Which statement(s) is / are true?

A. \(3^o\) alkyl halide undergoes \(S_N1\) reaction very fast because of high stability of carbocation.

B. \(S_N1\) reacts are generally carried out in polar protic solvents

C. \(S_N1\) reactions follow first order kinetics

D. \(S_N2\) reactions follow second order kinetics

Choose the correct answer from the options given below:

A, B, C, D only

The correct answer is option 4. A, B, C, D only.

Let us look at each of the given statements:

A. \(3^o\) alkyl halide undergoes \(S_N1\) reaction very fast because of high stability of carbocation: This statement is true. 

The \(S_N1\) (Substitution Nucleophilic Unimolecular) reaction mechanism involves two main steps:

[Let us take an example of tert-butyl bromide to understand better]

1. Formation of the Carbocation: The leaving group (such as a halide) departs from the alkyl halide, resulting in the formation of a carbocation intermediate. This step is the rate-determining step, meaning the reaction rate is dependent on the concentration of the alkyl halide.

   
2. Nucleophilic Attack: The nucleophile then attacks the carbocation, leading to the formation of the final product.

Carbocation Stability

The stability of the carbocation intermediate significantly affects the rate of the \(S_N1\) reaction. Carbocation stability is influenced by several factors

Hyperconjugation: Hyperconjugation refers to the delocalization of electrons from adjacent C-H bonds into the empty p-orbital of the carbocation. Tertiary carbocations (\(3^\circ\)) have three alkyl groups attached to the positively charged carbon. These alkyl groups provide a greater number of C-H bonds that can interact with the empty p-orbital of the carbocation. This interaction stabilizes the carbocation significantly.

Inductive Effect: The inductive effect is the electron-donating or electron-withdrawing effect exerted by the alkyl groups attached to the carbocation. Alkyl groups are electron-donating through the inductive effect, which helps to stabilize the positive charge on the carbocation by pushing electron density towards the positively charged carbon.

Resonance Stabilization: Resonance stabilization occurs when the positive charge of the carbocation can be delocalized over multiple atoms via resonance structures. Although resonance is more significant in certain carbocations (like benzyl and allyl carbocations), tertiary carbocations benefit from the inductive effects and hyperconjugation as well

Comparison of Carbocation Stabilities

Primary Carbocation (\(1^\circ\)): Only has one alkyl group. The carbocation is poorly stabilized due to minimal hyperconjugation and inductive effects. It is therefore less stable and less likely to form in an \(S_N1\) reaction.

Secondary Carbocation (\(2^\circ\)): Has two alkyl groups. It is more stable than a primary carbocation but less stable than a tertiary carbocation due to moderate hyperconjugation and inductive effects.

Tertiary Carbocation (\(3^\circ\)): Has three alkyl groups. This carbocation is the most stable due to extensive hyperconjugation and inductive effects. The greater stabilization makes it easier for the carbocation to form and thus speeds up the \(S_N1\) reaction.

The rapid rate of \(S_N1\) reactions for \(3^\circ\) alkyl halides is due to the high stability of the tertiary carbocation intermediate. This stability is a result of:

Extensive hyperconjugation from three alkyl groups.

Strong inductive effects from the three alkyl groups.

These factors make the formation of the tertiary carbocation favorable, allowing the \(S_N1\) reaction to proceed quickly. In contrast, primary and secondary carbocations are less stable, which makes their formation less favorable and thus slows down the \(S_N1\) reaction.

B. \(S_N1\) reacts are generally carried out in polar protic solvents: This statement is true.

\(S_N1\) reactions are generally carried out in polar protic solvents, and here is why:

Role of Polar Protic Solvents in \(S_N1\) Reactions

Stabilization of Carbocation:Polar protic solvents have molecules with hydrogen atoms bonded to electronegative atoms like oxygen or nitrogen. Examples include water, alcohols, and carboxylic acids. These solvents can stabilize the positively charged carbocation intermediate through solvation. The solvent molecules surround and stabilize the carbocation by forming hydrogen bonds or ion-dipole interactions with it. This stabilization helps in the formation of the carbocation, which is the rate-determining step in the \(S_N1\) mechanism.

Solvation of the Leaving Group: The leaving group in \(S_N1\) reactions is typically an anion, such as a halide ion.  Polar protic solvents can solvate and stabilize the leaving group through hydrogen bonding or dipole interactions. This stabilization helps in the departure of the leaving group, facilitating the formation of the carbocation.

Facilitating the Ionization Step: In \(S_N1\) reactions, the first step involves the ionization of the alkyl halide to form a carbocation and a leaving group. Polar protic solvents, being good ionizing solvents, support this ionization process by stabilizing both the carbocation and the leaving group. This makes the ionization step more favorable and helps in the overall reaction.

Examples of Polar Protic Solvents

Water (H₂O): Commonly used in aqueous \(S_N1\) reactions, where it helps in both stabilizing the carbocation and solvating the leaving group.

Alcohols (e.g., Methanol, Ethanol): These solvents also stabilize carbocations and leaving groups through hydrogen bonding and can be used in \(S_N1\) reactions.

Carboxylic Acids (e.g., Acetic Acid): Similar to alcohols, these solvents stabilize the carbocation and the leaving group, making them suitable for \(S_N1\) reactions.

Contrast with Polar Aprotic Solvents

Polar aprotic solvents, such as acetone, DMSO (dimethyl sulfoxide), and acetonitrile, do not have hydrogen atoms bonded to electronegative atoms and do not form strong hydrogen bonds. While polar aprotic solvents are excellent at solvating cations, they are not as effective at stabilizing carbocations because they do not stabilize anions as effectively. Hence, they are generally not preferred for \(S_N1\) reactions but are suitable for \(S_N2\) reactions where nucleophiles need to be well-solvated but carbocations are not involved.

In \(S_N1\) reactions, polar protic solvents are preferred because they stabilize the carbocation intermediate and the leaving group, facilitating the reaction. They support the ionization of the alkyl halide and enhance the overall reaction rate.

C. \(S_N1\) reactions follow first order kinetics: This statement is true.

\(S_N1\) reactions follow first-order kinetics. Here’s an explanation of why this is the case:

First-Order Kinetics in \(S_N1\) Reactions

Rate-Determining Step: The rate-determining step (RDS) is the slowest step in a reaction mechanism and determines the overall reaction rate.

For \(S_N1\) Reactions: The rate-determining step is the formation of the carbocation intermediate. This step involves the departure of the leaving group from the alkyl halide, forming the carbocation and the leaving group (e.g., halide ion). This step is unimolecular, meaning the rate is determined solely by the concentration of the alkyl halide.

Rate Law: The rate law expresses the rate of the reaction as a function of the concentrations of the reactants.

For \(S_N1\) Reactions: The rate law can be expressed as:

\(\text{Rate} = k[\text{R-X}]\)

where \(k\) is the rate constant and \([\text{R-X}]\) is the concentration of the alkyl halide.

This indicates that the rate of the reaction depends only on the concentration of the alkyl halide (\(\text{R-X}\)), not on the concentration of the nucleophile or any other species.

Mechanistic Explanation:

Formation of Carbocation: In the \(S_N1\) mechanism, the first step is the formation of a carbocation intermediate by the loss of the leaving group. This step is unimolecular because it involves only the alkyl halide and proceeds with the formation of the carbocation and the leaving group.

Nucleophilic Attack: The subsequent step, where the nucleophile attacks the carbocation, is not rate-determining and occurs rapidly once the carbocation is formed. Thus, the rate of the overall \(S_N1\) reaction is determined by the concentration of the alkyl halide and not by the concentration of the nucleophile.

Since the rate-determining step in an \(S_N1\) reaction involves the formation of the carbocation and is dependent solely on the concentration of the alkyl halide, \(S_N1\) reactions exhibit first-order kinetics. This means that the rate of the reaction is directly proportional to the concentration of the alkyl halide.

D. \(S_N2\) reactions follow second order kinetics: This statement is true.

\(S_N2\) reactions follow second-order kinetics. Here's a detailed explanation:

Second-Order Kinetics in \(S_N2\) Reactions

Mechanism of \(S_N2\) Reaction: In \(S_N2\) reactions, the nucleophile directly attacks the carbon atom bonded to the leaving group in a single, concerted step. This means the bond between the carbon and the nucleophile forms at the same time the bond between the carbon and the leaving group breaks. There is no intermediate like a carbocation, and both the nucleophile and the alkyl halide are involved in the rate-determining step. Let us consider an example to understand this:

Rate-Determining Step: In \(S_N2\) reactions, the nucleophile and the alkyl halide react simultaneously in the rate-determining step. The transition state involves both the nucleophile and the leaving group interacting with the carbon atom. Since both the nucleophile and the alkyl halide are involved in the rate-determining step, the reaction rate depends on the concentration of both the nucleophile and the alkyl halide.

Rate Law: The rate law for an \(S_N2\) reaction can be expressed as:

\(\text{Rate} = k[\text{Nucleophile}][\text{Alkyl Halide}]\)

where: \(k\) is the rate constant,

\([\text{Nucleophile}]\) is the concentration of the nucleophile,

\([\text{Alkyl Halide}]\) is the concentration of the alkyl halide.

This shows that the reaction rate is dependent on both the nucleophile and the alkyl halide, making the reaction second order overall (first order with respect to each reactant).

Second-Order Kinetics: A reaction is said to follow second-order kinetics if its rate depends on the concentration of two reactants, or the square of one reactant. In the case of \(S_N2\), the rate depends on both the alkyl halide and the nucleophile. Since both the nucleophile and alkyl halide are involved in the transition state, the rate depends on the concentrations of both reactants, making it a second-order reaction.

Energy Profile: The \(S_N2\) reaction proceeds through a single transition state, where the nucleophile and the leaving group are both partially bonded to the central carbon atom. This is known as a bimolecular transition state. The transition state has a high energy due to the partial bonds, but the reaction occurs in one concerted step, without the formation of intermediates.The \(S_N2\) reaction follows second-order kinetics because the rate-determining step involves both the nucleophile and the alkyl halide. The rate is directly proportional to the concentrations of both reactants, meaning the overall reaction rate depends on the product of their concentrations. This makes the reaction second order.