Chemistry Reference
In-Depth Information
decompose to inactive products; in the worst case the decomposition
may yield toxic compounds. The shelf-life is often taken to be the time
for decomposition of 10% of the active drug to occur, leaving 90% of
the activity. A similar expression to equation (9.3) can be obtained by
substituting ln(100/90) in place of ln 2 to give
0.105
t
90
—---
k
(9.4)
from which the shelf-life can easily be calculated once
k
, the reaction rate
constant, has been determined.
Second-order reactions
For reactions of the type
2A
1
products
or
A
B
1
products
the rate of the reaction will be first order with respect to each reactant
and hence second order overall. A useful integrated rate equation may
be obtained by a similar process to the derivation of equation (9.1) as
follows:
d
x
--
k
(
a
x
)
2
d
t
Therefore,
d
x
—----
k
d
t
(
a
x
)
2
Hence,
1
—----
c
kt
(
a
x
)
At
t
0,
x
0, therefore 1/
a
c
0 and
c
1/
a
to give
1
1
—----
-
kt
(
a
x
)
a
(9.5)
Equation (9.5) is the equation of a straight line of the type
y
c
mx
, so
that a plot of 1/(
a
x
) against
t
yields a straight line of slope
k
, with an
intercept on the vertical axis of 1/
a
.
