# Colligative Properties of Solutions

A non-volatile solute is one which does not change into the vapour. We assume that the solute is non-volatile. Certain properties of dilute solutions containing non-volatile solute depend only upon the concentration i.e. the number of particles of the solute present in the solution. Such properties are term as colligative properties of solutions.

The four well-known examples of the colligative properties of a solution are:

1. Lowering of the vapour pressure of the solvent.
2. Osmotic pressure of the solution.
3. Elevation in the boiling point of the solvent.
4. Depression in freezing point of the solvent. ## Colligative properties of the solution depend upon

The properties of dilute solutions containing non-volatile solute do not depend upon the nature of the solute dissolved.It depends upon the number of solute particles present in the solution, the simple case will be that when the solute is a nonelectrolyte.

In case the solute is an electrolyte, it may split to a number of ions each of which acts as a particle and thus will affect the colligative properties of solutions.

Each colligative property is exactly related to any other and thus if one property is measured, the other can be calculated. The study of colligative properties of the solution is very useful for the calculation of molecular weights of the solutes.

It is important to note that the statement of colligative properties of solutions is strictly true only for dilute solutions which behave as nearly ideal solutions. Thus these properties are termed as colligative properties of solutions.

Now let’s discuss Colligative Properties of Solutions one by one.

## Colligative Properties of Solutions: Lowering of vapour pressure

Pressure developed by vapours of the substance is called its vapour pressure at the given temperature. The vapour pressure of a liquid is a measure of its tendency to change from liquid to vapour state. ### Raoult’s Law

When a non-volatile substance is dissolved in a liquid, the vapour pressure of the liquid (solvent) is lowered. According to Raoult’s law (1887), at any given temperature the partial vapour pressure (p1of any component of a solution is equal to its mole fraction (x1) multiplied by the vapour pressure of this component in the pure state (p10). That is,

p1=x1p1o

The vapour pressure of the solution (Ptotal) is the sum of the partial pressures of the components, i.e. for the solution of two volatile liquids with vapour pressures p1 and p2.

Ptotal = p1 + p2 = (x1p1o )+ (x2p2o)

#### Raoult Statements

Alternatively, Raoult’s law may be stated as “the relative lowering of the vapour pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution.”

Relative lowering of vapour pressure is defined as the ratio of lowering of vapour pressure to the vapour pressure of the pure solvent. It is determined by Ostwald-Walker method.

The mole fraction of the solute is defined as the ratio of the number of moles of solute to the total number of moles in solution.

Thus according to Raoult’s law, • p = Vapour pressure of the solution.
• p0 = Vapour pressure of the pure solvent.
• n = Number of moles of the solute.
• N = Number of moles of the solvent.
• w and m = Weight and mol. wt. of solute.
• W and M = Weight and mol. wt. of the solvent.

It is important to note that the law is applicable only to ideal solutions.

It is clear now from the above formula that it depends on moles (number of particles) of the solute present in the solution. Such properties are term as colligative properties of solutions and not upon the nature of the solute.Hence, lowering of vapour pressure is a part of colligative properties of the solution.

## Colligative Properties of Solutions: Osmotic pressure

When a solution (say of sugar) is separated from the pure solvent (water in present case) by means of a semipermeable membrane (a membrane which allows only the solvent molecules but not the solute molecules to pass through it), the pure solvent passes through the membrane and goes to solution (osmosis) till the hydrostatic pressure of the liquid column exactly balances the tendency of water to pass inward through the semipermeable membrane. The hydrostatic pressure set up as a result of osmosis is a measure of the osmotic pressure of the solution. For instance, if the solution of density d rises to height h, then osmotic pressure

π = h x d x g

where g is the acceleration due to gravity.

Thus In Colligative Properties of Solutions, osmotic pressure may be defined as the excess pressure which must be applied to a solution in order to prevent the flow of solvent into the solution through the semipermeable membrane. Osmotic pressure may further be defined in several other ways.

(i) Osmotic pressure is the excess pressure which must be applied to a given solution in order to increase its vapour pressure until it becomes equal to that of the solution.

(ii) Osmotic pressure is the negative pressure which must be applied to (that is the pressure which must be withdrawn from) the pure solvent in order to decrease its vapour pressure until it becomes equal to that of the solution.

(iii) Osmotic pressure is the hydrostatic pressure produced when a solution is separated from the solvent by a semipermeable membrane.

### Reverse osmosis

If a pressure higher than osmotic pressure is applied to the solution, the solvent will flow from the solution into the pure solvent through the semipermeable membrane. Since here the flow of solvent is in the reverse direction to that observed in the usual osmosis, the process is called reverse osmosis. It is used in the desalination of sea water to obtain pure water.

### Isotonic solutions

A pair of solutions having the same osmotic pressure is known as isosmotic solutions. If two such solutions are separated by a semipermeable membrane, there will be no transference of solvent from one solution to the other. Isosmotic solutions separated by a semipermeable membrane are term as isotonic solutions. Isotonic solutions have the same molar concentration. 0.85% NaCl solutions are found to be isotonic with blood, while 0.91% NaCl solution is isotonic with human RBCs. A solution having lower or higher osmotic pressure than the other is said to be hypotonic or hypertonic respectively in respect to other solution. (i) When placed in water or hypotonic solutions, cells swell and burst (haemolysis).

(ii) When placed in hypertonic solutions, the fluid from the plant cells comes out and thus the cells contract in size (plasmolysis). When the excess of fertilisers (like urea) are applied, plasmolysis takes place and plants dry up (Wilt).

### Osmolarity

Osmolarity is the term used by physiologists to discuss the osmotic behaviour of solutes which either dissociate or associate in solution. Mathematically,

Osmolarity = Molarity x No. of particles produced per formula unit of the solute

#### Measurement of osmotic pressure

Following methods are used for the measurement of osmotic pressure.

• Pfeffer’s method.
• Morse and Frazer’s method.
• Berkeley and Hartley’s method.
• Townsend’s negative pressure method.
• De Vries plasmolytic method.

### Important relations of osmotic Pressure P or π

(i) PV = n RT    or    πV = n RT   or    π=(n/v)RT    or     π = CRT

• P or π = Osmotic pressure in atmospheres.
• n = Number of moles of the solute present in V litres of the solution.
• C = Concentration of the solution in moles per litre.
• T = Temperature in degree absolute.
• R = 0.0821  L atm deg-1 mole-1 .

(ii) •  w = Wt. of solute in g dissolved in V litre of solution.
• m = Molecular wt. of the solute.

(iii) π = h d g

where h = Height, d = density, g = Gravitational acceleration.

(iv) In isotonic solutions, since osmotic pressure, π is equal, their concentrations (C) must also be equal, i.e. (v) If a number of solutes are present in the solutions and π1, π2, π3 etc. are their individual osmotic pressures, then

Total osmotic pressure= π1 + π2 + π3 + ……

## Colligative Properties of Solutions: Elevation in boiling point

The boiling point of a liquid may be defined as the temperature at which its vapour pressure becomes equal to atmospheric pressure, i.e. 760 mm. The addition of a nonvolatile solute lowers the vapour pressure of the solvent, the solution always has lower vapour pressure than the solvent and hence it must be heated to a higher temperature to make its vapour pressure equal to atmospheric pressure with the result the solution boils at a higher temperature than the pure solvent. Thus sea water boils at a higher temperature than distilled water.

If Tb is the boiling point of the solvent and T is the boiling point of the solution, the difference in the boilings point (ΔT or ΔTb ) is called the elevation of boiling point.

T – Tb = ΔTb    or    ΔT

Elevation in boiling point is determined by Landsberger’s method and Cottrell’s method. Study of elevation in the boiling point of a liquid in which a non-volatile solute is dissolved is term as ebullioscopy.

### Important relations of elevation in boiling point

(i) The elevation of boiling point is directly proportional to the lowering of vapour pressure, i.e.

ΔT∝ p0 – p

(ii) ΔTb = Kb x m where K = Molal elevation constant or ebullioscopic constant of the solvent

•  Kb = Molal elevation constant or ebullioscopic constant of the solvent.
• m = Molality of the solution, i.e. the number of moles of solute per 1000 g of the solvent.
• ΔTb = Elevation in boiling point.

(iii) where Kь is molal elevation constant and defined as the elevation in b.p. produced when 1 mole of the solute is dissolved in 1 kg of the solvent. Sometimes the value of Kb is given per 0.1 kg (100g), in such case the expression becomes • where w and W are the weights of solute and solvent and
• m is the molecular weight of the solute.

(iv) • where T0 = Normal boiling point of the pure solvent.
• Lv = Latent heat of evaporation in cal/g of pure solvent.
• Kb, for water, is 0.52 deg-kg mol.

## Colligative Properties of Solutions: Depression in freezing point

Freezing point is the temperature at which the liquid and the solid states of a substance are in equilibrium with each other or it may be defined as the temperature at which the liquid and the solid states of a substance have the same vapour pressure.

It is observed that the freezing point of a solution is always less than the freezing point of the pure solvent. Thus the freezing point of sea water is low than that of pure water. The depression in freezing point (ΔTf   or ΔT ) of a solvent is the difference in the freezing point of the pure solvent (Ts) and the solution (Tsol).

Τs – Τsol = ΔΔTf     or   ΔT

NaCl or CaCl2 (anhydrous) are used to clear snow roads. They depress the freezing point of water and thus reduce the temperature of the formation of ice. Depression in freezing point is determined by Beckmann’s method and Rast’s camphor method.

Remember that depression in freezing point occurs only when the concentration of the solute is greater in the liquid phase than in the solid phase. However, if the concentration of solute is more in the solid phase than in the liquid phase there is a corresponding elevation in freezing point (e.g. in the case of solid solution system). Study of depression in freezing point of a liquid in which a non-volatile solute is dissolved in it is called as cryoscopy.

### Important relations of depression in freezing point

(i) Depression in freezing point is directly proportional to the lowering of vapour pressure.

ΔT∝ p0 – p

(ii) ΔTf = Kf x m

•  Kf = molal depression constant or cryoscopic constant.
• m = Molality of the solution, i.e. the number of moles of solute per 1000 g of the solvent.
• ΔTf = Depression in freezing point.

(iii) where Kf is molal elevation constant and defined as the depression in freezing point produced when 1 mole of the solute is dissolved in 1 kg of the solvent.

Relative lowering of vapour pressure, elevation of boiling point and depression in freezing point are directly proportional to osmotic pressure.

## Colligative properties of Solution: Electrolytes

The colligative properties of solutions, viz. lowering of vapour pressure, osmotic pressure, elevation in boiling point and depression in freezing point, depend solely on the total number of solute particles present in solution. Since the electrolytes ionise and give more than one particle per formula unit in solution, the colligative effect of an electrolyte solution is always greater than that of a non-electrolyte of the same molar concentration. All colligative properties are used for calculating molecular masses of non-volatile solutes. However, osmotic pressure is the best colligative property for determining the molecular mass of a non-volatile substance.

## Important to Remember: Colligative Properties of Solutions

(i) Colligative properties ∝ Number of particles.

•  Number of molecules (in case of non-electrolytes)
•  No. of ions (In the case of electrolytes).
• No. of moles of solute.
•  Mole fraction of solute

(ii) For different solutes of same molar concentration, the magnitude of the colligative properties is more for that solution which gives more number of particles on ionisation.

(iii) For different solutions o the same molar concentration of different non-electrolyte solutes, the magnitude of the colligative properties will be same for all.

(iv) For different molar concentrations of the same solute, the magnitude of colligative properties is more for the more concentrated solution.

(v) For solutions of different solutes but of same percent strength, the magnitude of the colligative property of solution is more for the solute with least molecular weight.

(vi) For solutions of different solutes of the same percent strength, the magnitude of the colligative property is more for that solute which gives more number of particles which can be known by the knowledge of molecular weight and its ionisation behaviour.

This is about the Colligative Properties of Solutions.

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