The Foundations of Chemistry

CONCENTRATIONS OF REACTANTS:

THE RATE-LAW EXPRESSION

As the concentrations of reactants change at constant temperature, the rate of reaction

changes. We write the rate-law expression(often called simply the rate law) for a reac-

tion to describe how its rate depends on concentrations; this rate law is experimentally

deduced for each reaction from a study of how its rate varies with concentration.

The rate-law expression for a reaction in which A, B,... are reactants has the

general form

ratek[A]x[B]y...

The constant kis called the specific rate constant(or just the rate constant) for

the reaction at a particular temperature. The values of the exponents, xand y,and

of the rate constant, kbear no necessary relationship to the coefficients in the balanced

chemical equationfor the overall reaction and must be determined experimentally.

The powers to which the concentrations are raised, xand y,are usually integers or zero

but are occasionally fractional or even negative. A power of onemeans that the rate is

directly proportional to the concentration of that reactant. A power of twomeans that the

rate is directly proportional to the squareof that concentration. A power of zeromeans

that the rate does not depend on the concentration of that reactant, so long as some of

the reactant is present. The value of xis said to be the orderof the reaction with respect

to A, and yis the order of the reaction with respect to B. The overall order of the reac-

tion is x
y.Examples of observed rate laws for some reactions follow.

1.3NO(g)88nN 2 O(g)
NO 2 (g)

ratek[NO]^2 second order in NO; second order overall

2.2NO 2 (g)
F 2 (g)88n2NO 2 F(g)

ratek[NO 2 ][F 2 ] first order in NO 2 and first order in F 2 ;

second order overall

3.2NO 2 (g)88n2NO(g)
O 2 (g) ratek[NO 2 ]^2 second order in NO 2 ;

second order overall

4.H 2 O 2 (aq)
3I(aq)
2H
(aq)88n2H 2 O(
)
I 3 (aq)

ratek[H 2 O 2 ][I] first order in H 2 O 2 and first order in I;

zero order in H
; second order overall

We see that the orders (exponents) in the rate law expression mayor may notmatch

the coefficients in the balanced equation. There is noway to predict reaction orders

from the balanced overall chemical equation. The orders must be determined exper-

imentally.

It is important to remember the following points about this specific rate constant, k.

16-3

The word orderis used in kinetics in
its mathematical meaning. This use is
unrelated to the order–disorder
discussion of entropy (Chapter 15).

656 CHAPTER 16: Chemical Kinetics

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 15.4, Control of Reaction Rates
(2): Concentration Dependence.

More details about values and units of
kwill be discussed in later sections.

Any number raised to the zero power
is one. Here [H
]^0 1.