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Chapter 13: Problem 51

The molar mass of benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) determined by measuring the freezing-point depression in benzene is twice that expected for the molecular formula, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2}\). Explain this apparent anomaly.

Short Answer

Expert verified
The anomaly is due to the dimerization of benzoic acid, resulting in hydrogen-bonded pairs of molecules in the solution that effectively behave as single particles. This 'doubles' the observed molar mass compared to the molar mass of a single benzoic acid molecule.

Step by step solution

01

Analyze the given information

The theoretical molar mass of benzoic acid (\(C_{7}H_{6}O_{2}\)) can be calculated by summing the molar masses of its constituent elements: 7C (with a weight of approximately 12.011 g/mol each), 6H (1.007 g/mol each), and 2O (approx. 15.999 g/mol each). This molar mass is half the one observed in the freezing-point depression experiment conducted in benzene.
02

Investigate possible reasons

Several reasons may contribute to an observed molar mass that is larger than expected. These include association by hydrogen bonding or dimer formation, where two molecules pair together. In this case, the reason is likely the dimerization of benzoic acid in benzene.
03

Explain dimerization

Benzoic acid (\(C_{7}H_{6}O_{2}\)) is known to form dimers in solution due to hydrogen bonding between the carboxylic acid groups. A dimer consists of two benzoic acid molecules that have paired together, effectively behaving as one particle in solution. This increases the effective size of the 'particle' in the solution and therefore, the observed molar mass appears to be twice as large as the actual molar mass of a single molecule of benzoic acid.

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