The reaction `NH_(4)^(+)+ OCN^(-) rarr OC (NH_(2))_(2)` , proceeds through the following mechanism.
`NH_(4)^(+)+OCN^(-) overset(k_(eq))rarr NH_(4)` OCN (fast)
`NH_(4)OCN overset(k) rarr OC(NH_(2))_(2)` (slow)
The rate constant of the reaction is

Options

A. k
B. `k K_(eq)`
C. `k//K_(eq)`
D. `K_(eq)//k`

Explanation

From slow step, we writer `r = k[NH_(4)OCN]`
where `[NH_(4)OCN]` from the fast equilibrium step is `[H_(4)OCN] = K_(eq)[NH_(4)^(+)][OCN^(-)]`. Hence, the rate law is `r = (k K_(eq)) [NH_(4)^(+)][OCN^(-)]`, The rate constant is `k K_(eq)`.