Physical Chemistry Third Edition

11.1 The Macroscopic Description of Chemical Reaction Rates 487

oscillatory reactions do exist.^2 Figure 11.1 shows schematically how a typical chemical

reaction that produces B from A approaches equilibrium. Both of the concentra-

tions eventually approach constant nonzero values and the net rate approaches zero.

At equilibrium the forward and reverse rates do not vanish, but cancel each

other.

[A]

Concentration

Rate

[B]

rf

rnet

rr

t

0

0

(a)

(b)

t

Figure 11.1 The Approach to Equi-
librium of a Hypothetical Reaction.
(a) The concentrations of the product
B and the reactant A as a function of
time. (b) The forward rate, the reverse
rate, and the net rate as a function of
time.

The rate of a reaction can depend on temperature, pressure, and the concentrations

or partial pressures of the substances in the system. In many reactions at constant

temperature the forward rate depends only on the concentrations of the reactants. If A

and B are the reactants,

rf−

1

a

d[A]

dt

rf([A],[B]) (11.1-6)

The functional relation expressed in this equation is called therate lawof the forward

reaction. Similarly, the reverse reaction rate often depends only on the concen-

trations of the products. If D and F are the products, the rate law of the reverse

reaction is

rr

1

a

d[A]

dt

rr([D],[F]) (11.1-7)

There is a large class of chemical reactions in which the forward reaction rate is

proportional to the concentration of each reactant raised to some power. If A and B are

the reactants, the forward rate law would be

rf−

1

a

d[A]

dt

kf[A]α[B]β (11.1-8)

This relation is called arate law with definite orders. The exponentαis called the

order with respect to substanceA and the exponentβis called theorder with respect to

substanceB. These orders are not necessarily equal to the stoichiometric coefficients

aandb. The sum of the orders with respect to the different substances is called the

overall order.Ifαandβboth equal unity, the reaction is said to be first order with

respect to substance A, first order with respect to substance B, and second order overall.

Other orders are similarly assigned. The orders are usually small positive integers, but

other cases do occur. Some reactions are not described by rate laws like Eq. (11.1-8).

Such reactions are said not to have a definite order. The proportionality constantkfin

Eq. (11.1-8) is independent of the concentrations and is called the forwardrate constant.

Rate constants depend on temperature and pressure, although the pressure dependence

is generally small.^3 We will discuss the temperature dependence of rate constants in

Chapter 12.

One of the objectives of the study of a reaction is to determine what the rate law is.

Knowledge of the rate law allows us to predict the rates of the reaction for new values

of the concentrations without doing additional experiments. The form of the rate law

can usually provide information about the sequence of molecular steps that constitute

the reaction (themechanism of the reaction).

(^2) R. J. Field and M. Burger,Oscillations and Traveling Waves in Chemical Systems, Wiley, New York,
1985.
(^3) R. E. Weston and H. A. Schwarz,Chemical Kinetics, Prentice Hall, Englewood Cliffs, NJ, 1972, p. 181ff.