Second order kinetics
A second order reaction in component A has a
time-dependence given by
d[A]/dt = -k[A]2
The integrated rate law is given by
–d[Α]
[Α]2
[Α]0
[Α]
= k dt
0
t
or 1
[Α]–1
[Α]0= kt
This can be expressed as [A] = [A]0/(1 + [A]0kt)
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The concept of second order kinetics, focusing on the time-dependence of a second order reaction, the integrated rate law, and the relationship between initial concentrations and half-life. It also covers specific examples of SN2 reactions and their rate laws, as well as the significance of the NO-O2 reaction.
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Second order kinetics
A second order reaction in component A has a time-dependence given by d[A]/dt = -k[A] 2 The integrated rate law is given by
d[Α]
[Α]
2 [Α] 0 [Α]
= k dt
0 t
or
[Α]
[Α]
0
= kt
This can be expressed as [A] = [A] 0 /(1 + [A] 0 kt)
Second order kinetics:
the half life
The half life, τ 1/ occurs when [A]= [A] 0 /
[Α]
0
[Α]
0
= kτ
1 / 2
1 / 2
k[Α]
0 For a second order process, the half life depends on the initial concentration [A] 0 .
Integrated rate law for second
order reaction A + B → P
The time course for the appearance of product is given the integrated rate law: Note that the half-life for a second order process depends on the initial concentration of A and B.
[ P ] =
[ A ]
0
[ B ]
0 1 – exp{([ B ] 0
– [ A ]
0 ) kt } [ A ] 0
– [ B ]
0 exp{([ B ] 0
– [ A ]
0 ) kt }
S
N
2 reactions
The net effect of a S N 2 reaction is that a leaving group is displaced by an attacking group (nucleophile). The process is inherently second order since the nucleophile must collide with the substrate in the rate-limiting step (labeled as slow above).
S
N
1 reactions
Bimolecular reaction example
The reaction of NO with O 2
- (superoxide anion) is an example of a second order reaction with a great biological significance. The reaction is: The bimolecular rate constant has been determined to be k = 6.7 x 10 9 L mol
s
. The reaction is important since the ratio of is a crucial indicator of health. If this ratio is > 4 an individual is healthy. As this ratio falls to < 1 it indicates poor health.