The following mechanism has been proposed for the reaction, A2 + 2 B → 2 P. Use these elementary steps in the mechanism shown below to derive the rate law.

Question

From the rate law that you derive, determine the overall order of the reaction.



A₂ <=> 2 A  Fast

A + B → P   Slow

Answer 1

A₂ <==> 2A (fast)

A + B <==> P (slow)

The rate law should be based on the slow step, so we could begin by writing...

rate = k[A][B] , but since A is an intermediate, it should not appear in the rate law.

We can express [A] in terms of [A₂] and k1 and k-1 as follows:

k1[A₂] = k-1[A]²

[A] = k1/k-1[A₂]^1/2

Substituting this back into the rate equation for the slow step, we have...

rate = k[k1/k-1[A₂]^1/2[B] and combining rate constants, we arrive at the final rate law:

rate = k'[A₂]^1/2[B]

Overall order = 1.5