Page 154 - Mechanism and Theory in Organic Chemistry

Strengths of Weak Bronsted Acids 143

T,he Bronsted law is a linear free-ener~relationsh&~. similar in form to the
Hammett and Taft correlations discussed in Section 2.2. We emphasize that the
connection between rate and equilibrium expressed by Equation 3.48 is in no
sense predicted by or derived from the laws of equilibrium thermodynamics.
The relationship is an empirical one that must be verified experimentally in each
particular case, and that is subject to severe limitations. We have assumed in
drawing Figure 3.4 and in making the arguments we have presented rationalizing
the catalysis law that the position of the transition state along the reaction co-
ordinate will not change as the acid strengths change. We have seen in Section
2.6, where we considered the Hammond postulate, that this assumption is
unlikely to be true if we make more than a rather small change in the reactant-to-
product free-energy difference. As a result, we can expect that over a wide range
of acidities a will not be a constant. It should be close to unity for a very endo-
thermic process of type 3.46 (the transition state closely resembles +
BH(*+l)+ and the entire AGO differences show up in AG*), and close to zero for a
very exothermic process (the transition state closely resembles AHm + Bn + and
+
none of the AGO differences show upin AG*) . For carbon acids, a changes relatively
slowly with changing equilibrium constant;62 we must nevertheless proceed
cautiously if we wish to use the catalysis law to assist us in estimating equilibrium
acidities, and we expect difficulties if the range of equilibrium constants is large.
We shall return to consider these points in more detail in Section 8.1.

Kinetic Acidity
The Bronsted catalysis law can be applied to the problem of determination of
acidity of very weak acids in the following way. First, a suitable base is chosen;
the base must be sufficiently strong to remove protons from the carbon acids in
question at a measurable rate. The acids to be investigated are then prepared
with deuterium or tritium substituted for hydrogen, and the rate of exchange of
the isotopic label out of the carbon acid in the presence of the base is measured.
Experiments of this type have been carried out with weak acids by various
In order to use the kinetic data to obtain information about equili-
bria, it is clearly necessary to know whether the catalysis law (Equation 3.48)
holds for the system under study and, if it does, what the value of the constant a is.

The approximation involved in stating the catalysis law is equivalent to dropping terms of order
higher than the first in the power-series expansion:
AG* =: constant + a(AGo - ACY)
This expression leads to Equation 3.53.
ea M. Eigen, Angew. Chem. Znt. Ed., 3, 1 (1964).
e3 R. G. Pearson and R. L. Dillon, J. Amer. Chem. Soc., 75,2439 (1953).
e4 A. I. Shatenshtein, Adv. Phys. Org. Chem., 1, 155 (1963).
e5 See for example: (a) A. Streitwieser, Jr., R. A. Caldwell, R. G. Lawler, and G. R. Ziegler, J.
Amer. Chem. Soc., 87, 5399 (1965); (b) A. Streitwieser, Jr., W. B. Hollyhead, G. Sonnichsen, A. H.
Pudjaatmaka, C. J. Chang, and T. L. Kruger, J. Amer. Chem. Soc., 93, 5096 (1971); (c) A. Streit-
wieser, Jr., and W. C. Langworthy, J. Amer. Chem. Soc., 85, 1757, (1963); (d) A. Streitwieser, Jr.,
R. A. Caldwell, and M. R. Granger, J. Amer. Chem. Soc., 86, 3578 (1964); (e) A. Streitwieser, Jr.,
and D. Holtz, J. Amer. Chem. Soc., 89, 692 (1967); (f) A. Streitwieser, Jr., A. P. Marchand, and A. H.
Pudjaatmaka, J. Amer. Chem. Soc., 89, 693 (1967); (g) A. Streitwieser, Jr., and F. Mares, J. Amer.
Chem. Soc., 90, 644, 2444 (1968). See also references cited in Table 3.1.
R. E. Dessy, Y. Okuzumi, and A. Chen, J. Amer. Chm. Soc., 84,2899 (1962).