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# Colligative Properties

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## Colligative Properties :-

Colligative properties are properties of solutions that depends on the ratio of the number of solute particles to the number of solvent molecules in a solution and not on the nature of the chemical species present .

• The vapour pressure of solution decreases when a non – volatile solute is added to a volatile solvent .
• There are following colligative properties of solutions which are connected with such decrease of vapour pressure .
• ( 1 ) Relative lowering of vapour pressure .
• ( 2 ) Depression of freezing point .
• ( 3 ) Elevation of boiling point .
• (4 ) Osmotic pressure.

All these colligative properties have the common characteristics that depend upon the number of Solute particles . since these properties are bound together through their common origin they are called colligative properties .

## Relative lowering of Vapour Pressure :-

In a Solution containing several non – volatile solutes , the lowering of the vapour pressure depends on the sum of the mole fraction of different solutes .

P₁ = X₁ P₁⁰

Reduction of Vapour Pressure of Solvent

∆P₁ = P₁⁰ – P₁ = P₁⁰ – P₁ X₁

= P₁ ( 1 – X₁ )

Knowing that X₂ = 1 – X₁

∆P₁ = X₂ P₁⁰

The equation can be written as

∆P₁ / P₁⁰ = ( P₁⁰ – P₁ ) /P₁⁰ = X₂

This equation is called relative lowering of Vapour Pressure and is equal to the mole fraction of the Solute .

i . e . ( P₁⁰ – P₂ ) / P₁ = n₂ / n₁ + n²

since X₂ = n₂ / n₁ + n₂

Here n₁ and n₂ are the number of moles of Solvent and Solute respectively .

For dilute Solution n₂ << n₁

Then

( P₁⁰ – P₁ ) / P₁ = n₂ / n₁

Or ( P₁⁰ – P₁ ) / P₁⁰ = W₂ X M₁ / W₁ x M₂

Here W₁ and W₂ are the masses , M₁ and M₂ are the molar masses of the Solvent and Solute respectively .

## Elevation of boiling point :-

The elevation of boiling point also depends on the number of Solute molecules rather than their nature .

A Solution of 1 gm of water boils at 373·52 K at one atmospheric Pressure .

Let T⁰₁ be the boiling point of pure Solvent and T₁ be the boiling point of Solution .

The increase in boiling point

∆T₁ = T₁ – T₁⁰ is known as elevation of boiling point .

• For dilute Solutions the elevation of boiling point is directly proportional to the molar concentration of the Solute in a Solution .

Thus

∆T₁ α m

∆T₁ = K₁ m

Here m is molality , K₁ is called boiling point elevation constant its SI unit is K kg mol⁻¹

• If W₂ gm of Solute of molar mass M₂ is dissolved in W₁ gm of Solvent , then molality

m = ( W₁ / M₂ ) / ( W₁ / 1000 ) = W₂ x 1000 / M₂ x W₁

Substituting the value of molality in equation

∆T₁ = K₁ m

∆T₁ = ( K₁ x W₂ x 1000 ) / M₂ x W₁

M₂ = ( K₁ x W₂ x 1000 ) / ∆T x W₁

## Depression of Freezing point :-

The freezing point of a substance may be defined as the temperature at which the vapour pressure of the substance in its liquid phase is equal to its vapour pressure in the solid phase .

According to Raoult’s law when a non – volatile solid is added to the solvent become equal to that of solid solvent at lower temperature .

Thus the freezing point of the solvent decreases .

Let T⁰f be the freezing point of pure Solvent and Tf be its freexing point when non- volatile Solute is dissolved in it .

The decrease in freezing point

∆Tf = T⁰f – Tf is known as depression in freezing point .

• Depression of freezing point for dilute Solution ( Ideal Solution ) is directly proportional to molality ( m ) of the Solution

I .e . ∆Tf α m

Where Kf is known as freezing point depression constant . The unit molar depression constant is K Kg mol⁻¹ . Its value is depends on the nature of the Solvent .

• If W₂ gm of the Solute having molar mass as M₂ , present in W₁ gm of Solvent , produce depression in freezing point ∆Tf of the Solvent then molality of the Solute is given by the equation –

m = ( W₂ / M₂ ) / W₁ / 1000

or ( m = W₂ x 100 ) / M₂ x W₁

Substituting this value of molality in equation ∆Tf = Kf m

∆Tf = Kf x W₂ x 1000 / M₂ x W₁

## Osmotic Pressure :-

The flow of the solvent from its side to solution side across a semipermeable membrane can stopped if some extra pressure is applied on the solution . This pressure that just stops the flow of solvent is called Osmotic pressure of the solution.

I . e . The Osmotic pressure of a solution is the the excess pressure that must be applied to a solution to prevent osmosis .

### Osmosis :-

If the semipermeable membrane is placed between the solvent and solution , the solvent molecules will flow through the membrane from pure solvent to the solution . This process of flow of the solvent is called osmosis .

#### Semipermeable membrane :-

Semipermeable membrane is the layer that only selected molecules can pass through . It can be both biological and artificial .

Assume that only solvent molecules can pass through these membranes .

• Osmotic pressure is directly proportional to the molarity ( C ) of the solution at a given temperature ( T ).

I .e .

π = C R T

Here π is the Osmotic Pressure and R is the Gas constant .

If n₂ is moles of Solutes and V is the Volume of Solution then Osmotic Pressure

π = n₂ R T / V

### Reverse Osmosis and water purification :-

The direction of osmosis can be reversed if a pressure larger than the osmotic pressure is applied to the solution side . I . e . the pure solvent flows out of the solution through the semipermeable membrane . This phenomenon is called reverse osmosis .

• Reverse osmosis is used in desalination of sea water . A schematic set up for the process in the above figure , when pressure more than osmotic pressure is applied , pure water is squeezed out of the sea water through the membrane .
• The pressure required for the reverse osmosis is quite high .
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