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The SN1 reaction is a substitution reaction in organic chemistry. "SN" stands for nucleophilic substitution and the "1" represents the fact that the rate-determining step involves only one molecule (unimolecular). The reaction involves a carbocation intermediate. Some common SN1 reactions are of secondary or tertiary alkyl halides under strongly basic conditions or, under strongly acidic conditions, with secondary or tertiary alcohols.  With primary alkyl halides, the alternative SN2 reaction occurs.  Among inorganic chemists, the SN1 reaction is often known as the dissociative mechanism. Christopher Ingold et al. first proposed the reaction mechanism in 1940.

Mechanism
An example of a reaction taking place with an SN1 reaction mechanism is the hydrolysis of tert-butyl bromide with water to form tert-butyl alcohol:

This SN1 reaction takes place in three steps:

 Formation of a tert-butyl carbocation by separation of a leaving group (a bromide anion) from the carbon atom; this step is slow and reversible.

 Nucleophilic attack: the carbocation reacts with the nucleophile. If the nucleophile is a neutral molecule (that is, a solvent) a third step is required to complete the reaction. When the solvent is water, the intermediate is an oxonium ion. This reaction step is fast.

 Deprotonation: Removal of a proton on the protonated nucleophile by water acting as a base forming the alcohol and a hydronium ion. This reaction step is fast.

Because the first step is the bottleneck or "rate-determining step" chemists classify the entire reaction mechanism as SN1. Only one molecule is needed for that step.

Scope of the reaction 
Sometimes a molecule can react using either an SN1 or an SN2 mechanism.
The SN1 mechanism will win this competition when the central carbon atom is surrounded by bulky groups because such groups sterically hinder the SN2 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 says that this too will increase the rate of carbocation formation.  The SN1 mechanism therefore dominates in reactions at tertiary alkyl centers and is further observed at secondary alkyl centers in the presence of weak nucleophiles.

An example of a reaction proceeding in a SN1 way 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 SN2 to SN1.

Stereochemistry
The carbocation intermediate formed in the reaction's rate limiting step is an sp2 hybridized carbon with trigonal planar molecular geometry.  This allows two different paths for the nucleophilic attack, one on either side of the planar molecule.  If neither path is preferentially favored, these two paths will be used equally, yielding a racemic mix of enantiomers if the reaction takes place at a stereocenter.  This is illustrated below in the SN1 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 close to the carbocation intermediate for a short time and block nucleophilic attack.  This is very different than the SN2 mechanism, which does not mix the stereochemistry of the product (a stereospecific mechanism).  The SN2 mechanism always inverts the molecule's stereochemistry.

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,  SN1 and E1 reactions are competitive reactions. So, 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 SN1 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
Solvents will change the reaction rate. Since the SN1 reaction involves formation of an unstable carbocation intermediate in the rate-determining step, anything that can help this will speed up the reaction.  The normal solvents of choice are both polar (to stabilize ionic intermediates in general) and protic (to solvate the leaving group in particular). Typical polar protic solvents include water and alcohols, which will also act as nucleophiles.

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

with m a reactant constant (m = 1 for tert-butyl chloride),
Y a solvent parameter, and
k0 is the reaction rate using a solvent of 80% ethanol (measured by volume).
For example 100% ethanol gives Y = −2.3, 50% ethanol in water Y = +1.65 and 15% concentration Y = +3.2.

References

Further reading
Electrophilic Bimolecular Substitution as an Alternative to Nucleophilic Monomolecular Substitution in Inorganic and Organic Chemistry / N.S.Imyanitov. J. Gen. Chem. USSR (Engl. Transl.) 1990; 60 (3); 417-419.
Unimolecular Nucleophilic Substitution does not Exist! / N.S.Imyanitov. SciTecLibrary

Other websites
 Diagrams: Frostburg State University
 Exercise : the University of Maine
Study Organic Chemistry, Resources for Success in Organic Chemistry