Page 331 - Mechanism and Theory in Organic Chemistry

substituted phenyl migrates 81 percent of the time if Z is m-chloro, but only 31
percent of the time if Z is p-metho~y.~~~ (Note that which group migrates can
be determined only if one of the carbonyl carbons is labeled with 14C.) Con-
sideration of the mechanism in Equation 6.50 explains the anomaly.

If the second step is rate-determining, then the observed rate is given in Equation
6.51,

where k, is the rate constant for step 2. The concentration of 103 is given by
Equation 6.52
[I031 = K,[benzil] [OH-] (6.52)
in which K, is the equilibrium constant for step 1. Substituting Equation 6.52
into Equation 6.51, we obtain Equation 6.53 : The observed rate is dependent
on the equilibrium constant for the formation of 103 as well as on the rate of
migration of the aryl group.

kobs = k2Kl[benzil] [OH-] (6.53)
If the substituted phenyl is to migrate, then the intermediate 103a must
be formed; migration of the phenyl requires 103b. Electron-withdrawing
substituents will increase K, for the formation of 103a; if K, is increased more
than k, is decreased, more substituted phenyl will migrate than unsubstituted
phenyl.

6.4 REARRANGEMENTS TO ELECTRON-DEFICIENT
NITROGEN AND OXYGEN143
Our consideration of rearrangements to electron-deficient heteroatoms must be
brief. In discussing migrations to electron-deficient nitrogen, we first discuss three
rearrangements that occur in carbonyl derivatives, the Beckmann, Hofmann,
and Schmidt rearrangements, and then consider rearrangements of nitrenium
ions.

14= M. T. Clark, E. C. Hendley, and 0. K. Neville, J. Amer. Chem. SOC., 77, 3280 (1955).
143 For a general review, see: (a) P. A. S. Smith, in Molecular Rearrangements, P. Mayo, Ed., Wiley-
Interscience, New York, 1963, Vol. I, p. 457. For reviews of rearrangements to electron-deficient
nitrogen, see: (b) D. V. Banthorpe, in The Chemisty of the Amino Group, S. Patai, Ed., Wiley-Inter-
science, New York, 1968, p. 623. For a review of rearrangements to electron-deficient oxygen, see:
(c) J. B. Lee and B. C. Uff, Quart. Rev. (London), 21,429 (1967); (d) R. Curci and J. 0. Edwards, in
Organic Peroxides, D. Swern, Ed., Wiley-Interscience, New York, 1970, Vol. I, p. 199.