Conisder the following mechanism:
`A_(2) hArr 2A (k)`
`A+B_(2)overset(k_(1))rarrC+B`, `B+A_(2)overset(A_(2))rarrC+A`
For the overall chemical equation `A_(2)+B_(2)rarr2C`.
Assumming that the equilibrium is rapidly established and the steady approximation is valid for `[B]`, write the rate expresison for `[C]`.

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)]`