1.
3) Consider the reaction for a reactant (A) to a product (C), involving an intermediate (B): a) Set
up rate equations for the above mechanism. b) Show that the mechanism is equivalent to: ARC
when B is an transient intermediate. Give expressions for kr an k, in terms of k./k,'/k,/kb
Solution
A is consumed to produce B and produced by the composition of B. Similarly, B is produced
from A and used up in the production of A and C.
(a) Rate of disappearance of A = k a [A] – k a’ [B] ……(1)
Rate of formation of B = k a [A] + k b’ [C] ……(2)
Rate of disappearance of B = k a’ [B] + k b [B] …..(3)
(b) B is an intermediate; hence, apply the steady state condition to the rates of formation and
disappearance of B, i.e, the rates of formation and disappearance of B are equal. Therefore,
k a [A] + k b’ [C] = k a’ [B] + k b [B]
=====> [B] = 1/(k a’ + k b )*(k a [A] + k b’ [C]) …..(4)
The rate of formation of C = k b [B] – k b’ [C]
= k b *[1/(k a’ + k b )*(k a [A] + k b’ [C])] – k b’ [C]
= k b *( k a [A] + k b’ [C])/(k a’ + k b ) – k b ’[C]
= [k a k b [A] + k b k b’ [C] – k b ’[C]*(k a’ + k b )]/(k a’ + k b )
= [k a k b [A] + k b k b’ [C] – k a’ k b’ [C] - k b k b’ [C])/(k a’ + k b )
= (k a k b [A] – k a’ k b’ [C])/(k a’ + k b )
= k a k b /(k a’ + k b )*[A] – k a’ k b’ /(k a’ + k b )*[C] ……(5)

2.
This is possible only when the reaction is
A <======> C
with k r as the rate constant of the forward reaction and k r’ is the rate constant of the reverse
reaction.
The rate of formation of C is given as
Rate = k r [A] – k r’ [C] ……(6)
Expressions (5) and (6) are similar and hence, B is an intermediate; therefore, we have,
k r = k a k b /(k a’ + k b )
and k r’ = k a’ k b’ /(k a’ + k b ) (ans).