What conditions are present to determine whether a reaction will be sn1 or sn2?

In this explanation, I shall cite the nucleophilic substitution of the molecule with molecular formula #"C"_3"H"_7"Br"#, undergoing nucleophilic attack by the #"OH"^-# (hydroxide) complex ion.

Also remember that nucleophilic substitution reactions are in competition with elimination reactions, but the sets of conditions to favour each of these two reaction types are different to those that cause one type of nucleophilic substitution to be favoured.

1) The Resulting Carbocation

The most important thing to point out is that primary alkyl halides (also known as haloalkanes or halogenoalkanes , since that is the example being used) always undergo #"S"_N2# reactions, whilst tertiary alkyl halides always undergo #"S"_N1# reactions.

Then first, let us consider the different types of alkyl halides we have at our disposal:

Where R represents an alkyl group (#"CH"_3#, #"CH"_3"CH"_2#, etc.), primary alkyl halides are those with #"C"# atoms sharing one bond with the #"X"# (halogen) group and exactly one bond with another #"C"# atom (the other two bonds being to hydrogen atoms). Secondary - one #"C - X"# bond, exactly two #"C - C"# bonds; tertiary - one #"C - X"# bond, exactly three #"C - C"# bonds.

When an alkyl halide undergoes an #S"_N1# reaction, a carbocation forms: it is of the same type as the alkyl halide was itself (i.e. primary, secondary, tertiary). However, primary carbocations are not stable, and so will not form if there is another possible route for the reaction to take (#"S"_N2#).

There is then increasing stability of carbocations, with secondary carbocations being more stable than primary ones (and so they are able to form) and tertiary carbocations being the most stable of all.

Therefore secondary and tertiary alkyl halides are capable of undergoing #"S"_N1# reactions, but primary ones are not.

2) The Extent of Steric Hindrance

This isn't too complicated: steric hindrance is basically the amount of space the entire molecule takes up, and is related to accessibility by complexity of the molecule.

Tertiary alkyl halides have a lot of steric hindrance, since they have three alkyl groups and so lots of hydrogen atoms - this makes it very difficult for a nucleophile to attack as the halogen group leaves (#"S"_N2# reaction).

Steric hindrance decreases in 'simpler' alkyl halides: both primary and secondary alkyl halides are capable of undergoing an #"S"_N2# reactions as a result, but tertiary alkyl halides are not.

3) Nucleophilic Strength

These final two factors apply only to secondary alkyl halides: the other two types are restricted to only one mechanism, but these may undergo either and will do so in a reaction mixture. These factors only affect which mechanism will occur more frequently.

Strong nucleophiles will attack an electrophilic carbon atom very aggressively; therefore, a strong nucleophile will favour an #"S"_N2# reactionm which forms a transition state (but no detectable intermediate), rather than an #"S"_N1# reaction that would involve them having to 'wait'.

As nucleophilic strength decreases (e.g. through increase in charge), #"S"_N1# reactions begin to become more prominent.

4) Solvent Type

There are two relevant types of solvents: polar protic solvents (EX: water, #"CH"_3"OH"#, etc) have a hydrogen atom bound to an oxygen or nitrogen atom, and polar aprotic solvents (EX: dimethyl sulfoxide/DMSO, acetone, etc) that do not.

Therefore, polar protic solvents exhibit hydrogen bonding: this also allows them to form hydrogen bonds with nucleophiles dissolved in them, which impedes the reactivity of said nucleophiles.

(However polar protics are not all bad, as they really help the original alkyl halide to dissociate, since both are polar.)

Polar protic solvents will favour an #"S"_N1# reaction because, despite the nucleophile being restricted, they greatly assist in the formation of carbocations that are far more readily attacked by nucleophiles.

Polar aprotic solvents are used to favour #"S"_N2# reactions, and a polar protic solvent would only serve to impede rate by deactivating your nucleophile (factor 3).