Chemistry Reference
In-Depth Information
from equation (9.1), where cancelling terms on the left-hand side of the
equation results in no units. The right-hand side of the equation must also
have no units if the equation is to be valid. The term
t
has the dimension of
'time', so
k
must have the dimension of time
1
. Units of 'inverse time' are
hard to comprehend, but it means that
k
, the rate constant, gives us a
measure of how much of the reaction occurs
per unit of time
, i.e.
per
second
, or
per hour
, or
per day
, etc.
On a practical point, the fact that the units of concentration cancel
out for a first-order reaction means that
any
physical quantity that is
proportional
to the concentration may be used in the equation in place of
concentration, e.g. light absorbance or titration volume. This is very useful,
since it means data measured in the laboratory can be inserted directly into
the integrated rate equation.
Half-life
The half-life (
t
) of a reaction is an important term that may be derived
from equation (9.1). The half-life is defined as the time taken for the
concentration of reactant to fall to half its original value:
a
ln —----
kt
(
a
x
)
a
ln —------
kt
(
a
a
)
ln 2
kt
0.693
t
—--
k
(9.3)
For first-order reactions (only),
t
is independent of concentration. This
means that the time taken for the reactant concentration to fall from 1
M
to
0.5
M
will be the same as the time taken to fall from 0.5
M
to 0.25
M
. This is
not
true for higher orders of reaction and occasionally this fact is used to
infer that a reaction is first order.
Shelf-life
The shelf life (
t
90
) of a pharmaceutical product is the length of time the
product may safely be stored on the dispensary shelf before significant
decomposition occurs. This is important since, at best, drugs may
