COLLIGATIVE PROPERTIES (Relative lowering of vapour pressure)

(Latin : co means together, ligare means to bind)

The properties of the solutions which depend only on the number of solute particles but not on the nature of the solute are called colligative properties.

There are four colligative properties :

1.      Relative lowering of vapour pressure

2.      Elevation of boiling point

3.      Depression of freezing point

4.      Osmotic pressure.

Relative lowering of vapour pressure

As we know that when we add a non-volatile solute to the solvent to form a solution, the vapour pressure of solution decreases.

Let P_A is the pressure of solution (because vapour pressure of solution is only due to the vapour pressure of water vapour, P_solution =P_A) , P_A⁰ be the vapour pressure of solvent, x_A and x_B are the mole fractions of solvent and solute in solutions.

Therefore lowering of vapour pressure,  

∆P_A = P_A⁰ - P_A(Difference of vapour pressure of pure solvent and vapour pressure of solution)

P_A = P_A⁰ x_A   (According to Raoult’s law)

∆P_A = P_A⁰ - P_A⁰ x_A 

∆P_A = P_A⁰ (1- x_A )

∆P_A = P_A⁰ x_B

∆P_A / P_A⁰ = x_B ,     ∆P_A / P_A⁰ = Relative lowering of pressure.

(P_A⁰ - P_A)/ P_A⁰ = x_B

(P_A⁰ - P_A)/ P_A⁰ = n_B / n_A + n_B

If n_B ‹‹ n_A , n_A can be neglected from denominator.

(P_A⁰ - P_A)/ P_A⁰ = n_B / n_A

(P_A⁰ - P_A)/ P_A⁰ = w_B M_A / w_A M_B

where w_A  and w_B are the masses of solvent and solute respectively.

for better explanation go through the video

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