CHEE 323J.S. Parent1 Acid Catalysis in Concentrated Solutions Protonation of the substrate is most often the first step of acid-catalyzed reactions.  The extent to which the substrate is protonated influences the reaction rate.  It is often desirable to raise [H 3 O + ] to increase the degree of substrate protonation, thereby enhancing the reaction rate.

CHEE 323J.S. Parent2 Standard Measure of Acidity - pH The most familiar measure of the acidity (tendency to protonate a base) of a solution is pH: For the protonation of a base B: we relate the extent of reaction to the pH through the acid dissociation constant, K a : or For concentrated solutions of strong acids, we find two problems:  Measuring the pKa of strong acids with respect to H 2 O protonation.  Accounting for the non-ideality of concentrated acid solutions that are much more “acidic” than their pH would suggest.

CHEE 323J.S. Parent3 Hammett Indicators Given that we are interested in knowing the extent to which our substrate (S) is protonated (SH + ) in a given acid solution, a relevant question is:  For a range of acidic solutions (0 mol% H 2 SO 4 to anhydrous H 2 SO 4 ), to what extent is a neutral base protonated? Hammett and coworkers have addressed this issue by measuring the tendency of an acidic solution to protonate various neutral bases, called Hammett Indicators. For example, The concentrations of BH + (nitroanilinium ion) and B (nitroaniline) can be measured by a spectrophotometric technique.

CHEE 323J.S. Parent4 Hammett Acidity Function The K a for this reaction is known: Taking logs yields: We define a new parameter, H o, the Hammett Acidity Function: which reduces our equilibrium relationship to:

CHEE 323J.S. Parent5 Hammett Acidity Function To a series of acid solutions of varying concentration, an indicator of known pK a is added, and the ratio of [B] to [BH + ] measured.  The Hammett acidity function is easily calculated for each solution by: The acidity function accounts for solution non-ideality by lumping the activity of H + (an essentially indeterminable quantity) with the activity coefficients  B and  BH+.  In dilute solutions, a H+  [H + ],  B  1 and  BH+  1, leaving

CHEE 323J.S. Parent6 Hammett Acidity Function The acidity function is by no means a universal indication of the tendency of an acid solution to protonate a base.   B and  BH+ relate to the Hammett indicator, and may not relate to your substrate.  H 0 measures the tendency of a solution to protonate a neutral base, not to a base of any other electrical charge.

CHEE 323J.S. Parent7 H o and Acid Catalyzed Reaction Kinetics For those acid catalyzed reactions in which protonation of a neutral substrate is a kinetically significant step, there may exist a relationship between the reaction rate and the acidity function. Consider a reaction proceeding by the following mechanism: r 1 : r 2 : where reaction 2 is rate limiting: and reaction1 is at equilibrium:

CHEE 323J.S. Parent8 H o and Acid Catalyzed Reaction Kinetics If we assume that our neutral substrate has great chemical similarity to the Hammett indicator used to determine H o of the acid: The rate of the reaction becomes: The observed rate constant for the reaction, relates to the acidity function according to:

CHEE 323J.S. Parent9 H o and Acid Catalyzed Reaction Kinetics