Chapter 15, Problem 71E

Consider the hypothetical reaction

$\text{B}\to \text{E}+\text{F}$

which is assumed to occur by the mechanism

$\begin{array}{l}\text{B}+\text{B}\underset{k_{-1}}{\overset{k_1}{\rightleftharpoons }}\text{B*+B}\\ \text{B*}\stackrel{k_2}{\to }\text{E}+\text{F}\end{array}$

where $\text{B*}$ represents a $\text{B}$ molecule with enough energy to surmount the reaction energy barrier.

1. Derive the rate law for the production of E using the steady-state approximation.
2. Assume that this reaction is known to be first order. Under what conditions does your derived rate law (from part a) agree with this observation?
3. Explain how a chemical reaction can be first order, since even in a simple case $\left(\text{B}\to \text{E}+\text{F}\right)$molecules must collide to build up enough energy to get over the energy barrier. Why aren't all reactions at least second order? In other words, explain the physical significance of the result from part b.