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Colligative Properties Examples

Dilute solution containing non-volatile solute exhibit some properties which depend only on the number of solute particles present and not on the type of solute present. These properties are called colligative properties. These properties are mostly seen in dilute solutions.

We can observe the colligative properties of solutions by going through the following examples. If we add a pinch of salt to a glass full of water its freezing temperature is lowered considerably than the normal temperature. Alternatively, its boiling temperature is also increased and the solution will have a lower vapour pressure. There are changes in its osmotic pressure as well.

Similarly, if we add alcohol to water, the solution’s freezing point goes down below the normal temperature that is observed for either pure water or alcohol.

Different Types of Colligative Properties of Solution

The four colligative properties that can be exhibited by a solution are:

1. Vapor pressure lowering: When a non-volatile solute is added to a solvent, it reduces the vapor pressure of the solvent. This means that the solvent evaporates more slowly compared to the pure solvent. This effect is explained by the presence of solute particles on the surface of the solvent, which hinders the escape of solvent molecules into the vapor phase.
2. Boiling point elevation: The addition of a non-volatile solute to a solvent raises the boiling point of the solvent. This occurs because the solute particles disrupt the formation of solvent vapor bubbles during boiling, requiring a higher temperature to overcome the increased vapor pressure.
3. Freezing point depression: When a solute is dissolved in a solvent, it lowers the freezing point of the solvent. This happens because the solute particles interfere with the formation of a regular crystalline structure of the solvent during freezing, making it more difficult for the solvent to solidify.
4. Osmotic pressure: Osmotic pressure is the pressure that must be applied to a solution to prevent the flow of solvent across a semipermeable membrane. It depends on the concentration of solute particles in the solution. Osmosis is the process in which solvent molecules move from an area of lower solute concentration to an area of higher solute concentration, through a semipermeable membrane.

To express the number of species, present in the solution, the mole fraction, the molality or the molarity have to be used, depending on the type of the colligative property.

1. Lowering of Vapour Pressure

In a pure solvent, the entire surface is occupied by the molecules of the solvent. If a non- volatile solute is added to the solvent, the surface now has both solute and solvent molecules; thereby fraction of surface covered by solvent molecules gets reduced.

Since the vapour pressure of the solution is solely due to solvent alone, at the same temperature the vapour pressure of the solution is found to be lower than that of the pure solvent.

If P₀ is the vapour pressure of pure solvent and Ps is the vapour pressure of the solution. The difference Po – Ps is termed as lowering in vapour pressure. The ratio Po – Ps / Po is known as the relative lowering of vapour pressure.

Raoult, in 1886, established a relation between relative lowering in vapour pressure and mole fraction. The relationship is known as Raoult’s law. It states that the relative lowering in vapour pressure of a dilute solution is equal to the mole fraction of the solute present in the solution

Raoult’s law states that for a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in solution.

if n moles of solute is dissolved in N moles of the solvent, then according to Raoult’s law

                   Po – Ps / Po = n / n + N

2. Elevation in Boiling Point

The boiling point of a liquid is the temperature at which the vapour pressure is equal to atmospheric pressure.

 We know that on the addition of a non-volatile liquid to a pure solvent, the vapour pressure of a solution decrease. Therefore to make vapour pressure equal to atmospheric pressure we have to increase the temperature of the solution.

The difference in the boiling point of the solution and the boiling point of the pure solvent is termed as elevation in boiling point.

If T⁰b is the boiling point of the pure solvent and Tb is the boiling point of the solution then elevation in boiling point is given as

                       ∆Tb =T⁰b-Tb

Experimental results show that there is a relation between elevation in boiling point and molality ‘m’ of the solute present in solution

∆Tb ∝ m

∆Tb = kb m

 Where,

kb = molal elevation constant

Substituting the value of ‘m’ in the above relation we get

           ∆Tb = 1000 x kb x m2 / M2 x m1

Where,

m₂ = mass of solvent in g

M₁ = mass of solvent in kg

M₂ = molar mass of solute

3. Depression in Freezing Point

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

According to Raoult’s law when a non-volatile solid is added to the solvent its vapour pressure decreases and now it would become equal to that of solid solvent at a lower temperature. The difference between the freezing point of the pure solvent and its solution is called depression in freezing point.

If T⁰_f is the boiling point of the pure solvent and T_f is the boiling point of the solution then depression in freezing point is given as

∆T_f =T⁰_f-T_f

Just like elevation in boiling point, depression in freezing point is also directly related to molality ‘m’.

∆T_f = 1000 x kf x m2 / M2 x m1

Where,

k _f = molal depression constant

m₂ = mass of solvent in g

M₁ = mass of solvent in kg

M₂ = molar mass of solute

4. Osmotic Pressure

When a semipermeable membrane is placed between a solution and solvent, it is observed that solvent molecules enter the solution through the semipermeable membrane and the volume of the solution increases.

The semi-permeable membrane allows only solvent molecules to pass through it but prevents the passage of bigger molecules like solute. This phenomenon of the spontaneous flow of solvent molecules through a semipermeable membrane from a pure solvent to a solution or from a dilute to a concentrated solution is called osmosis.

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 as it depends on the number of solute present and not on the nature of the solute. Experimentally it was proved that osmotic pressure (⫪) is directly proportional to molarity(C) and temperature(T).

Mathematically, ℼ = CRT where R is the gas constant.

⇒ ℼ = (n₂/V) RT

Here, V is the volume of solution in litres and n₂ is moles of solute

If m₂ is the weight of solute and M₂ molar mass of solute, then n₂= m₂/M₂

ℼ = W2 RT / M2V

Thus by knowing the values of ℼ,w₂, T and V we can calculate the molar mass of the solute.

Isotonic solution: Two solutions having the same osmotic pressure at a given temperature are known as an isotonic solution. When such solutions are separated by a semi-permeable membrane than there is no osmosis.

Hypotonic solution: A hypotonic solution has a lower osmotic pressure than that of the surrounding i.e, the concentration of solute particles is less than that of the surrounding. If the hypotonic solution is separated by semipermeable membrane then water moves out of the hypotonic solution.

Hypertonic solution: A hypertonic solution has a higher osmotic pressure than that of the surrounding i.e, the concentration of solute particles is more than that of the surrounding. If the hypertonic solution is separated by semipermeable membrane then water moves inside the hypertonic solution.

For determining the molar mass, Osmotic pressure method has the advantage over other methods as pressure measurement is around room temperature. It is particularly useful for determination of the molar mass of biomolecules as they are unstable at higher temperatures.

Solved Problems

1. The molal elevation constant for water is 0.513^oC kg mol^–. When 0.2mole of sugar is dissolved in 250g of water, calculate the temperature at which the solution boils under atmospheric pressure.

Solution:

The elevation in boiling point can be written as

∆Tb = moles of sugar x 1000 / weight of water in gram

∆Tb = 0.2 x 1000 / 250

∆Tb = 0.8

⇒ T⁰b-Tb = 0.8

For pure water, T⁰b =100^oC

⇒ Tb= 0.8 + 100

=100.80 ⁰C

2. A solution of CaCl₂was prepared by dissolving 0.0169g in 1 Kg of distilled water in ( molar mass of Ca²⁺= 41g mol^– and Cl= 35.5gmol^–). The molal depression constant of water is 2kg mol^–. The depression in freezing point of the solution is:

Solution:

Van’t Hoff factor(i) of CaCl₂ is 3

K_f = 2 kg mol^–

Given,

Mass of CaCl₂ (m₂) = 0.0169g

Molar mass of CaCl₂( M₂) =112g

Weight of water(m₁) =1000g

∆T_f = i x 1000X Kf x m2 / M2 x m1

= 3 x 1000 x 2 x 0.0169 / 112 x 1000g

= 9× 10^-4

3. Hexane and heptane were mixed to form an ideal solution. At 100⁰C, the vapour pressure of two liquids( Hexane and heptane) are 190kPa and 45kPa respectively. What will be the vapour pressure of the solution obtained by mixing 25g of hexane and 35 g of heptane will be:

Solution :

No of moles of hexane,n₁= 25/86= 0.29

No of moles of heptane, n₂=35/100=0.35

���₁ = n1 / n1 + n2

���₁ = 0.29 / 0.29 +0.35

���₁ = 0.45

���₂ = 1 – 0.45

���₂ = 0.55

P = P⁰₁���₁ +P⁰₂���₂

= 1900.45 + 450.55

=110 kPa

4. On adding non-volatile solute to a solvent which of the following effect is observed;
5. Increase in vapour pressure
6. Increase in freezing point
7. Decrease in osmotic pressure
8. Decrease in vapour pressure

Solution: Option d

In a pure solvent, the entire surface is occupied by the molecules of the solvent. If a non- volatile solute is added to the solvent, the surface now has both solute and solvent molecules; thereby fraction of surface covered by solvent molecules gets reduced. Since the vapour pressure of the solution is solely due to solvent alone, at the same temperature the vapour pressure of the solution is found to be lower than that of the pure solvent.