Page 369 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

350 Table 3.28. H as a Function of Composition of Aqueous
0
Sulfuric Acid a
CHAPTER 3
%H 2 SO 4 H 0 %H 2 SO 4 H 0
Structural Effects on
Stability and Reactivity 5 0 24 55 −3 91
10 −0 31 60 −4 46
15 −0 66 65 −5 04
20 −1 01 70 −5 80
25 −1 37 75 −6 56
30 −1 72 80 −7 34
35 −2 06 85 −8 14
40 −2 41 90 −8 92
45 −2 85 95 −9 85
50 −3 38 98 −10 41
a. From J. Jorgenson and D. R. Hartter, J. Am. Chem. Soc., 85, 878 (1963).

Not surprisingly, the results often reveal a dependence on the particular type of
base used, so no universal H scale can be established. Nevertheless, this technique
0
provides a very useful measure of the relative hydrogen ion activity of concentrated
acid solutions that can be used in the study of reactions that proceed only at high acid
concentrations. Table 3.28 gives H values for some water-sulfuric acid mixtures.
0
3.7.1.4. pH-Rate Profiles. pH-Rate profiles are a useful tool for analysis of acid and
base catalysis. 141 The rate of the reaction is measured as a function of the pH. Reactions
are typically studied under pseudo-first-order conditions so that the rates are first order
in the reactant at each pH:

Rate = k R
obs
Observed pH rate profiles typically consist of several regions including segments with
−
+
linear dependence on H or OH , pH-independent, and curved transitions between
linear areas. The occurrence of H (or OH ) in the rate expression indicates either
−
+
that a protonated (or deprotonated) form of the reactant is involved (preequilibrium) or
+
−
that H (or OH) is involved in the rate-determining step. Figure 3.28 shows some pH
dependencies that may be components of a specific profile. Curves (a) and (b) show
−
+
linear dependence on H and OH that is due to specific acid and base catalysis,
respectively. The horizontal portion of the profile corresponds to a reaction that does
not involve acid or base catalysis. Usually the slope of the linear part of the curve
is −1 H or +1 OH because there is only one protonation (or deprotonation) step.
+
−
The rate expressions for (a) and (b), respectively, would be:
a Rate = k + R H +k H 2 O R
+
H
b Rate = k R OH +k R
−
− OH H 2 O
where k H +, k − OH , and k H 2 O are the rate constants for the acid-catalyzed, base-catalyzed,
and uncatalyzed reactions, respectively.
+
−
For cases (c) and (d), the rates level off at high H and OH , respectively.
This circumstance occurs if the reactant is completely protonated (or deprotonated) so
141
J. M. Loudon, J. Chem. Educ., 68, 973 (1991).