Given the following initial rate data for the reaction A + B → products, what is the correct rate law?| [A] (mol/L) | [B] (mol/L) | Initial Rate (mol/L·s) ||-------------|-------------|------------------------|| 0.10 | 0.10 | 0.020 || 0.20 | 0.10 | 0.040 || 0.10 | 0.20 | 0.020 |Which of the following is the correct rate law for this reaction?

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

Answer: (C)

Verified step by step guidance

1. Examine how the initial rate changes when the concentration of A changes while keeping B constant. Compare the first and second experiments where [B] = 0.10 M: when [A] doubles from 0.10 to 0.20 M, the rate doubles from 0.020 to 0.040 mol/L·s. This suggests the rate is directly proportional to [A].
2. Next, examine how the initial rate changes when the concentration of B changes while keeping A constant. Compare the first and third experiments where [A] = 0.10 M: when [B] doubles from 0.10 to 0.20 M, the rate remains the same at 0.020 mol/L·s. This suggests the rate is independent of [B].
3. From these observations, write the general form of the rate law as \(rate = k[A]^m[B]^n\), where m and n are the reaction orders with respect to A and B, respectively.
4. Use the data to determine the reaction orders: since doubling [A] doubles the rate, m = 1; since changing [B] does not affect the rate, n = 0. Therefore, the rate law simplifies to \(rate = k[A]^1 = k[A]\).
5. Conclude that the correct rate law for the reaction is \(rate = k[A]\), meaning the reaction is first order in A and zero order in B.