Solved: Urea (NH2CONH2) is the end product in protein metabolism in animals. The

Chapter 20, Problem 14.106

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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

             \(\begin{aligned} \mathrm{NH}_2 \mathrm{CONH}_2(a q)+\mathrm{H}^{+}(a q)+& 2 \mathrm{H}_2 \mathrm{O}(l) \longrightarrow \\ & 2 \mathrm{NH}_4^{+}(a q)+\mathrm{HCO}_3^{-}(a q) \end{aligned}\)

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 \(4.00 \times 10^3\) s if the starting concentration is \(0.500 \mathrm{M}\)?

(c) What is the half-life for this reaction at \(61.05^{\circ} \mathrm{C}\)?