Discussion
3 g of benzoic acid dissolved in 25 g of benzene shows a depression in freezing point equal to 2.5 K. What is the experimental molar mass of benzoic acid in benzene? (Molal depression constant for benzene is 5 K kg mol-1).
Answer: C
The experimental molar mass is 240 g mol-1.
From \(\Delta T_{f} = K_{f}m\) with \(m = \frac{w_{2} \times 1000}{M_{2} \times w_{1}}\):
\[ \begin{aligned} M_{2} &= \frac{K_{f} \times w_{2} \times 1000}{\Delta T_{f} \times w_{1}} \\ &= \frac{5 \times 3 \times 1000}{2.5 \times 25} = 240\ \text{g mol}^{-1} \end{aligned} \]
This is about twice the true molar mass of benzoic acid, 122 g mol-1, because in benzene benzoic acid forms hydrogen-bonded dimers, halving the number of particles. 122 is the formula value, not the experimental one, and 244 is exactly twice it.
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