Page 72 - Mechanism and Theory in Organic Chemistry

Linear Free-Energy Relationships 61

donating or -withdrawing influence is transmitted through the relatively polariz-
able .rr electron system. The Hammett apsproach is to take as a standard reach
for evaluation of substitGnt effects the dissociation of substituted benzoic acids
(9 and 10, Y = COOH) at25"(TTinH2O.-Substitution of an electron-withdrawing
--
--
-
group (such as nitro) in the para position of benzoic acid causes an increase in
strength of the acid, while an electron-donating group (for example, amino)
decreases the strength. The same substituents in the meta position have slightly
different effects. -ts are not inclyde&pcause their proximity to
the reaction site introduces interactions not preaent if the substituent is at the
-- - - - - -
-
meta or para positi~n.~
If the free-energy change on dissociation of unsubstituted benzoic acid
(X = H) is designated as AG,", the free energy on dissociation of a substituted
benzoic acid (AGO) can be considered to be AG," plus an increment, AAGo, con-

tributed by the substituent (Equation 2.4). Because the substituent X will make
different contributions at the meta and para positions, it is always necessary to
designate the position of substitution.
In order to bring the relationship (2.4) into more convenient form, a para-
meter u is defined for each substituent according to Equation 2.5, so that equation
2.4 becomes Equation 2.6.

By using the relationship 2.7 between free energy and equilibrium, Equation 2.6
can be rewritten as Equation 2.8, which in turn simplifies to Equation 2.9.
- AGO = 2.303R T log,, K (2.7)
7
2.303RTlogl0 K = 2.303RTloglo KO + 2.303RTo (2.8)
-
K- = @KO - @K = o - \
1 log,, (2.9)
Table 2.1 lists u constants for some of the common substituents.
Ifwe now examine the effect of substituents on another reaction, for example
acid dissociation of phenylacetic acids (Equation 2. lo), we can anticipate that the

various substituents will exert the same kind of effects on these equilibrium con-
stants as they did on the benzoic acid equilibrium constants; b-&seater
separation between substitution site and reaction site in the phenylacetic acids
makes &e_reactio~bse.ns~tjveeto the substituent effects. The increment
--
\
2.303~Tu. which was appropriate for benzoic acid dissociations. must now be
multiplied by a factor - i v d
1 elec.tmn-ation and withdmxaLWe can therefore write Equation 2.1 1,
- AGO' = - AG:' + 2.303R Tpo (2.1 1)
AGO' is the free-energy change for the new reaction with substituent X and

The ortho effect is not entirely steric in origin. See M. Charton, Prog. Phys. Org. Chem., 8, 235 (1971).