Quinine was the first drug widely used to treat malaria, and it remains the treatment of choice for severe cases.

Question

Quinine was the first drug widely used to treat malaria, and it remains the treatment of choice for severe cases. A solution prepared by dissolving 10.0 g of quinine in 50.0mL of ethanol has a freezing point 1.55 °C below that of pure ethanol. Determine the molar mass of quinine. Assume quinine is a nonelectrolyte. (Density of ethanol is 0.789g/mL, Kf for ethanol is 1.99 °C/m).

Answer 1

ΔT_f = i K_f m

where ΔT_f is the freezing point lowering, K_f is the freezing point constant, and m is the molality.

i (van't Hoff factor) = 1 since quinine is a non-electrolyte.

T_f of pure ethanol (T_f°) = -114.1 °C

T_f of solution = -114.1°C - 1.55°C = -115.65 °C

ΔT_f = T_f° - T_f = -114.1 - (-115.65) = 1.55 °C

m = ΔT_f / K_f = 1.55 °C / 1.99 °C/m = 0.779 m

molality, m = moles of solute / kg of solvent

solute = quinine; solvent = ethanol

Convert mL of ethanol to g using its density. Then convert g to kg.

m = d x V = 0.789 g/mL x 50.0 mL = 39.5 g x (1 kg / 1000 g) = 0.0395 kg

Use the molality and kg of ethanol to calculate moles of quinine (solute).

moles of quinine = molality x kg of solvent = 0.779 mol/kg x 0.0395 kg = 0.0308 mol quinine

Molar mass = g / mol = 10.0 g / 0.0308 mol = 325 g/mol