Page 405 - Mechanism and Theory in Organic Chemistry

392 ADD~T~ON ELIMINATION REACTIONS
AND

Because the rate of substitution varies with position, in a benzene derivative
it is more informative and frequently more useful to talk about partial rate factors
than about relative rates. A partial rate factor is defined as the rate at oneparticular
position in the benzene derivative relative to the rate of substitution at one position
in benzene. Let us, for example, calculate the para and meta partial rate factors
(pf and mf, respectively) for bromination of toluene with bromine in aqueous
acetic acid. Toluene brominates 605 times faster than benzene under these
conditions. The product is 66.8 percent p-, 0.3 percent m-, and 32.9 percent o-
bromotoluene. Attack at the para position of toluene occurs 0.668 x 605 times
as fast as attack at all six positions of benzene but (0.668 x 605 x 6 = 2420)
times as fast as at one position of benzene. Therefore pfCH3 for bromination of
toluene under these conditions is 2420. There are only three times as many total
carbons in benzene as meta carbons in toluene. Therefore mfCH3 = 0.003 x
605 x 3 = 5.5. The definitions of the partial rate factors for monosubstituted
benzenes (+R) are given in Equations 7.78-7.80.

km-R
% para
p,R = - ----
X
kb-~/6 100

The rates of electrophilic substitutions at the para and meta positions of
benzene derivatives can be correlated by the linear free-energy relationships
shown in Equations 7.81 and 7.82.170

The substituents in a benzene derivative may affect the rate of electrophilic attack
at the ortho position by steric interaction and secondary bonding (e.g., hydrogen
bonding or charge-transfer complexing) as well as by electrical influence. There-
fore a,+ is not necessarily constant but depends on the size and nature of the
electrophile, and a correlation of rates of ortho substitution is less satisfactory.
(See Section 2.2, p. 61 and Figure 2.2.)
In general, the less reactive a reagent is, the more selective it is in attacking
an activated rather than a deactivated site. In 1953 H. C. Brown observed that
PJCH3
SJ = log -
mJCH3

See note 130(d), p. 379.