Page 73 - Mechanism and Theory in Organic Chemistry

62 SOME FUNDAMENTALS OF PHYSICAL ORGANIC CHEMISTRY

Table 2.1 0 VALUES OF COMMON SUBSTITUENTS

Substituent urneta upara U+ a u-~

-
SOURCE: Values are those given by C. D. Ritchie and W. F. Sager, Prog. Phys. Org. Chem., 2, 323
(1964). Reproduced by permission of Wiley-Interscience.
a a+ and a- values are given for para substituents only. a+ values for some meta substituents have
been measured, but because direct resonance interaction between meta substituents is impossible
they do not differ appreciably from the ornet, values.
AG:' is the free-energy change for the new reaction with no substituents. Re-
writing Equation 2.11 as before, we have the relationship in the more useful form
of Equation 2.12 :

Equations 2.1 1 and 2.12 express a linear relationshipof free energies .- known as the
---
_
Hammett _ ---
a~ _-_- relationship,_or simply as the Ha_m-mctt e-quation. It can be
*-ds-&tituted aromatic compounds as well as to equili-
-nd we shall find that it is a very useful tool for obtaining inform-
ation about reaction mechanisms. (See, for example, Problem 2.1 .)
Usually the most convenient way to use the Hammett equation is to plot
log KIK,, or just log K (for equilibria) or log klk,, or just log k (for rates) of the
reaction of interest on the vertical axis and u values for the substituents on the
horizontal axis. A straight line indicates that the free-energy relationship of
Equation 2.1 1 is valid. The slope of the line is p for the reaction. A positive value
ofpmeans that the reaction responds to substjtuents in the same sense as does
.. .
.. .
__ _ _ ---
.- - ------__
-- -
benzoic aud -thationstant (or ---. reaction rate) _is _in-
creased by electron-w-oups. Ifp > 1. then the reaction Is msi-
tiVptn-pffPrte_nzoFc acid dissociation; if 0 < p < 1,
tbP.ntron-withdr~~ stiUncrease the rate or equilibrium conztant
but less than in benzoic acid dissociatjop. A negati~2~~-shows that elegron-
--
-\ 4-
smallJ
~ther&c.a.ns~~&A w often means -. - that - the
-
-
- m . . the readan involves radi~ermediates-or a cyclicktr_~akio~
chargezeparation. Sometimes the plot of log k vs. a changes slope
as substituents are varied, so that two straight lines are