Question

A solution containing 0.73 g of camphor (molar mass 152 g . mol^-1) in 36.8 g of acetone (boiling point 56.3°C) boils at 56.55°C. A solution of 0.564 g of unknown compound in the same weight of acetone boils at 56.46^oC. Calculate the molar mass of the unknown compound.

Answer 1

Calculation for K_b of camphor:

Here, mass of solvent, W_A = 36.8g

mass of solute, W_B = 0.73g

molecular mass of solute, M_B = 152

elevation in boiling point,

ΔT_b = 56.55 - 56.30 = 0.25°C

Now,

ΔT_b = K_b × (W_B × 1000)/(W_A × M_B)

K_b = (ΔT_b × W_A × M_B)/(W_B × 1000)

K_b = (0.25 × 36.8 × 152)/(0.73 × 1000)

K_b =1.9156 °C kgmol^-1

Calculation of molecular mass of unknown solute

Here, mass of solvent, W_A = 36.8g

mass of solute, W_B = 0.564g

elevation in boiling point,

ΔT_b = 56.46 - 56.30 = 0.16°C

Now,

M_b = (K_b × W_B × 1000)/(W_A × ΔT_b)

M_b = (1.9156 × 0.564 × 1000)/(36.8 × 0.16)

M_b =183.4 g