Third Order Reactions
Definition
If some of exponent
of concentration in rate law is 3 then the reaction will be of third order.
Third order
reactions can have two cases
A + B +
C → P
1. Same
initial concentration a a a
2. different
initial concentration a b c
5.1 Kinetics of third order reaction with same initial concentration
Consider a
reaction
A + B +
C → P
At t=0 a a a 0
After time t a-x
a-x a-x x
Rate
Rate = K[A] [B] [C]
Here Rate = dx/dt
integrating
e.q. 5.1To 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. 5.1 we got
Putting the value of z in e.q.5.1 we got
Simplifying
e.q.
5.2Rate constant for third order reaction and its unit
Unit of rate constant for 3rd order reaction will be L2
mol-2 s-1.
5.2 Kinetics of third order reaction with different initial concentration
Consider a
reaction
A + B + C → P
At t=0 a b c 0
After time t a-x
a-b a-c x
Rate
Rate = K[A] [B] [C]
Here Rate = dx/dt
integrating 
e.q. 5.3By partial fraction method
e.q. 5.4Here we will
multiply (a-x)(b-x) (c-x) on both sides and we will get
1= A (b-x)(c-x) + B(a-x)(c-x) +
C(a-x)(b-x) e.q.5.5
In above
equation put x=a to find value of A.
 |
Similarly,
put x=b to find value of B.
Similarly,
put x=c to find value of C
Putting the values of A,B,
and C in e.q. 5.4
Multiplying this equation with dx on both sides
Integrating above equation we got
LHS of above equation and e.q. 5.3 are same so their RHS are also same
Simplifying
Taking LCM of above equation
To 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. 5.5 we got
Putting value of z in e.q. 5.5 we got
