Energy diagram of S_N1 mechanism

Because S_N1 is a multiple-step reaction, so the diagram has multiple curves, with each step can be represented by one curve. Out of the three steps, the activation energy for step 1 is the highest, therefore step 1 is the slowest step, that is the rate-determining step.

The connection between the first two curves represent the carbocation intermediate. Generally, intermediate is the product of one step of a reaction and the reactant for the next step. Intermediate is at a relatively lower energy level comparing to transition state (which is at the peak of a curve), but intermediate is also highly reactive and unstable.

The Effect of Substrate Structure on S_N1 Reaction Rate

Different substrates have different reaction rates towards S_N1 reaction, and the relative reactivity of substrates towards S_N1 reaction can be summarized as:

Comparing this trend to that for S_N2 reaction, you probably realize that they are just opposite. Tertiary  substrate is most reactive towards S_N1, but it does not undergo S_N2 at all; primary and methyl substrate are unreactive for S_N1, but they are the best substrates for S_N2. This comparison is very important and useful for us to choose the proper reaction condition for different substrate as we will see in next section. For now, we will need to understand the reasoning of the trend for S_N1.

This is because of the stability of carbocation intermediate. The mechanism shows that a carbocation is formed in the rate-determining step, so the more stable the carbocation, the more easily it is formed, the more it facilitates the rate-determining step and speed up the whole reaction. Therefore the more stable the carbocation intermediate is, the faster the rate of a S_N1 reaction.

The relative stability of carbocation is given below, that the tertiary carbocations are the most stable and methyl carbocation is the least stable.

The relative stability of carbocations can be explained by the hyperconjugation effect. Hyperconjugation is the partial orbital overlap between filled bonding orbital to an adjacent unfilled (or half-filled) orbital. Carbocation is the electron-deficient species that has the incomplete octet and empty 2p orbital. If there is an alkyl group connected with carbocation, then there are C-C or C-H sigma bonds beside the carbocation carbon, so the filled orbitals of  sigma bonds will be able to partially overlap with the empty 2p orbital, therefore sharing the electron density to carbocation and to get the carbocation stabilized. The more R group involved, the stronger hyperconjugation effect is. So tertiary (3°) carbocation is the most stable one. While there is no any R group in methyl carbocation, CH₃⁺, it is least stable.

Stereochemistry of S_N1 mechanism

The stereochemistry feature of the S_N1 reaction is very different to that of S_N2, and of course can be explained well with the SN1 mechanism.

Starting with (S)-3-bromo-3-methylhexane reactant, the S_N1 reaction produces a 50:50 mixture of both R and S enantiomers of 3-methyl-3-hexanol, that is the racemic mixture product. This is because the carbocation formed in the first step of an S_N1 reaction has the trigonal planar shape, when it react with nucleophile, it may react from either the front side or the back side, and each side gives one enantiomer. There is equal possibility for reaction to occur from either side, so the two enantiomers are formed with the same amount, and the product is a racemic mixture.

A reaction that coverts an optically active compound into a racemic form is said to proceed with racemization. For S_N1 reaction that start with (an optical active)one enantiomer as the reactant, and the chirality center is also the electrophilic carbon (i.e. the reaction occurs on the chirality center),  it proceeds with racemization as shown above.

Answers to Practice Questions Chapter 7

Please note that if the chirality center of the reactant is not the reaction center, or if there are more than one chirality center in the reactant, the SN1 reaction does not produce the racemic mixture as example below.

Leaving Group Effect on S_N1

Same as for S_N2 reaction, a good leaving group is also required for S_N1 mechanism, and all the discussions we had before in section 7.3 apply.

Nucleophile 

Unlike a S_N2 reaction, the rate-determining step of S_N1 reaction does not include nucleophile, so theoretically the strength of nucleophile has no effect on S_N1 reaction. However, a strong nucleophile has high tendency to go with S_N2 reaction instead of S_N1, so a weaker nucleophile is a better choice for S_N1. For the examples we had so far, H₂O is the nucleophile.

In practice, neutral substances such as H₂O, ROH, RCOOH are usually used as nucleophiles in S_N1 reaction. When these substances are applied in the reaction, they serve for another function as solvents. So they are used as both nucleophiles and solvents for S_N1 reaction, and such reaction is also called the solvolysis reaction. Solvolysis reaction is a nucleophilic substitution in which the nucleophile is a molecule of solvent as well. The term solvolysis comes from: solvent+lysis, that means cleavage by the solvent. A S_N1 reaction is usually a solvolysis reaction.

Examples

Show the structures of the products for the following solvolysis reaction.

Solution: