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

Answer: (C)

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 while [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 while [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. Analyze the results from steps 2 and 3 to identify the reaction orders \(m\) and \(n\). This will tell you how the rate depends on the concentrations of A and B.
5. Write the final rate law using the determined reaction orders: \(\text{rate} = k [A]^m [B]^n\). Based on the data, select the correct rate law from the given options.