Conisder the following proposed mehanism
`A_(2) hArr 2A (k_(1))`
`A+B hArr C(k_(2))`
`A_(2) + C rarr D + A (k)`
For the overall chemical equation `A_(2)+BrarrD`, assuming that the equlibria are rapidly established in the first two steps, write the rated expresison for `[D]`.

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]`