Mechanism of the reaction is:
`A_(2) overset(k_(2))hArr 2A`
`A + B overset(k_(2))rarr C`
`A_(2) + C overset(k)rarr D + A`
What is `(d[D])/(dt)` ?

Explanation

form the equlibria steps,
` [A]=[k_(1)[A_(2)]]^(1//2)`
`[C]=k_(2)[A][B]=k_(2)k_(1)[B]=k_(1)^(1//2)k_(2)[A_(2)]^(1//2)[B]`
Substituting these expresisons for `[A] and [C]` into the rate expresison for `[D]` gives
`(d[D])/(dt)=k[A_(2)][C]=k[A_(2)]k_(1)^(1//2)k_(2)[A_(2)]^(1//2)[B]`
`=kk_(1)^(1//2)k_(2)[A_(2)]^(3//2)[B]`