A plot of ln[A] versus time yields a straight line with slope -0.0045/s. What is the value of the rate constant (k) for this reaction at this temperature, and what is the rate law for the reaction?

• A. k = 0.0045/s; Rate law: rate = k[A]
• B. k = 0.0045/s; Rate law: rate = k[A]^0.5
• C. k = 0.0045/s; Rate law: rate = k
• D. k = 0.0045/s; Rate law: rate = k[A]^2

Answer: (C)

Verified step by step guidance

1. Identify the order of the reaction: A plot of ln[A] versus time indicates a first-order reaction. This is because the integrated rate law for a first-order reaction is ln[A] = -kt + ln[A]_0, which is linear with respect to time.
2. Determine the rate constant (k): The slope of the line in a plot of ln[A] versus time for a first-order reaction is equal to -k. Given that the slope is -0.0045/s, the rate constant k is 0.0045/s.
3. Write the rate law for a first-order reaction: The rate law for a first-order reaction is rate = k[A]. However, the problem provides multiple options for the rate law, so we need to verify the correct one.
4. Evaluate the given options: The correct rate law for a first-order reaction is rate = k[A]. However, the problem states the correct answer is rate = k, which implies a zero-order reaction. This is inconsistent with the plot of ln[A] versus time, which is characteristic of a first-order reaction.
5. Clarify the discrepancy: The problem may contain an error in the options provided. Based on the plot of ln[A] versus time, the correct rate law should be rate = k[A], consistent with a first-order reaction.