Using the information in the table below, what is the correct rate law for the reaction 2 A(g) + B(g) → C(g) + D(g)?| Experiment | [A] (M) | [B] (M) | Initial Rate (M/s) ||------------|--------|--------|--------------------|| 1 | 0.10 | 0.10 | 2.0 × 10^{-3} || 2 | 0.20 | 0.10 | 4.0 × 10^{-3} || 3 | 0.10 | 0.20 | 2.0 × 10^{-3} |Which of the following is the correct rate law?

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

Answer: (A)

Verified step by step guidance

1. Identify 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: The concentration of A doubles from 0.10 M to 0.20 M while B remains constant at 0.10 M. Observe how the initial rate changes between these two experiments.
3. Use the rate ratio from experiments 1 and 2 to find the order \(m\) with respect to A by setting up the equation: \(\frac{\text{rate}_2}{\text{rate}_1} = \left(\frac{[A]_2}{[A]_1}\right)^m\). Solve for \(m\).
4. Compare experiments 1 and 3 to determine the order with respect to B: The concentration of B doubles from 0.10 M to 0.20 M while A remains constant at 0.10 M. Observe how the initial rate changes between these two experiments.
5. Use the rate ratio from experiments 1 and 3 to find the order \(n\) with respect to B by setting up the equation: \(\frac{\text{rate}_3}{\text{rate}_1} = \left(\frac{[B]_3}{[B]_1}\right)^n\). Solve for \(n\). Then, write the final rate law using the determined orders.