The molecular weight of benzoic acid in benzene as determined by depression in freezing point method corresponds to:

Dimerization of benzoic acid

The correct answer is option 2. Dimerization of benzoic acid.

Let us delve into the explanation of how the depression of freezing point method determines the molecular weight of benzoic acid in benzene and why dimerization is a relevant factor:

Depression of Freezing Point Method:

The depression of freezing point method is a colligative property, which means it depends on the number of particles (ions or molecules) present in a solution, not their chemical identity.

Benzoic Acid in Benzene:

Benzoic acid \((C_6H_5COOH)\) is a weak acid that can form associations or aggregates in non-polar solvents like benzene due to its ability to participate in hydrogen bonding interactions between molecules. In benzene, which is non-polar, benzoic acid molecules tend to associate in clusters due to these interactions.

Role of Dimerization:

Dimerization refers to the association of two molecules of benzoic acid to form a dimer. This association is stabilized by intermolecular forces, particularly hydrogen bonding between carboxylic acid groups \((-COOH)\).

Effect on Freezing Point Depression: When benzoic acid molecules dimerize in benzene:

Each dimer effectively acts as a single particle in terms of colligative properties like freezing point depression. This means that the number of effective particles contributing to the freezing point depression is reduced compared to the number of individual benzoic acid molecules dissolved in the solvent.

Molecular Weight Determination: In the depression of freezing point method:

The extent of freezing point depression is directly proportional to the concentration of solute particles in solution. For benzoic acid in benzene, the observed freezing point depression corresponds to the effective number of particles in solution. Since dimerization reduces the effective number of particles (because two molecules are now considered as one in terms of colligative properties), the observed depression in freezing point suggests a higher molecular weight than expected for monomeric benzoic acid.

Conclusion:

In summary, the molecular weight of benzoic acid in benzene as determined by the depression of freezing point method corresponds to the presence of dimers formed through dimerization. The dimerization reduces the effective number of particles contributing to the freezing point depression, leading to an apparent higher molecular weight. Therefore, the correct explanation for the determination of molecular weight in this context is: Dimerization of benzoic acid.