral, then Z* = n,. The radius of the electronic orbit is assumed to be given by rg = n*2ao
(8)
Here n* is the effective principal quantum number as given by Rice,22and a. is the Bohr radius. Other expressions for this radius have also been considered, such as those derived from Slater atomic eigenfunctions; however, there seems to be considerable uncertainty about the proper expression for TO for the case of hydrated ions in solution. There seems little to choose between the different possible estimates of ro except that the present choice leads to a more reasonable distance of approach of _. the ions. From equations 3, 6 and 7,’ the height - of the electronic bariier is given by (9)
T o the same approximation as for the potentia1 energy of the electron given by equation 7, the kinetic energy W is, according t o the virial theorem
The expression for the transmission coefficient, based on the above approximations is now
The free energy of activation is assumed to be made up of the electrostatic repulsion energy contribution and of the energy AFr* arising from the re(22) 0. K. Rice, “Electronic Structure and Chemical Binding,” McGraw-Hill Book Co., Inc., New York, N. Y . , 1940. p. 96.
where AFr* is the activation free energy for rearrangement of the hydration and coordination shells and D is the dielectric constant. The best distance for electron transfer is usually a t a sufficiently large distance that the two reacting ions interfere negligibly with each other’s hydration shell. In this case a = dAFr*/dr,bwO. The ordinary atomic or nuclear transmission coefficient is assumed to be unity. Expression 12 for the rate constant includes in the exponent the contribution to the apparent entropy of activation ( - R In K ~ )made by the electronic transmission coefficient. There is also a positive activation entropy of rearrangement (As,*) as part of the free energy of rearrangement. This formulation of the rate constant expresses the competition between the two mechanisms that have been indicated: namely, the “easy” path of low repubive energy leading to the larger tunnelling distances for the electron, and the “hard” path of close approach where K~ has an increased value approacfiing unity. At some definite value of Tab these two tendencies will balance each other, and there will be a criticaI or “best” intercationic distance at which the rate of reaction mill have its maximum value. If this resistance to electron exchange did not exist, electron tunnelling would occur a t large distances. To find the critical value of the intercationic distance in the activated state, it is necessary to find the extrema1 value for the specific rate constant with respect to ?‘ab. By defining the following dimensionless parameters 64rr2me2roZ* 9h2 128rr2me2rof(n) b = 9h2D a=
C f -
e2n,nb kTDro
RUDOLPH J. MARCUS, BRUNOJ. ZWOLINSKIAND HENRY EYRING
43G
and the normalized variables
which expression is set equal to zero and on proper factoring reduces to
Y E -k'h kT
a'/z(l
equation 12 in logarithmic form can then be expressed as
- In y
=
(axe - bx)l/z
+
dx
JCY
+ c/x
(13)
Maximizing with respect to x, one obtains
- d In y/dz
=.(2ax
Vol. 58
- b)/2(ax2 - bx)'/r - c/x2
(14)
- b/2ax)/(l, - b/ax)'/t = c/x2
(15)
Using the binomial expansion on the square root term and retaining oiily the first two terms of the expansion, (15) simplifies t o 52 =
(164
c/al/z
The critical parameter in this expansion is the dielectric constant of the medium. If D is set equal to 8 and the values f(n) = 6.5, TO = 4.3 X cm., = 2 and Tab = 6.5 X em. are used for all the other parameters, the error is found to be about 7% if the quadratic term is neglected in the expansion. For D 3 70, this error is reduced to less than 0.1%. Substituting the parameters defined above, the explicit expression for the critical intercationic distance in the activated state is, in this approxima ti on
z*
(16b)
-
Discussion On the basis of the equations developed in the preceding section, values of the free energies of activation of electron-exchange reactions can be calculated provided values of AF,* are known. If AF,* is taken equal to 8.1 kcal. for all these reactions, one finds the calculated values given in the next to the last column of Table 111. In reactions where the coordination is different for the two reacting ions it is not surprising to find AF,* different the tunfrom 8.1 kcal. The critical values of ,,t$ nelling distance for the, exchanging electron, were found to varg from 3.4 A. for the Fe+2-FeC12+1system to 9.3 A. for the Ce+3-Ce+4 system. These distances appear to be of the right order of magnitude and so provide some justification of the proposed model for the electron-exchange process.
W5, kcal. -8mole
I
0-1 0
I
I
*
I 16
a
rob#
I-
*
Fig. 3.
TABLE I11 COMPARISON OF ELECTROSTATIC MODELWITH EXPERIMENTAL DATA" T*ab
In KB
Co(en)a+s-Co(en)a+' TI +1-T1OH
5.9 3.3 4.4 6.0 4.0 4.9 3.4 9.3
4.38 2.63 4.00 4.37 3.57 3.57 2.48 5.52
+'
z*.
Fa +"Fe +: Fe +z-FeOH +a Fe +z-FeCl +I Fe +:-FeCI: + I Ce +a-Ce +a
nanb. Fig. 4.
(1
I I
4
I
I
I
I
I
4
L
Fig. 5.
I 8
ro, A.
1/D X 102.
I
I
I
I112
,
AF*:rep.
4.32 2.57 3.86 4.25 3.47 3.47 2.50 5.48
Calcd. 16.8 13.3 16.0 16.7b 15.1 15.1 13.1 19.1
All energy values in kcal./mole for D = 78.
value.
i
AF*
(A.1
VOK +*-vo +:
l 0 Z k - - + +
-RT
Reaction
Total
Obs.
23.6 23.9 17.2 16.7 12.2 15.3 15.1 18.0
* Fitted
I t is of interest to examine the variation of the calculated free energies of activation with the individual parameters of this model. The results are illustrated in Figs. 3, 4 and 5. Figure 3 shows the variation of the calculated free energy of activation with the tunnelling distance. The curves represented in the three figures have been calculated by varying only the specific parameter named, while holding the other parameters constant. The Fe+2Fe+3 system has been the one chosen for these figures, although any of the other systems would have served as well. Figure 4 shows the relationship between the calculated free energy of activation
I
ABSTRACTION OF HYDROGEN ATOMSFROM MERCAPTANS
May, 1954
and (a) the charge (Z*) on the central ion of smaller ionization potential and (b) the product n a n b of the charges of the reactant complex ions. Both these curves show that as the charges on ions are increased, there is a corresponding increase of the free energy of activation. This in turn corresponds to the well known fact observed in electron-exchange studies that the reaction will be speeded up as the total charge on the reactant cations is reduced either by complexing with anions or by hydrolysis. Figure 5 shows the variation of the calculated free energy of activation with the reciprocal of the dielectric constant. This relation is particularly important, for it provides a convenient experimental approach for testing the correctness of the proposed model by studying the kinetics of an exchange reaction in media of varying dielectric constant. The dependence of the calculated free energy of activation on the value of ro, which, in turn, is a function of the principal and orbital quantum numbers of the exchanging electron, is also given in Fig. 5. Here it is seen that s, p, d and f electrons will exchange more rapidly in the order given, and
437
that the principal quantum number is only of secondary importance in determining the probability of exchange. Recently W. F. Libby18 reported some approximate quantum-mechanical calculations of the frequencies of electron exchange in the hydrogen molecular- ion. H e found appreciable frequencies of excbange for 3d electrons at distances of the order of 30 A. Though the expression for the free energy of activation is a complicated function of the temperature because of its dependence on rab* which in turn inversely depends on T ’ / f ,calculations show that over a limited temperature range AF* varies linearly with temperature. As mentioned earlier, the great speed of electron-exchange reactions involving two anions is presumably due to a low value for AFr*, in accord with their decreased tendency t o hydrate. Acknowledgment.-The authors wish to acknowledge many thought-provoking discussions with Professors Rufus Lumry (Department of Chemistry, University of Minnesota) and John D. Spikes (Division of Biology, University of Utah) in the preparation of this manuscript.
THE ABSTRACTION OF HYDROGEN ATOMS FROM MERCAPTANS BY 2,g-DIPHENYL-1-PICRYLHYDRAZYL BY KENNETHE. RUSSELL Frick Chemical Laboratory, Princeion University, Princeton, Neu, Jersey Received February 1 , 1964
The reaction between 2,2-diphenyl-l-picrylhydrmyland mercaptans in solution is a process of hydrogen atom abstraction in which the radical concentration is accurately known. The activation energy is approximately constant a t 15.0 kcal./mole for a number of mercaptans, and A factors for the normal mercaptans are in the range 2-6 X 1011. &Butyl mercaptan has a much lower rate constant than the normal mercaptans and this is reflected chiefly in a lower A factor. The results are discussed in relation to other hydrogen abstraction reactions in solution and in the gas phase.
Hydrogen abstraction reactions of the type CHs.
+ RH +CHI + Re
(1)
have been widely investigated in recent years. The results are initially expressed in terms of the rate of combination of methyl radicals, but an accurate study of this latter reaction2 has resulted in the evaluation of absolute rate constants for reaction 1. Data for the abstraction of hydrogen atoms in the gas phase from some fifty compounds are now available.a Investigation of hydrogen atom abstraction in solution has been limited mainly to the study of chain transfer in polymerization processes.4 A relationship between rate of polymerization and molecular weight of the polymer produced gives the ratio of the rate constants for transfer and propaga(1) J. 0. Smith and H. S. Taylor, J. Chem. Phys., 7 , 390 (1939): R. Gomer and W. A. Noyes. Jr., J. Am. Chem. Soc., T i , 3390 (1949): A. F. Trotman-Dickenson and E. W. R. Steaeie, J. Chem. Phye.. 18,
1097 (1950). (2) R. Gomer and G. B. Kistiakowsky, ibid., 19, 85 (1951). (3) A. F. Trotman-Dickenson, Quart. Reus. (London), 7 , 198 (1953). (4) R. A. Cregg and F. R. Mayo, Discs. Faraday Soc., 2 , 328 (1947).
tion, and the recent measurement of rate constans’) for the propagation process5permits the evaluation of absolute transfer constants. Edwards and Mayo6 have studied the decomposition of acetyl peroxide in mixtures of carbon tetrachloride and various solvents, and have compared the ease of abstraction of a hydrogen atom from the solvent with ease of abstraction of a chlorine atom from carbon tetrachloride. The results compare very well with those for methyl radical reactions in the gas phase,a but it is not certain whether methyl or acetate radicals are involved in the reaction in solution. The problem of studying hydrogen abstraction reactions in solution is simplified if the concentration of the attacking radical is accurately known, and if the system is not complicated by possible cage effects, The radical 2,2-diphenyl-l-picrylhydrazyl (DPPH) was chosen for the present work because it does not dimerize7 and the problem of a (5) E.&, M. 8. Matheson, E. E. Auer, E. B. Bevilacqua and E. J. Hart, J . A m . Chem. Soc., 7 8 , 1700 (1951). (6) F. 0.Edwards and F. R. Mayo, ibid., 79, 1265 (1950). (7) E. Muller, I. Muller-Rodloff and W. Bunge, Ann., 520, 235 (1935).
