Colligative properties of solutions

There are 4 colligative properties namely:
1. Vapor pressure lowering
2. Boiling point elevation
3. Freezing point depression
4. Osmotic pressure

The similarity among these 4 colligative properties is that, they all depend on the amount of solute present, and not on the identity of the solute. The necessary equations involved in colligative properties are:
1. For Vapor pressure lowering:

P = xsolvent P0
Where P = vapor pressure of solution
P0 = vapor pressure of pure solvent
xsolvent = mole fraction of the solvent

xsolvent = moles of solvent/(moles solvent + moles solute)

2. For Boiling point elevation
Tb = Kbm
Where Tb = boiling point elevation
Kb = boiling point elevation constant (specific for a given solvent)
m = molality of solution
m = moles solute/kilogram solvent

3. For Freezing point depression
Tf = Kfm
Where Tf = freezing point depression
Kf = freezing point depression constant (specific for a given solvent)
m = molality of solution
m = moles solute/kilogram solvent

4. Osmotic pressure is the pressure associated with the movement of water from a dilute solution (contains high amount of water as solvent) to a concentrated solution (contains low amount of water as solvent) across a semi-permeable membrane.

For Osmotic pressure ():
 = nRT / V
Where n = number of moles of solute
R = 0.08206 L-atm/K.mole
T = temperature
V = volume of solution

Obviously, from the equations above, the common factor among colligative properties is the number of moles of solute present in the solution. It is evident that the number of moles of solute dictates the magnitude of a certain colligative property. It determines the extent at which vapor pressure of the solution is lowered, boiling point is increased, freezing point is lowered, and also the magnitude of osmotic pressure of the solution.

ON REVERSE OSMOSIS
Osmosis can be driven in reverse direction, i.e. movement of water from a concentrated solution (contains low amount of water as solvent) to a dilute solution (contains high amount of water as solvent) across a semi-permeable membrane.
Reverse osmosis is related to colligative properties of solution since in order to carry it out, the amount of pressure to be applied should be greater than the osmotic pressure of the solution.
Reverse osmosis is a popular technique in water purification. For instance, seawater can be bottled for drinking after undergoing purification process by reverse osmosis.

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