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Saturday, February 11, 2017

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
PA = XA x P°A

 So the reduction in vapour pressure is given as
Δ PA = P°A - PA
i.e., Δ PA = P°A (1 - XA) = P°AXB

i.e., therefore, relative lowering of vapour pressure ΔPA/PA is equal to mole fraction of solute XB.

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

Relative lowering of vapour pressure
For dilute solution:


Where, wA = mass of solvent
MA = Molar mass of solvent
WB = mass of solute
MB = 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.
ΔTb = Tb - T°b
= elevation in boiling point
Tb= boiling point of solution
Tb0 = boiling point of pure solvent
Elevation of boiling point
For dilute solution:

Tb α m
Δ Tb = Kb x m
m = molality
Kb = molal elevation constant (Ebullioscopic Constant). Units: K kg mol-1
R = gas constant
M1 = molar mass of solvent
ΔvapH = 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.
ΔTf = T°f - Tf    
ΔTf = depression in freezing point
f = freezing point of pure solvent
Tf = freezing point of solution
Depression of freezing point
For dilute solution:

Δ Tf α m
Δ Tf = Kf x m
Kf = Molal depression constant (Cryoscopic constant). Units: K kg mol¯¹
R = gas constant
M1= molar mass of solvent
ΔfusH = enthalpy of fusion

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