Page 59 - Basic physical chemistry for the atmospheric sciences

Chemical kinetics

Therefore,
'
[
Ah d[A
f l f
-- = - k d t
A o
[ Alo [ l
where [Alo and [ Al, are the initial concentration of A and the concen­
l
tration at time t, respective y . Hence,

or, converting to logarithms to the base 1 0 (indicated by "log"),
- k t
l og[A]1 = + log[A] 0 (3 .5)
2 303
_
It follows from Eq. (3. 5 ) that for a first-order reaction in A, a plot of
log [A,l versus t will give a straight line of slope - k/2.303 and inter­
cept on the ordinate of log [A 0•
l
For a reaction that is second order (bimolecular) in just one reactant
A, and for which a = I in Reaction (3 . 1 ) ,

- d[Al = k"
[A ]2 (3 .6)
dt
where k" is the rate coefficient. Therefore,

f [ A l,d[Al - - 'ft
dt
!(
[ A lo [Alz -
0
and ,
I I
= (3. 7)
[A]t f(' t + [Alo
I
Hence, in this case, a plot of versus t will give a straight line of
[A]
,
I
slope /(' and i n tercept .
[Alo
In some cases it is possible and convenient to define a pseudo
.first-order rate coefficient even though a reaction is of higher order.
Consider, for example,
OH(g) + S02(g) + M- HOS02(g) + M