Chemistry Reference
In-Depth Information
Zero-order reactions
There are some reactions in which the rate of the reaction is independent of
the concentration of the reactants but does depend on some other factor,
such as the amount of catalyst present. These reactions are termed
zero-
order
reactions, and rate equations can be derived as follows:
d
x
--
k
[A]
0
d
t
Therefore,
∫
d
x
∫
k
d
t
which gives
x
kt
c
(9.7)
In zero-order reactions the amount of product formed varies with
time so that the amount of product formed after 20 minutes will be twice
that formed after 10 minutes. Reactions that follow zero-order kinetics are
quite rare, but they do occur in solid-phase reactions such as release of drug
from a pharmaceutical suspension.
Reaction rates and temperature
For most chemical reactions an increase in temperature will bring about an
associated increase in reaction rate, which can be measured by an increase
in
k
, the reaction rate constant. As a very rough guide, if the temperature of
a reaction increases by 10
C the reaction rate will approximately double.
The Swedish chemist Arrhenius first expressed mathematically the
relationship between reaction rate and temperature, namely,
k
A
e
E
/
RT
(9.8)
where
A
is a constant known as the
frequency factor
and is a measure of the
number of collisions taking place between reactants; e
E
/
RT
is the small frac-
tion of the total number of collisions that result in a successful reaction;
E
is the activation energy for the reaction, i.e. the energy required to force the
reactants to collide with enough energy to form a product;
R
is the universal
gas constant (
R
8.314 J K
1
mol
1
), which seems to crop up in almost
every physical chemistry equation; and
T
is the temperature in kelvin.
Taking logarithms of equation (9.8) gives
