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The rate expression for the reaction : N...

The rate expression for the reaction : `NH_(4)CNO hArr NH_(2)CONH_(2)` can be derived from the mechanism :
(i) `NH_(4)CNO underset(K_(2))overset(K_(1))hArr NH_(4)NCO` (Fast) (ii) `NH_(4)NCO overset(K_(3))hArr NH_(3) + HNCO` (Fast)
(iii) `NH_(3) + HNCO overset(K_(4))hArr NH_(2)CONH_(2)` (Slow)
Which of the following statements are correct about rate expression ?

A

`(d_(["urea"]))/(d t) = (K_(1)K_(3))/(K_(2))[NH_(4)CNO]`

B

`(d_(["urea"]))/(dt) = xx (K_(1)K_(3))/(K_(2)K_(4)) [NH_(4)CNO]`

C

`(d_(["urea"]))/(d t) = K[NH_(4)CNO]`

D

`(d_(["urea"]))/(d t) = xx (K_(1) xx K_(2))/(K_(3) xx K_(4))[NH_(4)CNO]`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`(d)/(dt)[NH_(2)CONH_(2)] = K_(4)[H_(3)][HNCO]` from (iii)
Applying steady state approximate to HNCO or `NH_(3)`
`(d[HNCO])/(d t) = 0 = K_(3)[NH_(4)NCO] - K_(4)[NH_(3)][HNCO] therefore (K_(3))/(K_(4)) = ([NH_(3)][HNCO])/([NH_(4)NCO])`
`(d["urea"])/(d t) = K_(4) xx [NH_(3)][HNCO] = K_(4) xx (K_(3))/(K_(4))[NH_(4)NCO]`
Also, `[N_(4)NCO] = (K_(1))/(K_(2)) xx [NH_(4)CNO]`
`(d["urea"])/(d t) = K_(3) xx (K_(1))/(K_(2))[NH_(4)CNO] = K[NH_(4)CNO]`
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