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For a solution of a solute dissolved in liquid ammonia (NH3, molar mass 17 g/mol), what is the correct relation between the mole fraction X_A of the solute and the molality m of the solution?

1. 55.56*(X_A)/(1-X_A) = m
2. 58.82*(X_A)/(1-X_A) = m
3. 58.82*(1-X_A)/(X_A) = m
4. 55.56*(1-X_A)/(X_A) = m

Correct answer: 58.82*(X_A)/(1-X_A) = m

Solution

Using m = n_A per kg solvent and X_A/(1-X_A) = n_A/n_solvent, and since 1 kg ammonia = 1000/17 = 58.82 mol, m = 58.82 * X_A/(1-X_A).

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