Colligative Properties

Properties of solution that depend on the ratio of no: of solute particles to the total no: of particles in the solution.

1. Relative lowering of vapour pressure:

⇒ Vapour pressure of solvent in solution is less than that of pure solvent.

According to Raoult’s law

P_A = X_A x P°_A

⇒ So the reduction in vapour pressure is given as

Δ P_A = P°_A - P_A

i.e., Δ P_A = P°_A (1 - X_A) = P°_AX_B

i.e., therefore, relative lowering of vapour pressure ΔP_A/P_A is equal to mole fraction of solute X_B.

⇒ If two or more non-volatile solutes are present then it is equal to sum of the mole fraction of the solutes

For dilute solution:

Where, w_A = mass of solvent

M_A = Molar mass of solvent

W_B = mass of solute

M_B = Molar mass of solute

2. Elevation of boiling point:

⇒ A liquid boils at a temperature where its vapour pressure becomes equal to atmospheric pressure.

⇒ Since in a solution the vapour pressure of solvent is reduced, the temperature needs to be raised to increase the vapour pressure to atmospheric pressure.

⇒ Therefore, the boiling point of solution is always higher than that of pure solvent.

ΔT_b = T_b - T°_b

= elevation in boiling point

T_b= boiling point of solution

T_b⁰ = boiling point of pure solvent

For dilute solution:

T_b α m

Δ T_b = K_b x m

m = molality

K_b = molal elevation constant (Ebullioscopic Constant). Units: K kg mol^-1

R = gas constant

M₁ = molar mass of solvent

Δ_vapH = enthalpy of vaporization

3. Depression of freezing point:

⇒ A solution freezes when its vapour pressure becomes equal to the vapour pressure of pure solid solvent.

⇒ As the vapour pressure of a solvent decreases when a non-volatile solute is added, the freezing point of solvent decreases.

ΔT_f = T°_f - T_f    

ΔT_f = depression in freezing point

T°_f = freezing point of pure solvent

T_f = freezing point of solution

For dilute solution:

Δ T_f α m

Δ T_f = K_f x m

K_f = Molal depression constant (Cryoscopic constant). Units: K kg mol¯¹

R = gas constant

M₁= molar mass of solvent

Δ_fusH = enthalpy of fusion