Physical Chemistry Third Edition

486 11 The Rates of Chemical Reactions

11.1 The Macroscopic Description of Chemical

Reaction Rates

In this chapter we discuss the rates of chemical reactions. We restrict our treatment to

fluid systems and we will not attempt to treat systems in which the temperature and

composition are not constant.^1 Consider a hypothetical chemical reaction:

aA+bB−→dD+fF (11.1-1)

where the capital letters stand for chemical formulas and the lower-case letters stand

for stoichiometric coefficients. We want to define the rate of the reaction, denoted by

r, in such a way that we can choose any of the substances to specify the rate:

r−

1

a

d[A]

dt

−

1

b

d[B]

dt



1

d

d[D]

dt

1

f

d[F]

dt

(definition ofr) (11.1-2)

where[A]denotes the molar concentration (in mol L−^1 or mol m−^3 ) of substance A,

and so on, and wheretis the time.

We can write a chemical equation in the form used in Chapters 3 and 8,

0 

∑s

i 1

viFi (11.1-3)

whereνistands for the stoichiometric coefficient andFistands for the chemical formula

of substance numberi. In this form the reaction of Eq. (11-1.1) is written as

0 dD+fF−aA−bB

with negative stoichiometric coefficients for reactants and positive coefficients for

products. Therate of the reactioncan now be written as

r

1

νi

d[Fi]

dt

(11.1-4)

This equation satisfies the inner urge of physical chemists to write one equation that

holds for all cases.

On the molecular level, a chemical reaction can occur in both directions at the same

time. While some reactant molecules are forming products at a rate called theforward

rate, other product molecules are forming reactants at a rate called thereverse rate.

The observable rate of a chemical reaction is anet rate:

rrnetrf−rr (11.1-5)

whererfis the forward rate and whererris the reverse rate. Chemical reactions

usually proceed smoothly toward a macroscopic equilibrium state in which the for-

ward and reverse rates cancel each other and the net rate vanishes. However, some

(^1) See for example R. G. Mortimer,J. Phys. Chem., 67 , 1938 (1963).