Problem 96 - A Complete Resource Book in Chemistry for JEE Main

Question

The order of reactivities of the following alklyl halides for a \(\mathrm{S}_{\mathrm{N}}^{2}\) reaction is (a) \(\mathrm{RF}>\mathrm{RCl}>\mathrm{RBr}>\mathrm{RI}\) (b) \(\mathrm{RF}>\mathrm{RBr}>\mathrm{RCl}>\mathrm{RI}\) (c) \(\mathrm{RCl}>\mathrm{RBr}>\mathrm{RF}>\mathrm{RI}\) (d) \(\mathrm{RI}>\mathrm{RBr}>\mathrm{RCl}>\mathrm{RF}\)

Step-by-Step Solution

Answer

The order of reactivity for \( \mathrm{S}_{\mathrm{N}}^{2} \) reactions is option (d): \( \mathrm{RI} > \mathrm{RBr} > \mathrm{RCl} > \mathrm{RF} \).

Step 1: Understand Polarizability and Bond Strength

The ability of an alkyl halide to participate in an \( \mathrm{S}_{\mathrm{N}}^{2} \) reaction is influenced by its bond strength and polarizability. A stronger bond and less polarizable halogen make \( \mathrm{S}_{\mathrm{N}}^{2} \) reactions less favorable.

Step 2: Analyze Bond Strength of Alkyl Halides

In alkyl halides, the bond strength to the carbon atom decreases in the order \( \text{C-F} > \text{C-Cl} > \text{C-Br} > \text{C-I} \). Stronger bonds resist bond-breaking steps required in \( \mathrm{S}_{\mathrm{N}}^{2} \) reactions.

Step 3: Assess Polarizability of Halides

The polarizability of halides increases from fluorine to iodine. Iodine is the most polarizable and weakest bonded, which facilitates \( \mathrm{S}_{\mathrm{N}}^{2} \) reactions by a better ability to accommodate developing charges in the transition state.

Step 4: Determine Optimal Conditions for \( \mathrm{S}_{\mathrm{N}}^{2} \) Reaction

For \( \mathrm{S}_{\mathrm{N}}^{2} \) reactions, weaker bonds and higher polarizability are favorable. Therefore, alkyl iodides (\( \mathrm{RI} \)) are most reactive, followed by bromides (\( \mathrm{RBr} \)), then chlorides (\( \mathrm{RCl} \)), and finally fluorides (\( \mathrm{RF} \)).

Step 5: Compare Provided Options

The correct order, based on decreasing reactivity for \( \mathrm{S}_{\mathrm{N}}^{2} \) reactions, is \( \mathrm{RI} > \mathrm{RBr} > \mathrm{RCl} > \mathrm{RF} \), matching option (d).

Key Concepts

Alkyl Halides

Alkyl halides are organic compounds where a halogen atom (like fluorine, chlorine, bromine, or iodine) is bonded to an alkyl group—the carbon chain. This bond, known as the carbon-halogen bond, plays a crucial role in chemical reactions, including the SN2 reaction.
Alkyl halides are important in organic chemistry because they can undergo various reactions due to the presence of the halogen atom. The halogens have different properties, often dictating the outcome and the rate of a reaction.

• Fluorine, chlorine, bromine, and iodine are the halogens typically involved in forming alkyl halides.
• The halogen's electronegativity and size affect the alkyl halide's chemical properties.

Alkyl halides' differing reactivities in SN2 reactions largely depend on these chemical properties.

Reactivity Order

In SN2 reactions, the order of reactivity of alkyl halides follows their tendency to participate in a nucleophilic substitution reaction. The defining characteristic of an SN2 reaction is a single-step mechanism where a nucleophile attacks the carbon center, displacing the halide.

• The reactivity is influenced by the strength of the carbon-halogen bond and the ability of the halogen to stabilize an evolving charge.
• Fluoride ions have the strongest C-X bonds, making them the least reactive in SN2 reactions.

In contrast, iodine has the weakest bond, leading to a higher reactivity order.

Thus, the reactivity of alkyl halides in SN2 reactions is typically observed as: \[ \text{RI} > \text{RBr} > \text{RCl} > \text{RF} \] where RI is most reactive due to its weak bond and high polarizability.

Polarizability

Polarizability refers to the ability of an atom or molecule to be distorted by an approaching electric field. In the context of alkyl halides, it concerns how the electron cloud around the halogen can stabilize a transition state during an SN2 reaction.

• Iodine, being the largest and most polarizable halogen, accommodates transition states more effectively than bromine or chlorine.
• This increased polarizability results in a smoother transition state, leading to faster reaction rates.

It's essential to understand that high polarizability contributes to the increasing reactivity as you move down the halogen group in the periodic table. Iodine's high polarizability is a key reason RI ranks highest in reactivity among alkyl halides.

Bond Strength

Bond strength in alkyl halides is determined by the strength of the carbon-halogen bond. The stronger this bond, the more energy required to break it during a chemical reaction.

• In general, bond strength decreases as you move down the group from fluorine to iodine. This trend is due to increasing atomic size and decreasing overlap between atomic orbitals.
• Therefore, C-F bonds are the strongest, and C-I bonds are the weakest in alkyl halides.

Understanding bond strength helps predict reaction behavior in SN2 processes. Weaker bonds are more readily broken, explaining why RI is most reactive, and RF is the least reactive. The understanding of these bond strength variations is vital for predicting the outcome of SN2 reactions with different alkyl halides.