# Colligative Properties

Colligative Properties

Colligative properties are those properties which depend only upon the number of solute particles in a solution irrespective of their nature.

A – solvent

B - solute

Relative Lowering of Vapour Pressure

·         It is the ratio of lowering in the vapour to vapour pressure of the pure solvent.

·         The relative lowering of the vapour pressure of the solution containing a nonvolatile solute is equal to the mole fraction of solute in the solution.

If the vapour pressure of the solution is P1, the vapour pressure of the pure solvent is P10 and mole fraction of solvent is x1, then according to Raoult’s Law:

P1 = P10 x1

The decrement in vapour pressure of solvent that is, Δ P1 will be

Decrement in Vapour Pressure = Vapour Pressure of Pure Solvent – Vapour Pressure of Solvent

Δ P1 = P10 – P1

Substituting P1 = P10 x1 in the above relation we get,

Δ P1 = P10 –  P10 x1

Δ P1 = P10 (1 – x1)

Since the sum of mole fraction of solute ( x2) and mole fraction of solvent ( x1) is 1, we can write

1 – x1 = x2

Δ P= P10 x2

It is obvious that decrease in vapour pressure depends on mole fraction of solute (x2) as mentioned by Raoult’s.

The equation can be re-written as:

The term is called Relative Lowering in vapour pressure and equals to mole-fraction of the solute.

If n1 and n2 are the respective moles of solute and solvent, then we can re-write the equation as:

If the solution is quite diluted, we can neglect moles of solute nin front of moles of solvent n2. So, in case of dilute solution, the equation becomes

We know that moles of any substance can be calculated by dividing the given mass by its molecular mass. Then moles of solute (n2) is equal to

where m2 and M2 are given mass and molecular mass of solute.

Similarly, a mole of solvent (n1) equals

Substituting the value of n1 and n2 in the dilute solution vapour pressure relation, we get

So, we know the other quantities, we can easily determine the molar mass of solute M2 with the above relation.

Elevation of Boiling Point

·    Boiling point of a liquid is the temperature at which its vapour pressure is equal to the atmospheric pressure.

·    As the vapour pressure of a solution containing a nonvolatile solute is lower than that of the pure solvent, it boiling point will be higher than that of the pure solvent. The increase in boiling point is known as elevation in boiling point.

Mathematically, if Tb0 is the boiling point of pure solvent and Tb denotes boiling point of the solution, then elevation in boiling point (denoted by Δ Tb) is

Δ Tb = Tb – Tb0

Experimentally it has been found that elevation in boiling point in dilute solutions is directly proportional to molality ‘m’ of solute present in a solution.

Δ Tb  m

Δ Tb = Km

The term molality ‘m’ denotes the number of moles of solute present in 1000 g or 1 kg of solvent. In the relation Kb is the called molal elevation constant or ebullioscopic constant. The standard unit of molal elevation constant Kb is K kg mol-1.

Let m1 and m2 be the given masses of solvent and solute respectively. And molar masses of solute be M2 and that of solvent is M1, then molality can be evaluated from the relation:

Putting the value of molality in the boiling elevation relation, we get

Hence, if know the remaining quantities we can easily determine the molar mass of solute with the boiling elevation relation.

Depression of Freezing Point

·         The freezing point of a liquid is the temperature at which its vapour pressure of the solvent in its liquid and solid phase become equal. ,

·         As we know that vapour pressure of a solution containing nonvolatile solute is lower than that of the pure solvent. Therefore, its freezing point will be lower than that of pure solvent. This decrease in freezing point is called depression in freezing point.

Depression in freezing point (∆Tf) = T0f – Tf

The freezing point depression is denoted by Δ Tf and equals to

Δ Tf = Tf0 - Tf

The freezing point depression for dilute solutions is directly proportional to molality of the solute, just like the boiling elevation point. That is

Δ Tf  m

Δ Tf = Kf m

The proportionality constant Kf is called Molal Depression Constant and is also known as Cryoscopic Constant, which depends upon the nature of the solvent.

We know that molality ‘m’ equals to

where m2 is a mass of solute, m1 is a mass of solvent and M2 is the molar mass of added non-volatile solute.

Putting the value of molality in above equation we get depression in freezing point as

Note- the value of Kf and Kb depend upon the nature of solvent.

Osmosis and Osmotic Pressure

Osmosis-

The phenomenon of the passage of pure solvent from a region of lower concentration (of the solution) to a region of its higher concentration through a semi-permeable membrane is called osmosis.

Example-

·         A raw mango placed in concentrated salt solution loses water via osmosis and shrivel into pickle.

·         Wilted flowers revive when placed in fresh water.

·         A carrot that has become limp because of water loss into the atmosphere can be placed into the water making it firm once again.

·         Red blood cells swelling up when exposed to fresh water and plant root hairs taking up water.

·         If we put a potato into a sugar solution, it shrinks over time through the process of osmosis.

·         If we put a raisin into pure water, it swells up over time.

Osmotic pressure-

The flow of solvent molecules through the semipermeable membrane can be stopped if some extra pressure is applied from the solution side. This pressure that just stops the flow of solvent is called osmotic pressure of the solution.

Osmotic pressure is a colligative property and depends on solute particles of the solution. Experimentally for dilute solutions, osmotic pressure is

π = CRT

where π is osmotic pressure, R is gas constant, T is constant and C denotes concentration or molarity of the solution.

Molarity (C) is defined as moles of solute divided by the volume of solution in liters. Mathematically

C = n2 / V

where n2 is moles of solute and V is the volume of the solution. Putting the value of c in osmotic pressure we get

π = (n2 / V) R T

Since moles n2 = m2 /M2, where m2 is given mass and M2 is molar mass, we can derive a new relation between osmotic pressure and molar mass of solute M2 as

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. That is, now the pure solvent flows out of the solution through the semi permeable membrane. This phenomenon is called reverse osmosis

Example –

·         Desalination of sea

·         (A porous membrane Cellulose acetate is used as a semi permeable membrane in desalination of sea and it is permeable to water but impermeable to impurities and ions present in sea water)

·         Wastewater treatment

·         Purification of water at homes