Chemistry Reference
In-Depth Information
Equation (9.5) is valid for second-order reactions in which the concen-
trations of the reactants are equal. A general second-order equation may
also be derived that will apply to reactions of the type A
products
when [A] does not equal [B], but this is outside the scope of this topic. In
most cases it is possible to arrange for the concentrations of the reactants
to be equal and equation (9.5) may be used.
The term
k
is, again, the rate constant for the reaction, but in a
second-order process
k
has dimensions of concentration
1
time
1
. The rela-
tionship between the half-life and the second-order rate constant,
k
, for
initial equal concentrations of reactant can be found by substituting
t
B
1
t
into equation (9.5) as follows:
1
1
—----
-
kt
(
a
x
)
a
1
1
—------
-
kt
(
a
a
)
a
11
--
-
kt
4
aa
-
kt
a
1
t
ak
(9.6)
Since
k
is a constant, the half-life of a second-order reaction where the
initial reactant concentrations are equal is inversely proportional to
a
, the
initial reactant concentration.
In some second-order reactions the concentration of one of the react-
ants is many times more than the concentration of the other, so large in
fact as to be considered constant throughout the reaction. In these cases, the
reaction appears to follow first-order kinetics, even though, strictly
speaking, it is still a second-order process. Reactions such as these are
termed
pseudo first-order
reactions. A good example is the acid- or base-
catalysed hydrolysis of an ester, in which the concentration of water is so
large compared to the concentration of ester as to be considered constant.
The rate of the hydrolysis appears to vary only with the concentration of
the ester.
