Numerical answer
Benzoic acid (molar mass ) associates into dimers in benzene. When of benzoic acid is dissolved in of benzene (taking ), the observed depression in freezing point is . The percentage of benzoic acid molecules that are present as dimers is ______. (Give the answer correct to two decimal places.)
Show answer and solution
Answer: 92.19
Molality is . If the observed depression is , then . For association with a fraction of the molecules dimerised, mol of monomer gives mol of particles, so . Therefore . The fraction of molecules present as dimers is thus . The value of is below one because the number of solute particles falls on association, which is the opposite of the dissociation case where . Had the acid not associated, would be and the depression would be ; the observed value, a little over half of that, shows that the molecules are almost completely present as hydrogen-bonded dimers, which is the reason the apparent molar mass in benzene is nearly double .
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