The highest peak in energy profile diagram for mechanism of alkaline hydrolysis of tertiary butyl bromide represents

The alkaline hydrolysis to tert-butyl bromide with aqueous alkali such as \(\mathrm{NaOH}\) or \(\mathrm{KOH}\) is as follows.

The rate of this reaction depends only on the concentration of the tert-butyl bromide and is independent of the concentration of alkali added.
Rate \(\alpha\left[\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{Br}\right]\)
Rate \(=\mathrm{K}\left[\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{Br}\right]\)
This is a first order reaction because rate of hydrolysis of \(\left(\mathrm{CH}_{3}\right)_{3}-\mathrm{Br}\) is independent of the concentration of alkali or \(\mathrm{OH}^{-}\)ions. This can be explained by two-step mechanism shown below. Each step is an elementary reaction with its own rate constant, step 1 proceeds much more slowly than step 2.

Rate of reaction \(=\mathrm{k}_{1}\left[\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{Br}\right]\)
The first step consists of breaking of \(\mathrm{C}-\mathrm{Br}\) bond and it determines the rate of overall reaction. So, step 1 is called the rate-determining step. The rate determining step in this reaction involves only a single molecule, therefore, it is said to be unimolecular. Also, this type of mechanism is known as \(\mathrm{SN}^{1}\) mechanism(substitution, nucleophilic, unimolecular).
Rate of reaction \(=\mathrm{k}_{2}\left[\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{+}\right]\left[\mathrm{OH}^{-}\right]\)
The second step involves the attack of \(\mathrm{OH}^{-}\)ion. This is the fast step, since it is the bond formation step.
Energy profile diagram of \(\mathrm{SN}^{1}\) mechanism shows that rate of a reaction is independent of the concentration of nucleophile. The first step requires larger activation energy \(\left(\Delta \mathrm{E}_{1}\right)\) than the second step \(\left(\Delta \mathrm{E}_{2}\right)\). The first step to form carbocation determines the rate of overall reaction. The second step, which is the attack of nucleophile on carbocation is exothermic i.e., it is a lower energy transition state. The intermediate carbocation appears at a low point in the diagram. The conditions and reagents which favour the formation of carbocation will accelerate the \(\mathrm{SN}^{1}\) reaction. The energy difference between products and reactants is \(\Delta \mathrm{H}\), i.e., Heat of reaction.