Question

What is the total number of colligative properties?
A.) 1
B.) 2
C.) 3
D.) 4

Answer 1

Hint: The properties of a solution that depend only upon the total concentration of solute species, regardless of their identity, are referred to as colligative properties. Now that you know their definition, try thinking of all the possible properties of a solution that could fit this definition.

Complete step-by-step answer:
Let us go through each colligative property of a solution one at a time to help facilitate your better understanding of this topic.
Lowering of Vapour Pressure:
Vapor pressure lowering is a colligative property of solutions.
The vapor pressure of a pure solvent is greater than the vapor pressure of a solution containing a non-volatile liquid.
This lowered vapor pressure leads to boiling point elevation.
The vapor pressure lowering is directly proportional to the mole fraction of the solute. This is Raoult's Law.
\[{{P}_{solution}}={{\chi }_{solvent}}{{P}^{o}}_{solvent}\]
where \[{{P}^{o}}_{solvent}\] is the vapor pressure of the pure solvent and \[{{\chi }_{solvent}}\] is the mole fraction of the solvent. Since this is a two-component system (solvent and solute), then
\[{{\chi }_{solvent}}+{{\chi }_{solute}}=1\]
where \[{{\chi }_{solute}}\] is the mole fraction of the solute. The change in vapor pressure (ΔP) can be expressed
\[\Delta P={{P}_{solution}}{{P}^{o}}_{solvent}\]= \[{{\chi }_{solvent}}{{P}^{o}}_{solvent}-{{P}^{o}}_{solvent}\]
Or
\[\Delta P=\left( {{\chi }_{solvent}}-1 \right){{P}^{o}}_{solvent}={{\chi }_{solute}}{{P}^{o}}_{solvent}\]

Boiling Point Elevation:
Boiling point elevation refers to the increase in the boiling point of a solvent upon the addition of a solute. When a non-volatile solute is added to a solvent, the resulting solution has a higher boiling point than that of the pure solvent.
For example, the boiling point of a solution of sodium chloride (salt) and water is greater than that of pure water.
Boiling point elevation is a colligative property of matter, i.e. it is dependent on the solute-to-solvent ratio but not on the solute’s identity.
This implies that the elevation in the boiling point of a solution depends on the amount of solute added to it. The greater the concentration of solute in the solution, the greater the boiling point elevation.

Freezing Point Depression:
Freezing point depression is the phenomena that describes why adding a solute to a solvent results in the lowering of the freezing point of the solvent.
When a substance starts to freeze, the molecules slow down due to the decreases in temperature, and the intermolecular forces start to take over.
The molecules will then arrange themselves in a pattern, and thus turn into a solid.
For example, as water is cooled to the freezing point, its molecules become slower and hydrogen bonds begin to “stick” more, eventually creating a solid.
If salt is added to the water, the Na+ and Cl–ions attract the water molecules and interfere with the formation of the large network solid known as ice.
In order to achieve a solid, the solution must be cooled to an even lower temperature.

Osmotic Pressure:
Osmosis is the diffusion of solvent molecules into a region where there is a higher concentration of solvent.
Osmotic pressure is defined as the hydraulic pressure required to prevent the migration of solvent from the area of low solute concentration to an area of high solute concentration.
For any solution, osmotic pressure is directly proportional to its absolute temperature, and at a constant temperature, it is directly proportional to the solute concentration.

Osmotic pressure is calculated by the Van’t Hoff equation which is:
Osmotic Pressure = $n\times (\dfrac{c}{M})\times R\times T$, where,
n = Number of particles into which the substance dissociates
c = Concentration in g/L
M= Molecular Weight of the molecules
R = Universal Gas Constant
T = Absolute Temperature

Therefore, per this analysis, the answer to this question is d) 4.

NOTE: Be very thorough with the definition of colligative properties and what they constitute to ensure that you answer this question correctly. Also, the mathematical expression governing each colligative property is an important part of the solution and cannot be omitted.