Physical Chemistry Third Edition

13.3 Autocatalysis and Oscillatory Chemical Reactions 585

to averages over microstates. From our discussion of statistical entropy in Chapter 4,

it is obvious that information is being lost in an irreversible process. Although much

progress has been made in understanding how to average over microstates to represent

a nonequilibrium macrostate, the question of how this information is lost has not yet

been answered.^18

PROBLEMS

Section 13.2: Competing Mechanisms and the Principle
of Detailed Balance

13.20A hypothetical reaction

AX+B+
A++BX

can proceed through either of two independent

mechanisms:

Elementary mechanism:

(1) AX+B+
A++BX

Two-step mechanism:

(2) AX
A++X−

(3) B++X−
BX

Given the values at some fixed temperature,

k 2  1. 0 × 106 s−^1

k′ 2  2. 4 × 108 L mol−^1 s−^1

k 3  3. 8 × 104 L mol−^1 s−^1

k′ 3  1. 4 × 101 s−^1

k′ 1  6. 7 × 102 s−^1

find the value of the equilibrium constant and the value of

k 1 at this temperature.

13.21Insert a reverse reaction in step 3 of Problem 12.36. Write

the expression for the equilibrium constant in terms of the

rate constants. Write the relation between the rate

constants for the chain mechanism and the other

mechanisms, using the principle of detailed

balance.

13.22Insert a reverse reaction in the second step of the mecha-

nism of Eq. (13.1-16), assuming a single product,P,

and assuming that the reverse reaction in step 2 is

elementary.

a.Write an expression for the equilibrium constant of the

reaction in the absence of the catalyst.

b.Write an expression for the equilibrium constant in

terms of the rate constants in the assumed mechanism.

Express the rate constant for the reverse reaction of

step 2 in terms of the other rate constants and the

equilibrium constant, using the principle of detailed

balance.

13.23Insert reverse reactions into steps 2 and 3 in the

mechanism of Problem 13.14. Write an expression for the

equilibrium constant for the reaction in terms of the rate

constants of the three steps. Expressk′ 3 in terms of the

equilibrium constant for the uncatalyzed reaction and the

other rate constants.

13.3 Autocatalysis and Oscillatory Chemical

Reactions

Autocatalysis

If a product of a reaction catalyzes that reaction, the reaction is said to exhibitauto-

catalysis. The simplest hypothetical autocatalytic reaction

A→F (13.3-1)

(^18) Many years ago while at a meeting, the author approached George Uhlenbeck, a prominent theoretical
physicist, and asked him to comment on this question. He simply stated “Irreversibility is just a human
illusion.” Who knows if his opinion is correct?