Urea \(\left(\mathrm{NH}_{2} \mathrm{CONH}_{2}\right)\) is the end product in
protein metabolism in animals. The decomposition of urea in \(0.1 \mathrm{M}
\mathrm{HCl}\) occurs according to the reaction
$$
\begin{aligned}
\mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}^{+}(a q)+2 \mathrm{H}_{2}
\mathrm{O}(l) \longrightarrow & \mathrm{NH}_{4}^{+}(a
q)+\mathrm{HCO}_{3}^{-}(a q)
\end{aligned}
$$
The reaction is first order in urea and first order overall. When
\(\left[\mathrm{NH}_{2} \mathrm{CONH}_{2}\right]=0.200 \mathrm{M},\) the rate at
\(61.05^{\circ} \mathrm{C}\) is \(8.56 \times 10^{-5} \mathrm{M} / \mathrm{s}\).
(a) What is the rate constant, \(k ?\) (b) What is the concentration of urea in
this solution after \(4.00 \times 10^{3} \mathrm{~s}\) if the starting
concentration is \(0.500 \mathrm{M}\) ? (c) What is the half-life for this
reaction at \(61.05^{\circ} \mathrm{C}\) ?