Conisder the following proposed mechanism
`A underset(k_(2))overset(k_(1))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

form the equilibrium step.
`[A]=k^(1//2)`, applying steady state approximation for `[B]` gives
`(d[B])/(dt)=k_(1)[A][B_(2)]-k_(2)[B][A_(2)]=0`
`[B]=(k_(1)[A][B_(2)])/(k_(2)[A_(2)])=(k_(1)k^(1//2)[A_(2)]^(1//2)[B])/(k_(2)[A_(2)])`
The rate expresison for `[C]` is
`(d[C])/(dt)=k_(1)[A][B_(2)]+k_(2)[B][A_(2)]`
`=k_(1)k^(1//2)[A_(2)]^(1//2)[B_(2)]+(k_(1)k_(2)k^(1//2)[A_(2)]^(1//2)[B_(2)])/(k_(2)[A_(2)]^(2))`
`2k_(1)k^(1//2)[A_(2)]^(1//2)[B_(2)]`