Animated Solution for Chemistry - Organic Chemistry: Which of the following potential energy (PE) diagrams represents the $S_{N}1$ reaction?

The potential energy diagram of a chemical reaction is like a topographic map of a mountain hike. It tells us exactly how much energy is required to climb over the barriers (transition states) and where the resting points (intermediates) lie. Let's decode the energy profile of the $S_{N}1$ reaction.

Unlike the concerted $S_{N}2$ mechanism, the $S_{N}1$ (Substitution Nucleophilic Unimolecular) reaction is a two-step process.

Step 1: The Slow Climb The first step involves the heterolytic cleavage of the carbon-halogen bond to form a carbocation intermediate. Breaking a stable bond requires a massive input of energy. This makes the first step the rate-determining step (RDS). On our energy graph, this is represented by a steep climb to the first transition state ($T{S}_1$). Once the bond breaks, the energy drops into a "valley," which represents the formation of the carbocation intermediate.

Step 2: The Fast Descent In the second step, the nucleophile attacks the highly reactive carbocation. Because the carbocation is electron-deficient and desperate to react, this step is incredibly fast. It requires very little activation energy. The graph shows a small bump to a second transition state ($T{S}_2$) before dropping down to the final, stable energy level of the products.

When we look at a potential energy diagram, two key features tell us the story of the reaction: 1. Number of Peaks: Each peak represents a transition state. Since $S_{N}1$ has two steps, its graph must have two peaks. This immediately eliminates options (a) and (c), which show single-step concerted reactions (like $S_{N}2$). 2. Height of the Peaks: The height of the peak from the starting valley is the activation energy ($E_a$). Because the first step is the slow, rate-determining step, it must have the highest activation energy. Therefore, the first peak must be taller than the second peak ($E_{a1}>E_{a2}$).

Looking at our remaining options, option (b) perfectly illustrates a two-step reaction where the first energy barrier is significantly higher than the second. Option (d) shows the reverse, which would imply the second step is the slow one—a physical impossibility for an $S_{N}1$ reaction.

Thus, the correct potential energy diagram is (b).