Reaction Order from Initial Rates with a Suspect Data Point
A student studies the reaction A + B → C by the method of initial rates. The student performs four experiments at 25 °C and obtains the following data (concentrations in mol/L, initial rate in mol/(L·s)): Experiment 1: [A] = 0.100, [B] = 0.100, rate = 2.50 × 10^-4 Experiment 2: [A] = 0.200, [B] = 0.100, rate = 5.00 × 10^-4 Experiment 3: [A] = 0.100, [B] = 0.200, rate = 2.50 × 10^-4 Experiment 4: [A] = 0.200, [B] = 0.200, rate = 1.00 × 10^-3 The student suspects that Experiment 4 is unreliable because the rate is much higher than expected. The student must determine the rate law, the rate constant, and decide whether to include Experiment 4 in the analysis.
1. Determine the reaction order with respect to A and B using Experiments 1–3, and write the rate law. Calculate the rate constant with units.
Read the worked answer
Compare Experiments 1 and 2: [B] is constant, [A] doubles, rate doubles (2.50e-4 to 5.00e-4). Therefore, order with respect to A is 1. Compare Experiments 1 and 3: [A] is constant, [B] doubles, rate remains 2.50e-4. Therefore, order with respect to B is 0. Rate law: rate = k[A]. From Experiment 1: k = rate/[A] = 2.50e-4 / 0.100 = 2.50e-3 s^-1. Units: since rate is mol/(L·s) and [A] is mol/L, k has units of s^-1. The reaction is first order overall.
2. Assess whether Experiment 4 is consistent with the rate law from Experiments 1–3. If not, propose a plausible reason and explain how you would handle the data point.
Read the worked answer
Using the rate law rate = k[A] with k = 2.50e-3 s^-1, predict the rate for Experiment 4: rate = (2.50e-3 s^-1)(0.200 M) = 5.00e-4 mol/(L·s). The observed rate is 1.00e-3, which is twice the predicted value. Experiment 4 is not consistent with the zero-order dependence on B. A plausible reason is that at higher concentrations, a different mechanism or a side reaction occurs, or there was an experimental error (e.g., incorrect concentration, contamination, temperature fluctuation). Since Experiments 1–3 are internally consistent and support a simple rate law, the student should repeat Experiment 4 to check reproducibility. If the high rate is reproducible, the student should investigate whether B participates in a subsequent step that becomes significant at higher [B]. For the purpose of determining the rate law under the studied conditions, the student might exclude Experiment 4 as an outlier, but should report the anomaly and not ignore it without explanation.