Question

Menthol is a crystalline substance with a peppermint taste and odor. When 1.45 g of menthol is dissolved in 25.0 g of cyclohexane, the freezing point of the solution is lowered by 7.74 °C. Calculate the molar mass of menthol.

Answer 1

Depression in freezing point of solution is expressed as,

\(\Delta T_{f}=7.74^{\circ} \mathrm{C}\)

Model depression constant of cyclohexane is,

\(\mathrm{K}_{\mathrm{f}}=20.5^{\circ} \mathrm{Clm}\)

Molality of the solution is,

\(m=\frac{\Delta T_{f}}{K_{f}}=\frac{7.74^{\circ} \mathrm{C}}{20.5^{\circ} \mathrm{Clm}}=0.377 \mathrm{~m}\)

\(=0.377 \mathrm{~m} \circ 1 / \mathrm{kg} \mathrm{H}_{2} \mathrm{O}\)

mass of cyclohexane solvent \(=25.0 \mathrm{~g}=0.025 \mathrm{~kg}\)

Amount of menthol water \(=0.025 \mathrm{~kg} \mathrm{C}_{6} \mathrm{H}_{14} \times \frac{0.377 \mathrm{~m} \circ 1}{\mathrm{~kg} \mathrm{C}_{6} \mathrm{H}_{14}}\)

\(=0.009425 \mathrm{~mol}\)

Molar mass of menthol \(=\frac{1.45 \mathrm{~g}}{0.009425 \mathrm{~mol}}\)

\(=153.84 \mathrm{~g} / \mathrm{mol}\)