Given the reaction A + B → C + D and the following experimental data:| Experiment | [A] (M) | [B] (M) | Initial Rate (M/s) ||------------|--------|--------|---------------------|| 1 | 0.10 | 0.10 | 2.0 × 10^{-4} || 2 | 0.20 | 0.10 | 4.0 × 10^{-4} || 3 | 0.10 | 0.20 | 2.0 × 10^{-4} |Which of the following is the correct rate law for this reaction?

• A. rate = k[A]
• B. rate = k[A][B]
• C. rate = k[A]^2
• D. rate = k[B]

Answer: (A)

Verified step by step guidance

1. Write the general form of the rate law for the reaction: \(\text{rate} = k [A]^m [B]^n\), where \(m\) and \(n\) are the reaction orders with respect to A and B, respectively.
2. Compare experiments 1 and 2 to determine the order with respect to A: In these experiments, [B] is constant, and [A] doubles from 0.10 M to 0.20 M. Observe how the initial rate changes and use the ratio \(\frac{\text{rate}_2}{\text{rate}_1} = \left(\frac{[A]_2}{[A]_1}\right)^m\) to solve for \(m\).
3. Compare experiments 1 and 3 to determine the order with respect to B: In these experiments, [A] is constant, and [B] doubles from 0.10 M to 0.20 M. Observe how the initial rate changes and use the ratio \(\frac{\text{rate}_3}{\text{rate}_1} = \left(\frac{[B]_3}{[B]_1}\right)^n\) to solve for \(n\).
4. Based on the values of \(m\) and \(n\) found, write the rate law by substituting these orders into the general rate law expression.
5. Confirm the rate law by checking if it correctly predicts the initial rates given in the experiments.