The rate expresison for the reaction:
`NH_(4)CNO hArr NH_(2)CONH_(2)` can be derived form the mechanism:
(i) `NH_(4)CNO underset(k_(2))overset(k_(1))hArr NH_(4)NCO ("Fast")`
(ii) `NH_(4)CNO overset(k_(3))rarrNH_(3) + HNCO` ("fast")
(iii) `NH_(3)+HNCo overset(k_(4))rarr NH_(2)CONH_(2)` (Slow)
Which of the following statement `(s)` is/are correct about the rate expresison?

Options

A. `(d_(["urea]))/(dt) = (k_(1)k_(3))/(k_(2))[NH_(4)NCO]`
B. `(d_(["urea]))/(dt) = (k_(1)k_(3))/(k_(2)k_(4))[NH_(4)NCO]`
C. `(d_(["urea]))/(dt) = k[NH_(4)NCO]`
D. `(d_(["urea]))/(dt) = (k_(1) xx k_(2))/(k_(3) xx k_(4))[NH_(4)NCO]`

Answer

A, C

Explanation

`(d)/(dt)[NH_(2)CONH_(2)] = k_(4)[NH_(3)][HNCO]` from (iii)
Applying steady state approximation to `HNCO` or `NH_(3)`
`(d[HNCO])/(dt) = O = k_(3) [NH_(4)NCO]-k_(4)[NH_(3)][HNCO]`
`:. (k_(3))/(k_(4)) = ([NH_(3)][HNCO])/([NH_(4)CNO])`
`(d["urea"])/(dt) = k_(4) xx [NH_(3)][HNCO] = k_(4) xx (k_(3))/(k_(4))[NH_(4)NCO]`
Also, `[NH_(4)NCO] = (k_(1))/(k_(2)) xx [NH_(4)CNO]`
`:. (d["urea"])/(dt) = k_(3) xx (k_(1))/(k_(2)) xxx [NH_(4)CNO]`
`= k[NH_(4)CNO]`