135.

1 Taft equation

Acting on a suggestion originally made by Ingold, Taft began by comparing the relative
susceptibility to polar substituent effects (the ρ value) of the hydrolysis-under acid-catalysed
(AAC2, p. 241) and under base-catalysed (BAC2, p. 239) condition of m- and p- substituted benzoate
esters (42).

The ρ value for base-catalysed hydrolysis (+2.51) is +ve and quite large, reflecting the
development of not inconsiderable -ve charge at the reaction centre in the rate-limiting step- attack
on this centre by ⁺OH (step a in the BAC2 pathway). By contrast, the ρ value for acid-catalysed
hydrolysis (+0.03) is very nearly zero; which means, of course, that the rate of this hydrolysis does
not vary significantly from one ester to another, no matter what the m- or
p-substituent present. The ρ value for this hydrolysis is so small, despite their being considerable
redistribution of +ve charge in the slow step (step a), because the overall rate of reaction, i.e. kobs,
(which is plotted to evaluate ρ), is determined not solely by k2, for this slow step, but involves also K1,
for the preceding, reversible, step 1. These two terms all but cancel each other out, in so far as
susceptibility of the two steps to electron-donation/-withdrawal by
polar substituents is concerned, and the overall ρ value for the reaction is thus virtually zero. If we now
extend our consideration of base-catalysed (BAC2), and acid-catalysed (AAC2), hydrolysis to esters in
general, including aliphatic ones (RCO2Et), we see that there is a close similarity between the transition
states (42b or 42a) for the rate-limiting step in each of the two pathways: they are both tetrahedral; and
differ only in the second of them having two protons more than the first. Protons, being very small, exert
comparatively little steric influence; it is therefore a not unreasonable assumption that any steric effect
stemming from the group R is
 because of the close spatial similarity of the two transition states, substantially the same in both acid- and
base-catalysed hydrolysis.? It then becomes possible to write a Hamrnett type equation, [9], to represent the
operation of the polar effect only of substituent R in ester hydrolysis:

As the steric effect exerted by R is essentially the same in both modes of hydrolysis, the two steric terms will
cancel each other out, and will thus not appear in equation [9].
Taft then gave ρ* in [9], the value 2.48, derived by subtracting the ρ value for acid-catalysed hydrolysis of
benzoate esters (0.03) from the ρ value for base-catalysed hydrolysis of the same esters (2.51). He took as his
reference substituent R= Me, rather than R= H, so that ko in [9] refers to MeCO2Et rather than HCO2Et. Then
Then by kinetic measurements on the acid- and base-catalysed hydrolysis of a series of esters containing R
groups other than Me, it is possible-using [9] to evaluate σ*R; for each of these different R groups with respect

to Me, for which by definition σ*Me,= 0 (cf. H with σH ,= 0 for benzoic acid ionisation, p. 363). By giving ρ*

here the value 2.48, the resulting σ*R values-which are a measure of the polar effect only exerted by R-do not

differ too greatly in magnitude from the values of σX , σX⁺ , σX ‾ with which we are already familiar (p. 363).
Then, employing the more general equation [10], it is possible to use these σ*R values, in conjunction with
suitable kinetic measurements of kR, and kMe,, to evaluate ρ* for other reactions of a whole range of aliphatic
compounds in addition to esters.
13.5.2 Steric parameters, Es and δ
It is not necessary to look very far to find aliphatic reactions that do not yield straight line plots with [10],
however; and, as with previous deviations from linearity (p. 379) these departures are commonly much more
informative about the details of reaction pathways than are neat straight lines. Where such departures from
linear (polar effects only) plots are observed, suggesting the operation of significant- and changing-steric
effects, it is possible to incorporate a steric substituent parameter, Es, whose evaluation is based on an earlier
observation.
Thus we have already seen (p. 384) that the acid-catalysed hydrolysis of m- and p-substituted benzoate
esters (42) is (with a value of 0.03) essentially uninfluenced by any polar effect exerted by the substituent,
X; and this substituent is sufficiently far removed from the reaction centre to be clearly incapable of
exerting any steric effect on it either. These esters thus all undergo acid-catalysed hydrolysis at essentially
the same rate. There is no reason to believe that acid-catalysed hydrolysis of aliphatic esters, RCOOEt,
will be any more susceptible to polar effects than was the corresponding hydrolysis of benzoate esters. If
then different hydrolysis rates are observed with aliphatic esters as R is varied, these must reflect differing
steric effects exerted by the different R groups. Such aliphatic esters are indeed found to undergo
hydrolysis at markedly different rates, so it is possible, taking Me as the standard substituent once again,
to use equation [l11
From the form of equation [ll], the Es, value for Me, the reference substituent, will of course be 0. All
substituents other than H have -ve Es, values because all substituents other than H are larger than Me, and
the rate of hydrolysis of any ester RCOOEt (R# H) will thus be slower than that of MeCOOEt, in a
reaction whose rate is governed solely by the steric effect of R.
It is found in practice that the value of the steric parameter, Es, for a particular group, R, differs to some
extent from one reaction to another.
This is not altogether surprising as both the local environment of R and the size of the attacking reagent will vary
from one reaction to another. It means, however, that on incorporating Es, into the Hammett type equation, [12],
it is necessary to introduce a yet further parameter, δ, as a measure of a particular reaction's

susceptibility towards steric effects. In that sense δ is the steric parallel to ρ*-which measures the reaction's
susceptibility towards polar effects. The δ parameter is given the value 1.00 for acid- catalysed ester hydrolysis,
as the standard reaction, and its value for other reactions can then be determined experimentally in the usual
way.
13.6 SOLVENT EFFECTS
13.6.1 Change of ρ with solvent

It is, of course, true that some implicit consideration is given to the solvent in that the ρ value for a
particular reaction is found to change when the solvent in which the reaction is carried out is changed:
For ionisation of m- and p-substituted benzoic acids (44), the hydroxylic solvent is capable of solvating both the
undissociated acid (44) and the carboxylate anion (45) obtained from its ionisation.
The relative effectiveness of such solvation-of negatively charged anion (45) with respect to neutral,
undissociated acid (44)-is a major factor in determining the position of equilibrium, i.e. Kx. As the solvent is
changed from water, with a dielectric constant of 79, to ethanol, with a dielectric constant of only 24, there will
be a marked decrease in advantageous solvation of the charged anion (45) with respect to the uncharged acid
(44). The relative importance of the polar effect exerted by electron-withdrawing substituents, in overall
stabilisation of the carboxylate anion (i.e. in acid-strengthening: increasing Kx), will therefore increase as the
dielectric constant of the solvent decreases. The value of ρ, the susceptibility of the reaction to the polar effect
of a substituent, will also increase, therefore, on changing the solvent from water to ethanol.
13.6.2 Grunwald-Winstein equation
Attempts to correlate the differing rate of a particular reaction, when carried out in a range of different solvents,
with the dielectric constant values for these solvents have not proved very rewarding. Attempts have therefore
been made to establish empirical reactivity\solvent correlations along general Hammett lines. Among the more
significant of these attempts has been that of Grunwald and Winstein on the solvolysis of halides. They sought to
establish a solvent parameter, designated Y, which would correlate with the different rate constants found for
solvolysis of the same halide in a range of different solvents.
They took as their standard reaction the SN1 solvolysis of the tertiary halide, 2-chloro-2-methylpropane (46), and
selected as their standard solvent 80% aqueous ethanol (80% EtOH/20% H2O):
in which the rate constants, kA and k0 refer to solvolysis of the tertiary halide (46) in a solvent A and in the

standard solvent (80% aq. EtOH), respectively; while YA, and Yo, are the empirical solvent parameters for

solvent A and for this standard solvent. By setting the value of YO, at zero and measuring kA , for the
It is now possible to go a stage further, and write a not unfamiliar relation, [14], that now covers the
solvolysis of halides in general, and not merely that of the
The major defect of the Grunwald-Winstein treatment is that it is limited in its scope. It has been applied to
reactions other than halide solvolysis, but is in general restricted to those reactions for which the major
contribution to the rate-limiting step is of the form: