Question

Write a rate equation for each reaction, given the indicated mechanism.

a.

b.

Short answer

Answer

1. $\mathrm{rate}=\mathrm{k}\left[{\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{CH}}_2\mathrm{Br}\right]\left[{}^{-}\mathrm{OH}\right]$
2. $\mathrm{rate}=\mathrm{k}\left[{\left({\mathrm{CH}}_3\right)}_3\mathrm{CBr}\right]$
   

Step-by-step solution

Step-by-Step SolutionStep 1: Rate of a reaction

The rate of a reaction depends on the concentration of the reacting species involved in a chemical reaction.

The rate of a reaction depends on the slowest step.

Rate equation

The rate of a reaction is proportional to the concentration of the species participating in a chemical reaction.

For a chemical reaction: $\mathrm{A}\to \mathrm{B}$

$\mathrm{rate}=\mathrm{k}\left[\mathrm{A}\right]$, k is the proportionality constant or the rate constant.

Rate equation for the given reactions

a.

Reaction a

The given reaction involves only a single step, and the rate of the reaction depends on the concentration of both the reacting species.

The rate equation for the given reaction is:

$\mathrm{rate}=\mathrm{k}\left[{\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{CH}}_2\mathrm{Br}\right]\left[{}^{-}\mathrm{OH}\right]$

b.Reaction b

The given reaction involves two steps (a slow and a fast step).

The rate of a reaction depends on the slowest step, and hence the rate equation involves the concentration of the species present in the slowest step.

The rate equation of the given reaction is:

$\mathrm{rate}=\mathrm{k}\left[{\left({\mathrm{CH}}_3\right)}_3\mathrm{CBr}\right]$