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 + f F
(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 of r)
(11.1-2)
where [A] denotes the molar concentration (in mol L −1 or mol m −3 ) of substance A,
and so on, and where t is the time.
We can write a chemical equation in the form used in Chapters 3 and 8,
0
s
i1
v i F i
(11.1-3)
where ν i stands for the stoichiometric coefficient and F i stands for the chemical formula
of substance number i. In this form the reaction of Eq. (11-1.1) is written as
0 dD + f F − aA − bB
with negative stoichiometric coefficients for reactants and positive coefficients for
products. The rate of the reaction can now be written as
r
1
ν i
d [F i ]
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 the forward
rate, other product molecules are forming reactants at a rate called the reverse rate.
The observable rate of a chemical reaction is a net rate:
r r net r f − r r
(11.1-5)
where r f is the forward rate and where r r is the reverse rate. Chemical reactions
usually proceed smoothly toward a macroscopic equilibrium state in which the forward 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).
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 + f F
(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 of r)
(11.1-2)
where [A] denotes the molar concentration (in mol L −1 or mol m −3 ) of substance A,
and so on, and where t is the time.
We can write a chemical equation in the form used in Chapters 3 and 8,
0
s
i1
v i F i
(11.1-3)
where ν i stands for the stoichiometric coefficient and F i stands for the chemical formula
of substance number i. In this form the reaction of Eq. (11-1.1) is written as
0 dD + f F − aA − bB
with negative stoichiometric coefficients for reactants and positive coefficients for
products. The rate of the reaction can now be written as
r
1
ν i
d [F i ]
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 the forward
rate, other product molecules are forming reactants at a rate called the reverse rate.
The observable rate of a chemical reaction is a net rate:
r r net r f − r r
(11.1-5)
where r f is the forward rate and where r r is the reverse rate. Chemical reactions
usually proceed smoothly toward a macroscopic equilibrium state in which the forward 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).