Question

A mixture of 1 g naphthalene (Mol. mass 128) and 10 g camphor melts at 147°C whereas pure camphor melts at 177.5°C. What is cryoscopic constant (K_f) of camphor?

Answer 1

Given: Mass of solute (naphthalene) = 1 g

Molar mass of naphthalene = 128 g/mol

Mass of solvent (camphor) (w₁) = 10 g

Melting point of pure camphor `(T_f^circ)`= 177.5°C

Melting point of solution (T_f) = 147°C

Depression in freezing point ΔT_f = 177.5 − 147 = 30.5°C

We know that

ΔT_f​ = K_f ​⋅ m

⇒ `Delta T_f = K_f * (w_2 xx 1000)/(M_2 xx w_1)`

⇒ `K_f = (Delta T_f xx M_2 xx w_1)/(w_2 xx 1000)`

= `(30.5 xx 128 xx 10)/(1 xx 1000)`

= `3904/1000`

= 39.04°C

∴ The cryoscopic constant of a camphor is 39.04°C kg/mol.