Chapter 13, Problem 13.89QP

The isomerization of cyclopropane, C₃H₆, is believed to occur by the mechanism shown in the following equations:

$\begin{array}{llll}{\text{C}}_3{\text{H}}_6+{\text{C}}_3{\text{H}}_5\hfill & \stackrel{k_1}{\to }\hfill & {\text{C}}_3{\text{H}}_6+{\text{C}}_3{\text{H}}_6{}^{*}\hfill & (\text{Step}1)\hfill \\ {\text{C}}_3{\text{H}}_6{}^{*}\hfill & \stackrel{k_2}{\to }\hfill & {\text{C}}_2\text{}=\text{}{\text{CHCH}}_3\hfill & (\text{Step}2)\hfill \end{array}$

Here ${\text{C}}_3{\text{H}}_6^{*}$ is an excited cyclopropane molecule. At low pressure, Step 1 is much slower than Step 2. Derive the rate law for this mechanism at low pressure. Explain.