Problem 69 - A Complete Resource Book in Chemistry for JEE Main

Question

Benzoic acid undergoes dimerization in benzene solution, the van't Hoff factor 'i' is related to the degree of association ' \(\mathrm{x}\) ' of to the acid as (a) \(\mathrm{i}=(1+\mathrm{x})\) (b) \(\mathrm{i}=(1-\mathrm{x})\) (c) \(\mathrm{i}=(1-\mathrm{x} / 2)\) (d) \(\mathrm{i}=(1+\mathrm{x} / 2)\)

Step-by-Step Solution

Answer

The correct relation is \( \mathrm{i} = 1 - \frac{x}{2} \), which is option (c).

Step 1: Understand Dimerization Concept

Dimerization involves two molecules of benzoic acid associating to form a single dimeric molecule. This implies that from 'n' individual benzoic acid molecules, the number of particles will decrease since they combine to form dimers.

Step 2: Setup Initial and Final Particle Count

Initially, we have 'n' molecules of benzoic acid. After dimerization, the number of particles decreases as two molecules associate to form one dimer. This means if 'x' fraction of molecules dimerize, the number of molecules remaining is decreased by half of the dimerized molecules.

Step 3: Calculate Van't Hoff Factor

The van’t Hoff factor 'i' is defined as the ratio of the number of particles in solution after dissociation or association to the number of formula units initially dissolved. After dimerization, the number of particles is \( n(1-\frac{x}{2}) \). Thus, \( i = \frac{n(1-\frac{x}{2})}{n} = 1 - \frac{x}{2} \).

Step 4: Identify Correct Expression

Among the options provided, the correct relation for the van’t Hoff factor considering dimerization is \( \mathrm{i} = 1 - \frac{x}{2} \). This matches with option (c).

Key Concepts

Dimerization

Dimerization is a fundamental chemical process where two identical molecules join to form a larger molecule called a dimer. This process is important when studying reactions in chemical solutions, as it influences both the physical properties and the behavior of the solution.

In the context of benzoic acid, dimerization occurs when two benzoic acid molecules bond together due to hydrogen bonding. This bonding reduces the total number of particles in the solution, which affects the van’t Hoff factor, an important parameter in calculating colligative properties like boiling point elevation or freezing point depression.

In simple terms, if you start with 'n' individual molecules of benzoic acid, after dimerization, the number of particles in the solution reduces because two molecules become one dimer. This reduction in particle number is crucial for understanding the solution's behavior and characteristics.

Benzoic Acid

Benzoic acid is an organic compound widely used in food preservation, medicine, and the production of various chemicals. Its molecular formula is C₇H₆O₂. In solutions, particularly organic solvents like benzene, benzoic acid exhibits interesting behaviors such as dimerization.

This compound can form hydrogen bonds, which are interactions between the hydrogen atom of one molecule and the oxygen atom of another molecule. This hydrogen bonding is the reason behind the dimerization process of benzoic acid in benzene.

When dissolved in a non-polar solvent like benzene, benzoic acid molecules tend to associate more readily to form dimers. This association decreases the effective concentration of the acetic molecules, influencing the solution's colligative properties.

Degree of Association

The degree of association, often denoted as 'x', is a measure of the extent to which molecules associate in a solution. It is expressed as a fraction or percentage, indicating the proportion of molecules that combine to form dimers or larger aggregations.

In the case of benzoic acid in benzene, the degree of association represents how much of the acid undergoes dimerization.

• A degree of association of 0 means no dimerization (all molecules remain separate).
• An association degree of 1 means full dimerization (all molecules have formed dimers).

Understanding the degree of association helps in predicting and calculating the van’t Hoff factor, which impacts the colligative properties of the solution.

The van’t Hoff factor 'i', the ratio of actual particles to initial particles in a solution, can be determined using the degree of association. For benzoic acid undergoing dimerization, the factor is calculated as shown: \[ i = 1 - \frac{x}{2} \].
This formula shows how a partial association (0 \< x \< 1) decreases the number of effective particles due to dimer formation.