Conisder the following proposed mechanism
`A underset(k_(1))overset(k_(2))hArr B` , `B+C overset(k_(3))rarrD`
For the overall reaction `A+CrarrD`, assuming `B` to be an intermediate described by the steady state approximation, write the rate expresison for `[A]`.

Explanation

Applying steady state approximation for `[B]`, gives
`(d[B])/(dt) = k_(1)[A] -k_(2)[B] - k_(3)[B][C] = 0`
`[B] = (k_(1)[A])/(k_(2)+k_(3)[C])`
Writing rate expresison for `[A]` and substituting the expresison for `[B]` gives
`(-d[A])/(dt) = k_(1)[A]-k_(2)[B] = k_(1)[A] - k_(2) (k_(1)[A])/(k_(2)+k_(3)[C])`
`= (k_(1)k_(3)[A][C])/(k_(2)+k_(3)[C])`