Second Order Reactions
Definition
If some of
exponent of concentration in rate law is 2 then the reaction will be of second
order.
Second order
reaction can have same initial concentration of reactants as well as different.
A + A → P
Rate ∝ [A]2
Rate = K [A]2
OR A + B → P
Rate ∝ [A] [B]
Rate = K[A] [B]
In both cases sum of
powers is equal to two so both are second order reaction.
4.1 Kinetics
of second order reaction with same initial concentration
Consider a
reaction
A +
B → P
At t=0 a
a 0
After time t
a-x a-x x
Rate
Rate
= K[A] [B] e.q.
4.1
Here Rate = dx/dt
integrating
e.q. 4.2To find value of z consider that at initial time t=0, the concentration is x=0. So, putting values of x and t in e.q. 4.2 we got z = 1/a
Putting value of z in e.q. 4.2 we got
e.q.
4.3
Figure 4.1:
straight line graph for second order reaction (equation 4.3)
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Rearranging e.q. 4.3
Taking LCM of LHS
Figure 4.2:
straight line graph for second order reaction (equation 4.5)
Rate constant for second order reaction and its unit
From e.q. 4.4 rate constant is
Unit of rate constant for 2nd order reaction will be Lmol-1
s-1.
4.2 Kineticsof second order reaction with different initial concentration
Consider a
reaction
A
+ B → P
At t=0 a
a 0
After time t
a-x b-x x
Rate ∝ [A] [B]
Rate
= K[A] [B] e.q.
4.6
Here Rate = dx/dt, A= a-x, B= b-x. Put all values in e.q. 4.6
integrating
e.q. 4.7By using partial fraction method we know that
e.q. 4.8As A and B
are constants so we will modify e.q.4.8 by comparing it with e.q. 4.7 and 4.8.
Here we will multiply (a-x)(b-x) on both sides and we will get
1= A (b-x) + B(a-x)
In above equation
put x=a to find value of A.
1 = A
(b-a) + B (a-a)
1 = A (b-a)
So, 
Similarly, put x=b to find value of B.
1= A (b-b) +
B (a-b)
1= B (a-b)
So, 
Putting the values of A
and B in e.q. 4.8
Multiplying this equation with dx on both sides
e.q. 4.9Integrating e.q. 4.9 we got
e.q.
4.10
As LHS of
e.q. 4.7 and 4.10 is same so their RHS are also equal.
Taking 1/(a-b) common
e.q.
4.11To find value of z consider that at initial time t=0,
the concentration is x=0. So, putting values of x and t in e.q. 4.11 we got
Put value of z in e.q. 4.11 we got
e.q. 4.12Click Here To Read More Articles
