Consider the basic hydrolysis (reaction with aqueous base) of \(\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr}\). \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}(a q)+\mathrm{OH}^{-}(a q) \rightarrow\) $$\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{COH}(a q)+\mathrm{Br}^{-}(a q)$$ The rate law is first order with respect to \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}\) and zero order with respect to \(\mathrm{OH}^{-}\). What does this imply about the mechanism of this reaction?

The rate law given for this reaction is first order with respect to \(\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr}\) and zero order with respect to \(\mathrm{OH}^{-}\). Mathematically, it can be expressed as: $$\text{Rate} = k\left[\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr}\right]$$ where k is the rate constant. This means that the rate of the reaction is directly proportional to the concentration of \(\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr}\) and does not depend on the concentration of \(\mathrm{OH}^{-}\).

A reaction mechanism is the detailed step-by-step description of a chemical reaction that explains how the reactants are converted into products. In this case, we are given the overall reaction and the rate law, so we need to make an interpretation about the underlying mechanism.

Due to the fact that the rate law does not depend on the concentration of \(\mathrm{OH}^{-}\), we can suggest that the hydrolysis reaction occurs in a two-step process: 1. In the first step, \(\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr}\) undergoes a dissociation into a carbocation and a bromide ion: $$\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr} \rightarrow \left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{C}^{+} + \mathrm{Br}^{-}$$ This step is likely the rate-determining step, as the overall rate depends only on the concentration of \(\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr}\). 2. In the second step, the carbocation reacts with the hydroxide ion to form the alcohol product: $$\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{C}^{+} + \mathrm{OH}^{-} \rightarrow \left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{COH}$$ Since this step does not affect the rate law, it is assumed to be faster than the first step.

Based on the information given and the analysis of the rate law, we can make the following conclusions about the mechanism of the basic hydrolysis of \(\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr}\): 1. The reaction likely proceeds in a two-step process. 2. The first step is the rate-determining step, involving the dissociation of \(\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr}\) into carbocation and bromide ion. 3. The second step is faster than the first step and involves the reaction between the carbocation and hydroxide ion to form the alcohol product. This interpretation of the reaction mechanism is consistent with the given rate law and the overall reaction.