Inversion of configuration of alkyl halides takes place:

In \(S_N2\) reaction

The correct answer is option 2. In \(S_N2\) reaction.

Inversion of configuration of alkyl halides primarily occurs in nucleophilic substitution reactions.

Let us analyze each option:

1. In \(S_N1\) reaction: In \(S_N1\) (substitution nucleophilic unimolecular) reactions, the alkyl halide undergoes dissociation to form a carbocation intermediate before the nucleophilic attack. Since the nucleophile can attack from either side of the planar carbocation, both retention and inversion of configuration are possible. However, inversion predominates only if the nucleophile attacks from the opposite side of the leaving group. Thus, inversion may occur, but it's not exclusive to \(S_N1\) reactions.

2. In \(S_N2\) reaction: In \(S_N2\) (substitution nucleophilic bimolecular) reactions, the nucleophile attacks the alkyl halide at the same time as the leaving group leaves. This concerted mechanism leads to inversion of configuration at the stereocenter, as the incoming nucleophile replaces the leaving group from the side opposite to the leaving group's departure. Therefore, inversion is a characteristic feature of \(S_N2\) reactions.

3. In electrophilic substitution: In electrophilic aromatic substitution reactions, such as the Friedel-Crafts reaction, inversion of configuration does not typically occur. These reactions involve the addition of an electrophile to an aromatic ring, where the substitution usually takes place without inversion of configuration.

4. In elimination reaction: Elimination reactions, such as \(E_2\) (bimolecular elimination), involve the removal of a leaving group and a proton from adjacent carbons to form a double bond. In these reactions, there is no direct inversion of configuration at a stereocenter, as the reaction proceeds through the concerted removal of atoms to form a new bond.

Therefore, the correct option is 2. In \(S_N2\) reaction, where inversion of configuration is a characteristic feature due to the concerted mechanism of nucleophilic substitution.

Additional Information:

Substitution Nucleophilic Bimolecular (S_N2)

The reaction between methyl chloride (CH₃Cl) and hydroxide ion to yield methanol (CH₃OH) and chloride ion follows a second order kinetics, i.e., the rate depends upon the concentration of both the reactants.

The rate of the reaction is expressed as:

Rate = k[CH₃Cl][OH^–]

In fact, methyl or primary alkyl halides follow this type of mechanism and it may, in general, be written as

Rate = k[RX] [OH^–]

This reaction is also called nucleophilic substitution bimolecularbecause two molecules take part in determining the rate of the reaction. It is written as S_N2, short form for substitution nucleophilic bimolecular.

This type of reaction occurs in single (concerted) step through the formation of a transition state. In this mechanism, the nucleophile, OH^– attacks the partially positively charged carbon atom of carbon halogen bond from the direction 180° away from the halogen atom i.e., from the backside. This leads to a transition state with a partially formed C—OH bond and a partially broken C—Cl bond. This process is a one-step reaction. In the transition state, the negative charge is shared by both the incoming nucleophile as well as outgoing chloride. Hydroxide has a diminished negative charge because it has begun to share its electrons with carbon while chlorine has developed a partial negative charge because it has partly removed a pair of electrons from carbon. Therefore, both OH and Br have a partial negative charge i.e., δ^–. The remaining three bonds to carbon in the transition state adopt a planar arrangement. This arrangement may be described as the C—H bonds being arranged like the spokes of a wheel with C—OH and C—Br bonds lying along the axle.

It is clear from the above one-step mechanism, that the formation of the transition state is a rate-determining step, and therefore, the rate of the reaction depends upon the concentration of both alkyl halide and \(OH^-\). Hence, it is a second order reaction or a bimolecular reaction.

It is interesting to note that in S_N2 reactions, the attack of the nucleophile occurs from the back side and the leaving group leaves from the front side. As a result, S_N2 reactions are always accompanied by inversion of configuration. This inversion of configuration is also called Walden inversion.