Hammett plots the most common linear free energy relationship. It is important to know effects of substituents on chemical properties. In particular, this contributes to understanding reaction mechanisms and to predicting rate constants and equilibrium constants. Hammett equation relates rates and equilibria for many reactions of compounds containing substituted phenyl groups. There is a relationship between the acid strengths of substituted benzoic acids
and the rates of many other chemical reactions, for instance, the rates of hydrolysis of substituted ethyl benzoates. CO2Et CO2H + EtOH
X X ko: rate constant for hydrolysis of ethyl benzoate
k: rate constants for hydrolysis of substituted esters Ko: acid dissociation constant of benzoic acid (= Keq for X = H) K: acid dissociation constant of substituted acids (= Keq for X = substituents) log(k/ko) = mlog(K/Ko) G = mGo
Linear free-energy relationship Go = -RTlogKeq kBT -G++/RT e
k= h Hammett linear free-energy relationship log(k/ko) = log(K/Ko) =
: substituent constant : reaction constant (should be measured for given reactions) -> sensitivity of a particular reaction to substituent effects measurement of values = 1 : reference reaction, the ionization of benzoic acids CO2H
CO2+ X H+
log(K/Ko) = x X can be determined for specific substituents (measured, known) values: negative, the substituted benzoic acid is less acidic than benzoic acid itself
-> electron donating groups have negative values positive, the substituted benzoic acid is more acidic than benzoic acid itself -> electron withdrawing groups have positive values inductive effect
inductive and resonance effects + : used for reactions in which there is direct resonance interaction between an electron donor substituent and a cationic reaction center - : used for reactions in which there is direct resonance interaction between an electron donor substituent and the electron-rich reaction site
+ O OMe
OMe O- O
N O -O
O- Summary using Hammett equation for a particular reaction 1. 2.
3. log(k/ko) = x log(K/Ko) = x Measure kx or Kx for substituents
Plot log(kx/ko) vs Determine and interpret the results log(k/ko) Slope =
1. When > 1, the reaction under study is more sensitive to substituents than benzoic acid, and negative charge is building during the reaction. -> an electron withdrawing group stabilizes the developed negative charge. 2. When 0 < < 1, the reaction is less sensitive to substituents than benzoic acid, but negative charge is still building.
3. When is equal to or close to 0, the reaction shows no substituent effects. 4. When is negative, the reaction is creating positive charge. -> electron donating groups increases in rates. 5. ll large: much positive or negative charge separation
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