Page 144 - Mechanism and Theory in Organic Chemistry

Strengths of Weak Bronsted Bases 133

desired information about proton-donating ability.20

Because of the magnitudes of the numbers involved, it is more convenient to use a
logarithmic scale. A new quantity, Ho, is therefore defined by Equation 3.37.

Ho is known as the Hammett acidity function, and the series of substituted anilines
used to establish the scale are called Hammett indicators.
The procedure outlined above serves to define Ho for mixtures of water and
various strong acids. Once Ho has been found for a number of different mixtures,
one can obtain, by use of Equation 3.38, the pK, for bases other than those used
in setting up the scale. All that is needed is a method of measuring the ratio
[AII/[AH+], together with the assumption that the ratio of the activity coefficients
of the new base and its conjugate acid is the same as that of the indicator bases.
Ranges of pK, values that have been found for various types of compounds are
given in Table 3.2 in Section 3.4. Values for particular compounds may be found
in the reviews by Arnett21 and by Paul and Long,22 where references to the origi-
nal literature are given.

Other Acidity Scales
We return now briefly to the question of uniqueness of the Ho scale. We have seen
that for the treatment to be successful, the different bases involved in determining
the Ho scale, and also those bases that are to be investigated using the scale, must
be of sufficiently similar structure that the activity coefficient ratio of Equation
3.33 will be unity. It has become increasingly evident as data have accumulated
that this requirement is more restricting than one might have hoped. Arnett
and Mach,23 using a set of N,N-dialkylnitroanilines and N-alkylnitroanilines as

20 The equations are usually written in such a way that Equation 3.35 comes out:

This relationship results if the original acid dissociation is written:

We have chosen the formulation of Equation 3.28 because it seems to be more consistent with our
discussion in Section 3.1 about the nature of Brgnsted acid-base reactions. Since the quantity ho is
empirically determined and cannot be broken down experimentally into its component parts, it
makes little difference in practice which derivation is used. For direct measurements of hydrogen
ion activity coefficients in these solvents, see T. A. Modro, K. Yates, and J. Janata, J. Amer. Chem.
Soc., 97, 1492 (1975).
21 E. M. Arnett, Prog. Phys. Org. Chem., 1, 223 (1963).
22 See note 17 (a), p. 130.
23 E. M. Arnett and G. W. Mach, J. Amer. Chem. Soc., 86, 2671 (1964).