Question

When a 33.8-g sample of an unknown compound is dissolved in 500. g of benzene, the freezing point of the resulting solution is 3.77°C. The freezing point of pure benzene is 5.48°C, and Kf for benzene is 5.12°C/m. Calculate the molar mass of the unknown compound.

Answer 1

The molar mass of the unknown compound is 202.40 g/mol.

Step-by-step explanation:

Let the molar mass of compound be M.

The depression in freezing point is given by:

`\Delta T_f=K_f* m`

`\Delta T_f=T-T_f`

where,

`\Delta T_f`= change in boiling point = 0.81 K

`T_f`=Boiling point of the solution = 3.77°C

T = freezing point of the pure solvent here benzene =5.48°C

`K_f`= freezing point constant = 5.12°C/m

m = molality =
`\frac{\text{Mass of solute}}{\text{Molar mass of solute}\text{Mass of solvent in kg}}`

`\Delta T_f=5.48^oC-3.77^oC=1.71^oC`

`1.71^oC=5.12^oC/m* (33.8 g)/(M* 0.500 kg)`

M = 202.40 g/mol

The molar mass of the unknown compound is 202.40 g/mol.