Page 141 - Mechanism and Theory in Organic Chemistry

processes are bases, it is reasonable to postulate that the reactions involve acid-
base interactions. In order to obtain further information about the detailed
course of these types of reactions, it is often desirable to be able to make quanti-
tative measurements of the acid-base properties of the substances involved.

Acidity Functions
One solution to the problem of achieving appreciable concentrations of the
protonated form of very weak bases is to use as a solvent a mixture of water with
some strong mineral acid. It can be demonstrated by measurement of freezing-
point depressions13 that many organic compounds that contain basic atoms such
as N, 0, or S, but that are too weakly basic to be protonated to a significant
extent in water, are essentially completely converted to their conjugate acids in
concentrated sulfuric acid.14 In appropriately chosen mixtures of water and
sulfuric acid, appreciable concentrations of both base and conjugate acid may be
expected to be present. In order to study these phenomena, one must have a
procedure for determining acidity over a very wide range of proton-donating
capacity, from pure water to pure sulfuric acid.
Hammett and Deyrup, in 1932, were the first to propose a method of
determining quantitatively acid-base behavior in water-strong acid mixtures.15 - l7
In order to understand their contribution, we begin with the general expression
for the equilibrium constant for the dissociation of an acid (compare Equation
3.16) :

We have chosen to write the reaction in the particular form 3.28 because this form
corresponds to acids and bases of the same charge type as those on which Ham-
mett and Deyrup based their original work. AH+ corresponds to the protonated
form of the weak base (for example, (CH,) &=OH + , @-NO,-C,H,NH3 + ,
l3 For a discussion of freezing-point depression, see W. J. Moore, Physical Chemistry, 3rd ed., Prentice-
Hall, Englewood Cliffs, N.J., 1962, p. 132.
l4 For example, the observation that the freezing point of a 1 molal solution of acetone in sulfuric acid
is depressed by twice the molal freezing-point depression constant of sulfuric acid is interpreted in
terms of the reaction

Similar results are obtained with many other compounds that are neutral in water but contai
unshared electron pairs.
l5 L. P. Hammett and A. J. Deyrup, J. Amer. Chem. Soc., 54, 2721 (1932).
l6 L. P. Hammett, Physical Organic Chemistry, 2nd ed., McGraw-Hill, New York, 1970, chapter 9.

Ed., Wiley-Interscience, London, 1966 (applications to carbonyl compounds only).