For the decomposition of urea, NH₂CONH₂ (aq) + H⁺(aq) + 2 H₂O (l) → 2 NH₄⁺ (aq) + HCO₃^– (aq), the rate constant is 3.24 × 10^–4 s^–1 at 35°C. The initial concentration of urea is 2.89 mol/L. What fraction of urea has decomposed after 3.5 minutes?

• A. 0.934
• B. 0.0658
• C. 1.13×10^–3
• D. 0.0235

Answer: (B)

Verified step by step guidance

1. Identify the order of the reaction. Since the rate constant has units of s^{-1}, this indicates a first-order reaction with respect to urea concentration.
2. Write the integrated rate law for a first-order reaction: \(\ln\left(\frac{[A]_0}{[A]}\right) = k t\), where \([A]_0\) is the initial concentration, \([A]\) is the concentration at time \(t\), and \(k\) is the rate constant.
3. Convert the given time from minutes to seconds because the rate constant is in s^{-1}. Use \(t = 3.5 \, \text{minutes} \times 60 \, \frac{\text{seconds}}{\text{minute}}\).
4. Rearrange the integrated rate law to solve for \([A]\): \([A] = [A]_0 \, e^{-k t}\).
5. Calculate the fraction of urea decomposed using the formula: \(\text{fraction decomposed} = 1 - \frac{[A]}{[A]_0}\). This gives the proportion of urea that has reacted after time \(t\).