Chapter 13, Problem 13.28QP

Kinetics II

You and a friend are working together in order to obtain as much kinetic information as possible about the reaction $\text{A}(g)\stackrel{}{\to }\text{B}(g)+\text{C}(g)$. One thing you know before performing the experiments is that the reaction is zero order, first order, or second order with respect to A. Your friend goes off, runs the experiment, and brings back the following graph.

1. a After studying the curve of the graph, she declares that the reaction is second order, with a corresponding rate law of Rate = k[A]². Judging solely on the basis of the information presented in this plot, is she correct in her statement that the reaction must be second order?

Here are some data collected from her experiment:

Time (s)	[A]
0.0	1.0
1.0	0.14
3.0	2.5 × 10−3
5.0	4.5 × 10−5
7.0	8.3 × 10−7

1. b The half-life of the reaction is 0.35 s. Do these data support the reaction being second order, or is it something else? Try to reach a conclusive answer without graphing the data.
2. c What is the rate constant for the reaction?
3. d The mechanism for this reaction is found to be a two-step process, with intermediates X and Y. The first step of the reaction is the rate-determining step. Write a possible mechanism for the reaction.
4. e You perform additional experiments and find that the rate constant doubles in value when you increase the temperature by 10^oC. Your lab partner doesn’t understand why the rate constant changes in this manner. What could you say to your partner to help her understand? Feel free to use figures and pictures as part of your explanation.