© Ultrafast Systems LLC /Vernier Software & Technology
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Under conditions where the initial concentrations of A and B are equal, the rate equation is as in
Equation 7, viz
[ ]
[ ][ ]
d A
k A B
dt
Integrating this and setting [A] = [B] leads to
1
1
0
[ ]
[ ]
A
A
kt
Equation 12
This is also the result for the case of the reaction
2
A
products
At the half-time point [A] = 0.5[A]
0
then
1/ 2
0
0
0
1/ 2
0
2
1
1
[ ]
[ ]
[ ]
or
1/ [ ]
kt
A
A
A
t
k A
Thus we see that the half time depends on the initial concentration, unlike the first order case.
5.7 Pseudo
Order
In the bimolecular elementary process
A B
products
If the initial concentration of one of the reacting species, say B, is very much higher than that of
the other, A, then changes in concentration of B through reaction become negligible compared to those of
A, which go from 100% to zero during the course of the reaction. Then the rate equation
[ ]
[ ][ ]
d A
k A B
dt
becomes
0
[ ]
[ ] [ ]
'[ ]
d A
k B A
k A
dt
where k’ = k[B]
0
Upon integration this becomes
0
[ ] [ ] exp(
' )
A
A
k t
This bimolecular process is seen to be first order in A and first order overall. This is referred to as
“pseudo-first order” by some practitioners, but the important thing to realize is that the process behaves in
a first order manner in the experiment. This behavior can be detected by evaluating the first order rate
constant at different initial concentrations of B, when the behavior will be found to depend linearly on [B].
