CHEE 323 J.S. Parent 1

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 [H3O+] to increase the degree of substrate protonation, thereby enhancing the reaction rate.

CHEE 323 J.S. Parent 2

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, Ka:

or

For concentrated solutions of strong acids, we find two problems: Measuring the pKa of strong acids with respect to H2O

protonation. Accounting for the non-ideality of concentrated acid solutions

that are much more “acidic” than their pH would suggest.

]Hlog[pH

]OH[]B[OHBH 3

K

2

A

]BH[

]B[]H[Ka

]BH[

]B[logpKpH a

CHEE 323 J.S. Parent 3

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% H2SO4 to anhydrous H2SO4), 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.

NH3

+N

+

O

ONH2N

+

O

OpKa=0.99

+ H+

p-Nitroanilinium ion p-Nitroaniline

CHEE 323 J.S. Parent 4

Hammett Acidity Function

The Ka for this reaction is known:

Taking logs yields:

We define a new parameter, Ho, the Hammett Acidity Function:

which reduces our equilibrium relationship to:

NH3

+N

+

O

ONH2N

+

O

OpKa=0.99

+ H+

p-Nitroanilinium ion p-Nitroaniline

]BH[

]B[a

a

aaK

BH

BH

BH

BHa

]BH[

]B[log

alogKlog

BH

BHa

]BH[

]B[logHpK oa

BH

BHo

alogH

CHEE 323 J.S. Parent 5

Hammett Acidity Function

To a series of acid solutions of varying concentration, an indicator of known pKa 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, aH+[H+], B1 and BH+1, leaving

]BH[

]B[logpKH ao

pH]Hlog[

alogH

BH

BHo

CHEE 323 J.S. Parent 6

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.

H0 measures the tendency of a solution to protonate a neutral base, not to a base of any other electrical charge.

CHEE 323 J.S. Parent 7

Ho 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:

r1:

r2:

where reaction 2 is rate limiting:

and reaction1 is at equilibrium:

RHHRK

PHRH2k

]RH[kr 22

]R[K

a]RH[

a

aaK

RHa

RH

RH

HRa

CHEE 323 J.S. Parent 8

Ho and Acid Catalyzed Reaction Kinetics

If we assume that our neutral substrate has great chemical similarity to the Hammett indicator used to determine Ho of the acid:

The rate of the reaction becomes:

The observed rate constant for the reaction,

relates to the acidity function according to:

aBH

BH

aRH

RH

K]R[a

K]R[a

]RH[

aBH

BH222 K

]R[ak]RH[kr

BH

BH

a

2obs

a

Kk

k

o

BH

BHobs

Httancons

alogttanconsklog

CHEE 323 J.S. Parent 9

Ho and Acid Catalyzed Reaction Kinetics