Chapter 11, Problem 53QAP

Ammonium cyanate, ${\text{NH}}_4\text{NCO}$, in water rearranges to produce urea, a common fertilizer, (NH₂)₂CO:

${\text{NH}}_4\text{NCO}\left(aq\right)\to {\left({\text{NH}}_2\right)}_2\text{CO}\left(aq\right)$

The rearrangement is a second-order reaction. It takes 11.6 h for the concentration of ${\text{NH}}_4\text{NCO}$ to go from 0.250 M to 0.0841 M.

(a) What is k for the reaction?

(b) What is the half-life of the reaction when ${\text{NH}}_4\text{NCO}$ is 0.100 M?

(c) How long will it take to rearrange 39% of a 0.450 M solution?

(d) How fast is a 0.839 M solution being changed to urea?