Question

Prove that osmotic pressure is a colligative property.

Answer 1

Hint: Colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution. The colligative property does not depend on the nature of the chemical species present in solution. Keeping this fact about colligative property, we can move on to prove osmotic pressure is a colligative property.

Step by step answer:
According to the definition of colligative properties in chemistry we can define colligative properties as those properties of solutions which depend upon the number of solute particles in the solution irrespective of their nature.
Osmotic pressure is defined as the tendency of solvent molecules to move in the direction of lower solvent activity. Osmotic pressure is considered to be proportional to the molarity and temperature of the solution. By molarity we mean the number of moles of solute in one liter solution.
Osmotic pressure can be defined using the following equation:
$\mathrm{\Pi }\text{ V = nRT}$
This is the basic equation for all the ideal solutions.
From the equation we can say that:
$\mathrm{\Pi }\text{ = CRT}$, where $\text{C = }{\displaystyle \frac{\text{n}}{\text{V}}}$
In the above-mentioned formula,
$\mathrm{\Pi }$represents the osmotic pressure
C is the concentration which is ${\displaystyle \frac{\text{n}}{\text{V}}}$
V represents the volume
T represents the absolute temperature
n represents the number of moles of solute in the solution
R represents the gas constant 8.314 J${\text{K}}^{\text{-1}}$ $\text{mo}{\text{l}}^{\text{-1}}$.
Since osmotic pressure is directly proportional to the number of moles (or we can say the concentration) of the solute, it resembles the definition of colligative property.
Hence, we can say that it is considered as a colligative property.

Note: Osmotic pressure is the best colligative property to measure molecular mass of biomolecules. The colligative properties are of four types which include relative lowering in vapour pressure, boiling point elevation, depression in freezing point and osmotic pressure.