The molar mass of benzoic acid (C6H5COOH) determined by measuring the freezing-point depression in benzene is twice what we would expect for the molecular formula, C7H6O2. Explain this apparent anomaly.
The Correct Answer and Explanation is:
The apparent anomaly in the molar mass of benzoic acid being twice the expected value when determined using freezing-point depression in benzene is due to dimerization of benzoic acid molecules in the nonpolar solvent benzene.
In nonpolar solvents like benzene, benzoic acid tends to form dimers through hydrogen bonding between the carboxylic acid groups. Two molecules of benzoic acid associate to form a hydrogen-bonded pair. This dimer behaves as a single unit in solution, which effectively halves the number of solute particles in the solution compared to what would be expected if all benzoic acid molecules remained as individual monomers.
Freezing-point depression is a colligative property, which means it depends on the number of solute particles in a given amount of solvent, not their identity or size. If dimerization occurs, the number of solute particles is reduced. This leads to a smaller freezing-point depression than expected for the undimerized form, and as a result, the calculated molar mass appears larger—specifically, approximately double the actual molar mass of benzoic acid.
The dimerization of benzoic acid in benzene is favored because benzene is nonpolar and does not strongly solvate the polar carboxylic acid groups. This lack of solvation encourages the acid molecules to associate with each other through hydrogen bonding rather than disperse individually in the solvent.
Therefore, the measured molar mass is about 242 g/mol, which is roughly twice the actual molar mass of 122 g/mol. This doubling provides strong evidence that benzoic acid exists predominantly as dimers in benzene solution, explaining the discrepancy between expected and observed values.
