SN1 reaction

Rate law

Although the rate law of the S_N1 reaction is often regarded as being first order in alkyl halide and zero order in nucleophile, this is a simplification that holds true only under certain conditions. While it, too, is an approximation, the rate law derived from the steady state approximation (SSA) provides more insight into the kinetic behavior of the S_N1 reaction. Consider the following reaction scheme for the mechanism shown above:

Though a relatively stable tertiary carbocation, tert-butyl cation is a high-energy species that is present only at very low concentration and cannot be directly observed under normal conditions. Thus, the SSA can be applied to this species:

(1) Steady state assumption: ${\displaystyle \frac{d[{\text{tBu}}^{+}]}{dt}=0=k_1[\text{tBuBr}]-k_{-1}[{\text{tBu}}^{+}][{\text{Br}}^{-}]-k_2[{\text{tBu}}^{+}][{\text{H}}_2\text{O}]}$

(2) Concentration of t-butyl cation, based on steady state assumption: ${\displaystyle [{\text{tBu}}^{+}]=\frac{k_1[\text{tBuBr}]}{k_{-1}[{\text{Br}}^{-}]+k_2[{\text{H}}_2\text{O}]}}$

(3) Overall reaction rate, assuming rapid final step: ${\displaystyle \frac{d[\text{tBuOH}]}{dt}=k_2[{\text{tBu}}^{+}][{\text{H}}_2\text{O}]}$

(4) Steady state rate law, by plugging (2) into (3): ${\displaystyle \frac{d[\text{tBuOH}]}{dt}=\frac{k_1{k}_2[\text{tBuBr}][{\text{H}}_2\text{O}]}{k_{-1}[{\text{Br}}^{-}]+k_2[{\text{H}}_2\text{O}]}}$

Under normal synthetic conditions, the entering nucleophile is more nucleophilic than the leaving group and is present in excess. Moreover, kinetic experiments are often conducted under initial rate conditions (5 to 10% conversion) and without the addition of bromide, so ${\displaystyle [{\text{Br}}^{-}]}$ is negligible. For these reasons, ${\displaystyle k_{-1}[{\text{Br}}^{-}]\ll k_2[{\text{H}}_2\text{O}]}$ often holds. Under these conditions, the SSA rate law reduces to:

${\displaystyle \text{rate}=\frac{d[\text{tBuOH}]}{dt}=\frac{k_1{k}_2[\text{tBuBr}][{\text{H}}_2\text{O}]}{k_2[{\text{H}}_2\text{O}]}=k_1[\text{tBuBr}]}$

the simple first-order rate law described in introductory textbooks. Under these conditions, the concentration of the nucleophile does not affect the rate of the reaction, and changing the nucleophile (e.g. from H₂O to MeOH) does not affect the reaction rate, though the product is, of course, different. In this regime, the first step (ionization of the alkyl bromide) is slow, rate-determining, and irreversible, while the second step (nucleophilic addition) is fast and kinetically invisible.

However, under certain conditions, non-first-order reaction kinetics can be observed. In particular, when a large concentration of bromide is present while the concentration of water is limited, the reverse of the first step becomes important kinetically. As the SSA rate law indicates, under these conditions there is a fractional (between zeroth and first order) dependence on [H₂O], while there is a negative fractional order dependence on [Br^–]. Thus, S_N1 reactions are often observed to slow down when an exogenous source of the leaving group (in this case, bromide) is added to the reaction mixture. This is known as the common ion effect and the observation of this effect is evidence for an S_N1 mechanism (although the absence of a common ion effect does not rule it out).

Scope

The S_N1 mechanism tends to dominate when the central carbon atom is surrounded by bulky groups because such groups sterically hinder the S_N2 reaction. Additionally, bulky substituents on the central carbon increase the rate of carbocation formation because of the relief of steric strain that occurs. The resultant carbocation is also stabilized by both inductive stabilization and hyperconjugation from attached alkyl groups. The Hammond–Leffler postulate suggests that this, too, will increase the rate of carbocation formation. The S_N1 mechanism therefore dominates in reactions at tertiary alkyl centers.

An example of a reaction proceeding in a S_N1 fashion is the synthesis of 2,5-dichloro-2,5-dimethylhexane from the corresponding diol with concentrated hydrochloric acid:

As the alpha and beta substitutions increase with respect to leaving groups, the reaction is diverted from S_N2 to S_N1.

Stereochemistry

The carbocation intermediate formed in the reaction's rate determining step (RDS) is an sp² hybridized carbon with trigonal planar molecular geometry. This allows two different ways for the nucleophilic attack, one on either side of the planar molecule. If neither approach is favored, then these two ways occur equally, yielding a racemic mixture of enantiomers if the reaction takes place at a stereocenter. This is illustrated below in the S_N1 reaction of (S)-3-chloro-3-methylhexane with an iodide ion, which yields a racemic mixture of 3-iodo-3-methylhexane:

However, an excess of one stereoisomer can be observed, as the leaving group can remain in proximity to the carbocation intermediate for a short time and block nucleophilic attack. This stands in contrast to the S_N2 mechanism, which is a stereospecific mechanism where stereochemistry is always inverted as the nucleophile comes in from the rear side of the leaving group.

Side reactions

Two common side reactions are elimination reactions and carbocation rearrangement. If the reaction is performed under warm or hot conditions (which favor an increase in entropy), E1 elimination is likely to predominate, leading to formation of an alkene. At lower temperatures, S_N1 and E1 reactions are competitive reactions and it becomes difficult to favor one over the other. Even if the reaction is performed cold, some alkene may be formed. If an attempt is made to perform an S_N1 reaction using a strongly basic nucleophile such as hydroxide or methoxide ion, the alkene will again be formed, this time via an E2 elimination. This will be especially true if the reaction is heated. Finally, if the carbocation intermediate can rearrange to a more stable carbocation, it will give a product derived from the more stable carbocation rather than the simple substitution product.

Solvent effects

Since the S_N1 reaction involves formation of an unstable carbocation intermediate in the rate-determining step (RDS), anything that can facilitate this process will speed up the reaction. The normal solvents of choice are both polar (to stabilize ionic intermediates in general) and protic solvents (to solvate the leaving group in particular). Typical polar protic solvents include water and alcohols, which will also act as nucleophiles, and the process is known as solvolysis.

The Y scale correlates solvolysis reaction rates of any solvent (k) with that of a standard solvent (80% v/v ethanol/water) (k₀) through

${\displaystyle \log \left(\frac{k}{k_0}\right)=mY}$

with m a reactant constant (m = 1 for tert-butyl chloride) and Y a solvent parameter. For example, 100% ethanol gives Y = −2.3, 50% ethanol in water Y = +1.65 and 15% concentration Y = +3.2.