Question

Menthol is a crystalline substance with a peppermint taste and odor. When 1.19 g of menthol is dissolved in 25.0 g of cyclohexane, the freezing point of the solution is lowered by 6.34 ∘ C. Look up the freezing point and K f constant for cyclohexane in the Colligative Constants table. Calculate the molar mass of menthol.

Solvent	Formula	Kf value* (°C/m)	Normal freezing point (°C)	Kb value (°C/m)	Normal boiling point (°C)
water	H2O	1.86	0.00	0.512	100.00
benzene	C6H6	5.12	5.49	2.53	80.1
cyclohexane	C6H12	20.8	6.59	2.92	80.7
ethanol	C2H6O	1.99	–117.3	1.22	78.4
carbon tetrachloride	CCl4	29.8	–22.9	5.03	76.8
camphor	C10H16O	37.8	176

Answer 1

Mass of menthol is 1.19 g

Menthol is a non-electrolyte and hence has van't Hoff factor, i =1.

Now, the depression in freezing point for the solution is given as

Now, the depression in freezing point is calculated as follows:

Where i = van't Hoff factor of the solute (here for menthol, i = 1)

molal freezing point depression constant of solvent (for cyclohexane, )

molality is the moles of solute per kg of solvent where 1 mol/kg = 1 m

Now, we can write

Hence, the molality of the solution is 0.3048 mol/kg.

i.e. there are 0.3048 moles of menthol per kg of cyclohexane.

Given that the mass of cyclohexane = 25.0 g = 0.0250 kg, we can calculate the moles of menthol present in the solution as follows:

Hence, 0.00762 mol of menthol must be equivalent to 1.19 g of menthol.

Hence, the molar mass of menthol can be calculated as

Hence, the molar mass of menthol is about 156.2 g/mol.