Autumn 2004
2
Linear Free Energy Relationships
• Linear free energy relationships are attempts to develop quantitative
relationships between structure and activity.
Consider a particular reaction between two substrates. We might
carry out a series of reactions by varying one of the reactants
slightly, for example by examining substituents with a range of
electronegativities.
We might expect that the reaction rate, or the position of the
equilibrium between reactants and products, will change as we
change the reactant in this way.
If the same series of of changes in conditions affects a second
reaction in exactly the same way as it affected the first reaction, we
say that there exists a linear free energy relationship between
the two sets of effects.
Such relationships can be useful in helping to elucidate reaction
mechanisms and in predicting rates or equilibria.
Autumn 2004
3
The Hammett Equation
One of the earliest examples of a LFER between:
• the rate of base catalysed hydrolysis of a group of
ethyl esters to form a series of carboxylic acids.
• the equilibrium position of the ionisation in water of
the corresponding group of acids.
• Caveats:
– Ortho isomers do not fall
on the line.
– Aliphatic acids do not fall
on the line.
!
log k=
"
logK+C
• A direct relationship was found between these processes for a specific set
of compounds, the p- and m-substituted benzoic acids (R=Ar).
!
RCOOEt +OH"k
# $ # RCOO"+EtOH
!
RCOOH +OH"
K
# $ #
% # # RCOO"+H2O
