Question

A solution containing 0.513 g of naphthalene (molar mass = 128) in 50 g of CCl₄ gives a boiling point elevation of 0.402°C, while a solution of 0.625 g of an unknown solute gives a boiling point elevation of 0.650°C. Find the molecular mass of the unknown solute.

Answer 1

Given: For naphthalene (known solute):

Mass of solute (w₁) = 0.513 g

Molar mass (M₁) = 128 g/mol

Solvent mass = 50 g = 0.050 kg

Elevation in boiling point `(Delta T_(b_1))` = 0.402°C

For unknown solute:

Mass of solute (w₂) = 0.625 g

Same solvent mass = 50 g = 0.050 kg

Elevation in boiling point `(Delta T_(b_2))` = 0.650°C

Molar mass (M₂) = ?

Since the same solvent and mass is used, we can write:

`(Delta T_(b_1))/(Delta T_(b_2)) = (w_1//M_1)/(w_2//M_2)`

`0.402/0.650 = (0.513//128)/(0.625//M_2)`

`0.402/0.650 = (0.513 * M_2)/(0.625 * 128)`

`0.402/0.650 = (513 M_2)/80000`

⇒ `0.6185 = (513 M_2)/80000`

⇒ `M_2 = (0.6185 xx 80000)/513`

M₂ = 96.44 g/mol

∴ The molecular mass of the unknown solute is 96.44 g/mol.