Question

The reaction follows the mechanism
$ A + B \xrightleftharpoons[k_{-1}]{k_1}AB \, \, \, \, \, \, \, \, \, \, \, \, \, \, (fast)$ $ AB + B \xrightarrow {k_2} \, A + B_2 (slow)$
then rate law is

• A. $r = k [A][B]$
• B. $r = k [AB][B]$
• C. $r = k [A][B]^2$
• D. $r = k [A]^2 [B]$

Answer 1

Answer: (C)

Mechanism,
$ A + B \xrightleftharpoons[k_{-1}]{k_1}AB \, \, \, \, \, \, \, \, \, \, \, \, \, \, (fast)$ $ AB + B \xrightarrow {k_2} \, A + B_2 (slow)$
For fast reaction (steady state step)
$ k_1 [A][B] = k_{-1} [AB]$
$ [AB] = \frac{k_1 [A][B]}{k_{-1}}$
The value of [AB] put into rate law
$ Rate \, law = \frac{k_2 k_1}{k_{-1}} [A] [B]^2$
$ = k [A][B]^2$