Physical Chemistry Third Edition

574 13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics

Adding Eqs. (13.1-30b) and (13.1-30c) gives an equation that is combined with Eq. (13.1-31)

and solved to give

[NO 3 ]

(

k 1 k 2

2 k′ 1 k 3

[N 2 O 5 ][O 3 ]

) 1 / 3

(13.1-32)

Equation (13.1-32) is substituted into Eq. (13.1-31), which is substituted into Eq. (13.1-30a)

to give our solution:

rate−

1

2

d[O 3 ]

dt

k 3

(

k 1 k 2

2 k′ 1 k 3

[N 2 O 5 ][O 3 ]

) 2 / 3

kapp[N 2 O 5 ]^2 /^3 [O 3 ]^2 /^3 (13.1-33)

Exercise 13.8

Carry out the steps to obtain Eq. (13.1-33).

Catalysis in Solution

Various reactions are catalyzed by substances in the same phase as the reactants.

A number of reactions in aqueous solutions are catalyzed by acids or bases. Ingeneral

acid catalysisthe rate depends on the concentration of unionized weak acid. Inspecific

hydrogen-ion catalysisthe rate depends on the concentration of hydrogen ions. Acid

and base catalysis are illustrated by^6 the isomerization ofα-d-glucose toβ-d-glucose

(or vice versa). The reaction is

H

HO

O

HO

H

O

(13.1-34)

where the structure on the left representsα-d-glucose. The structural formulas are

abbreviated by omission of some H’s and OH’s.

When the reaction is carried out in pure water both the forward and reverse reactions

are found to be first order. The rate law for the uncatalyzed forward reaction of the alpha

isomer is

forward ratek 0 [α] (13.1-35)

where [α] stands for the concentration of the alpha isomer. The rate constant

k 0  0 .0054 min−^1 at 18◦C. In the presence of a strong acid, the rate law is

forward ratek 0 [α]+kH+[H+][α] (13.1-36)

wherek 0 has the same value as before and wherekH+ 0 .0040 L mol−^1 min−^1 at

18 ◦C. The second term corresponds to specific hydrogen-ion catalysis, since hydrogen

ions from any strong acid give the same contribution to the rate.

(^6) S. W. Benson,The Foundations of Chemical Kinetics, McGraw-Hill, New York, 1990, p. 558ff.