502 J. Phys. Chem. A, Vol. 106, No. 3, 2002
Beals et al.
not mass transport controlled under conditions of rapid diffusion.
First-order heterogeneous rate constants are on the order of 10-4
cm/s. By measuring rate constants over a range of temperatures,
we have determined that about half of the free energy barrier
to this reaction at room temperature is due to the entropy of
activation. (See Table 3.) The small dependence of the rate
constant upon the nature of the halide (Br or Cl) is partially
due to the large contribution of entropy to the total free energy
barrier.
reaction of the organohalide with a magnesium atom at the
surface. The transition state in the rate-limiting step probably
resembles structure 1, which is consistent with all of our results.
This species would have the very low entropy suggested by
the high entropic barrier to the reaction. Furthermore, there is
partial breakage of the bond consistent with the dependence of
the enthalpy of activation on the halide.
To draw conclusions from these data about the rate-limiting
step in Grignard reagent formation, it is necessary to compare
these values to those for reactions that are possibly related.
Comparable data have been reported for: (1) uncomplicated
heterogeneous electron transfer, (2) irreversible electron transfer
to alkyl and aryl halides (studied by both spectroscopic and
electrochemical techniques).
We have surveyed the literature for Arrhenius parameters for
uncomplicated electron transfer (ET) to organic and organo-
metallic molecules in a wide variety of nonaqueous solvent
including THF. (See refs 46 and 48-52 and references therein.)
These reactions show a range of enthalpies of activation from
10 to 25 kJ/mol. Thus, the enthalpy of activation we measure
for bromoethane and bromobenzene reacting with magnesium
are within this range (albeit at the high end), whereas our value
for the reaction of 2-chloro-2-methylbutane is outside of this
range.
On the other hand, the entropic barrier to uncomplicated ET
(+10 to -25 J/mol-K) is much smaller than we measure for
any of our compounds, resulting in a smaller free energy barrier
and much larger rate constants for ET relative to Grignard
reagent formation. This comparison suggests that the rate-
limiting step for Grignard reagent formation is not simple ET.
Further supporting the rejection of ET as the rate-limiting
step is the lack of correlation between half-wave voltages for
the reduction of RX and their rates of Grignard reagent
formation (using either our absolute rate constants or others'
relative rates9-12,25).
A second source of data that may be compared to ours is the
spectroscopic studies of the kinetics of irreversible homogeneous
electron transfer from polyaromatic anions to alkyl halides.53,54
These studies have shown a dramatic dependence of rate on
the halide (I, Br, Cl, or F) as well as rates that correlate well
with half-wave voltages for the reduction of the organohalides.
Thus, the rate-limiting steps must be very different between
homogeneous ET to alkyl halides and Grignard reagent forma-
tion.
Of most direct significance to Grignard reagent formation
are the studies of Saveant et al.26,27,55 Using direct electrochemi-
cal techniques as well as redox catalysis, the kinetics and
thermodynamics of heterogeneous and homogeneous ET to
organohalides are well understood.
Perhaps most revealing, the free energy of activation for
electron transfer to organohalides (at their E°) is 60-90 kJ/
mol, significantly greater than the free energy of activation of
Grignard reagent formation (see Table 3). This could be
explained if the E° for the Mg0/2+ couple were negative of the
E° of the organohalide, but this is not the case. The E° for
Mg0/2+ is -2.3 V vs Ag/AgClO4 (-2 V vs SCE)56 ap-
proximately 0.5 V positive of both the E° of bromobenzene26
and of the peak potentials for the heterogeneous reductions of
alkyl bromides.27
Structure 1 is also consistent with all of the data presented
by Whitesides et al.9-12 They considered a wide range of
possible transition states9,11 and were unable to reject three of
them: an anion, a radical, and a structure similar to 1. As
discussed, our data are not consistent with either an anion or a
radical. Structure 1 is also similar to the structure of the
intermediate proposed by Walborsky et al.3-6 Finally, our
proposal that magnesium is directly involved in the cleavage
of the organohalide bond is consistent with the free energy of
activation being lower for Grignard reagent formation than for
unassisted electron transfer/bond cleavage to organohalides.
Acknowledgment. Acknowledgment is made to the donors
of the Petroleum Research Fund, administered by the ACS, for
partial support of this research. This material is also based upon
work supported by the National Science Foundation under Grant
No. CHE-9405038. The authors thank Mr. John Sherman of
Hobart and William Smith Colleges for construction of the flow
cells and the thermostated stainless steel jacket.
References and Notes
(1) Kharasch M. S.; Reinmuth, O. Grignard Reactions of Nonmetallic
Substances; Prentice Hall: New York, 1954.
(2) Walborsky, H. M.; Young, A. E. J. Am. Chem. Soc. 1961, 83,
2595-2596.
(3) Walborsky, H. M.; Hamdouchi, C. J. Am. Chem. Soc. 1993, 115,
6406-6408.
(4) Rachon, J.; Walborsky, H. M. Tetrahedron Lett. 1989, 30, 7345-
7348.
(5) Walborsky, H. M.; Topolski, M. J. Am. Chem. Soc., 1992, 114,
3455-3459.
(6) Hamdouchi, C.; Topolski, M.; Goedken, V.; Walborsky, H. M. J.
Org. Chem. 1993, 58, 3148-3155.
(7) Walborsky, H. M.; Zimmerman, C. J. Am. Chem. Soc. 1992, 114,
4996-5000.
(8) Markies, P. R.; Akkerman, O. S.; Bickelhaupt, F.; Smeets, W. J. J.
Spek, A. L. J. Am. Chem. Soc. 1988, 110, 4284-4292.
(9) Rogers, H. R.; Hill, C. L.; Fujiwara, Y.; Rogers, R. J.; Mitchell,
H. L.; Whitesides, G. M. J. Am. Chem. Soc. 1980, 102, 217-226.
(10) Rogers, H. R.; Deutch, J.; Whitesides, G. M. J. Am. Chem. Soc.
1980, 102, 226-231.
(11) Rogers, H. R.; Rogers, R. J.; Mitchell, H. L.; Whitesides, G. M. J.
Am. Chem. Soc. 1980, 102, 231-238.
(12) Barber, J. J.; Whitesides, G. M. J. Am. Chem. Soc. 1980, 102, 239-
243.
(13) Garst, J. F.; Deutch, J. E.; Whitesides, G. M. J. Am. Chem. Soc.
1986, 108, 8, 2490-2491.
(14) Garst, J. F.; Swift, B. L.; Smith, D. W. J. Am. Chem. Soc. 1989,
111, 234-241.
(15) Garst, J. F.; Swift, B. L. J. Am. Chem. Soc. 1989, 111, 241-250.
(16) Garst, J. F.; Ungva´ry, F.; Batlaw, R.; Lawrence, K. E. J. Am. Chem.
Soc. 1991, 113, 5392-5397.
(17) Garst, J. F.; Ugvary, F.; Baxter, J. T. J. Am. Chem. Soc. 1997,
119, 253-254.
(18) Ashby, E. C.; Oswald, J. J. Org. Chem. 1988, 53, 6068-6076.
(19) Hill, C. L.; Vander Sande, J. B.; Whitesides, G. M. J. Org. Chem.
1980, 45, 1020-1028.
All of these comparisons allow a rejection of the hypothesis
of electron transfer as the rate-limiting step in Grignard reagent
formation. Rather, we propose that the rate-limiting step is
(20) Ault, B. S. J. Am. Chem. Soc. 1980, 10, 02, 3480-3484.
(21) Vogler, E. A.; Stein, R. L.; Hayes, J. M. J. Am. Chem. Soc. 1978,
100, 3163-3166.