Page 368 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

Since relates the sensitivity of the proton transfer process to that of dissociation of 349
the acid, it is sometimes suggested that the value of can be used as an indicator of
TS structure. The closer approaches unity, the greater the degree of proton transfer SECTION 3.7
in the TS. There are limits to the generality of this interpretation, however. 139 Catalysis

3.7.1.3. Acidity Functions. Some organic reactions require acid concentrations
considerably higher than can be accurately measured on the pH scale, which applies
to relatively dilute aqueous solutions. For example, concentrated acidic solutions can
have formal proton concentrations of 10M or more, but these formal concentrations
are not a suitable measure of the activity of protons in such solutions. For this reason,
acidity functions have been developed to measure the proton-donating strength of
concentrated acidic solutions. The activity of the hydrogen ion (solvated proton) can
be related to the extent of protonation of a series of bases by the equilibrium expression
for the protonation reaction:

+
+
B+H B H
BH + BH BH +
+
K = = (3.52)
+ + + B B
H
B
H
where is the activity coefficient for the base and its conjugate acid. A common
measure of acidity is referred to as h and is defined by measuring the extent of
0
protonation of a series of bases for which K is measured. The relative concentration
of the base and its conjugate acid then defines h for any particular acidic solution:
0
+
BH BH +
h = (3.53)
o
K B
B
The quantity H defined as −logh is commonly tabulated and it corresponds to the
0 0
pH of very concentrated acidic solutions. The H values are established by making
0
measurements in increasingly acidic solutions with a series of successively weaker
bases. The series is begun by measuring a reference base in aqueous solution where
H ∼ pH. This base can than be used to find the H of a somewhat more acidic solution.
0
0
The K of a somewhat weaker base is then determined in the more acidic solution.
This second base can then be used to extend H into a still more acidic solution. The
0
process is continued by using a series of bases to establish H for successively more
0
acidic solutions. 140 The assumption involved in this procedure is that the ratio of the
activity coefficients for the series of base cations does not change from solvent to
solvent, that is,
+
+
H H H
+
B 1 B 2 B 3
= = = ··· (3.54)

B 1 B 2 B 3
139 A. J. Kresge, J. Am. Chem. Soc., 92, 3210 (1970); R. A. Marcus, J. Am. Chem. Soc., 91, 7224 (1969); F.
G. Bordwell and W. J. Boyle, Jr., J. Am. Chem. Soc., 94, 3907 (1972); D. A. Jencks and W. P. Jencks,
J. Am. Chem. Soc., 99, 7948 (1977); A. Pross, J. Org. Chem., 49, 1811 (1984).
140
For reviews and discussion of acidity functions, see E. M. Arnett, Prog. Phys. Org. Chem., 1, 223
(1963); C. H. Rochester, Acidity Functions, Academic Press, New York, 1970; R. A. Cox and K. Yates,
Can. J. Chem., 61, 225 (1983); C. D. Johnson and B. Stratton, J. Org. Chem., 51, 4100 (1986).