The mechanism for the overall reaction is
`A_(2) + B rarr C`
`A_(2) rarr 2A` (slow)
`2A + B rarr X` (fast)
If a catalyst `D` changes the mechanism to
`A_(2) + D rarr A_(2) D` (slow)
`A_(2) D rArr 2A+D` (fast)
`2A +B rarr C` (fast)
Which is the rate expresison for the reaction with and without a catalyst ?

Options

A. `r = k'[A_(2)][D], r = k[A_(2)]`
B. `r = k[A_(2)], r = k'[A_(2)][D]`
C. `r = k'[A_(2)D], r = k[A_(2)][B]`
D. `r = k[A_(2)][B], r = k'[A_(2)D]`

Answer

A

Explanation

(i) Slow step in the reaction with catalyst is
`A_(2) + D rarr A_(2)D (Slow)`
Hence, `r = k'[A_(2)][D]`
(ii) Slow step in the reaction without catalyst is:
`A_(2) rArr 2A (slow)`
Hence, `r = k[A_(2)]`