Multiple Choice
Which of the following represents the integrated rate law for a first-order reaction?
15. Chemical Kinetics
Integrated Rate Law
Multiple Choice
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
Verified step by step guidance1
Identify the order of the reaction. Since the rate constant has units of s⁻¹, this suggests a first-order reaction with respect to urea concentration.
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.
Convert the given time from minutes to seconds because the rate constant is in s⁻¹: \(t = 3.5 \, \text{minutes} \, \times \, 60 \, \frac{\text{seconds}}{\text{minute}}\).
Rearrange the integrated rate law to solve for the concentration of urea remaining at time \(t\): \([A] = [A]_0 \, e^{-k t}\).
Calculate the fraction of urea decomposed by subtracting the fraction remaining from 1: \(\text{fraction decomposed} = 1 - \frac{[A]}{[A]_0}\).
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