A quantity of 7.85 g of a compound having the empirical formula C₅H₄ is dissolved in 301 g of benzene. The freezing point is 1.05 ° C below that of pure benzene (k_f = 5.12 ° C/m). The molar mass of the species in solution in benzene is:

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The freezing point depression formula is ΔTf = i * Kf * m, where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent, and m is the molality of the solution. Given ΔTf = 1.05 °C and Kf for benzene = 5.12 °C/m, we can find the molality (m) of the solution. First, calculate molality: m = ΔTf / Kf = 1.05 °C / 5.12 °C/m = 0.205 mol/kg. Then, to find the molar mass of the solute, we use the mass of the solute (7.85 g) and the mass of the solvent (301 g, which is 0.301 kg) to find the number of moles of solute: moles of solute = mass of solute / molar mass of solute. Since molality (m) = moles of solute / kg of solvent, rearranging gives molar mass of solute = mass of solute / (molality * kg of solvent) = 7.85 g / (0.205 mol/kg * 0.301 kg) = 127 g/mol.

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