The properties of solutions which depend on the number of solute particles and are independent of their chemical identity are called colligative properties. These are lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmotic pressure. The process of osmosis can be reversed if a pressure higher than the osmotic pressure is applied to the solution. Colligative properties have been used to determine the molar mass of solutes. Solutes which dissociate in solution exhibit molar mass lower than the actual molar mass and those which associate show higher molar mass than their actual values. Quantitatively, the extent to which a solute is dissociated or associated can be expressed by van’t Hoff factor i. This factor has been defined as ratio of normal molar mass to experimentally determined molar mass or as the ratio of observed colligative property to the calculated colligative property.

Which of the following relation represents correct relationship of osmotic pressure with concentration of the solution?

π ∝ c

The correct answer is option 4. \(\pi \propto c\)

Osmotic pressure (\(\pi\)) is the pressure required to stop the flow of solvent through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. The relationship between osmotic pressure and concentration can be understood through the van't Hoff equation for dilute solutions, which is analogous to the ideal gas law:

\(\pi = iCRT\)

Here is a breakdown of the terms in this equation:

\(\pi\) is the osmotic pressure.

\(i\) is the van't Hoff factor, which accounts for the number of particles into which a solute dissociates in solution. For example, for NaCl, \(i = 2\) because it dissociates into two ions (Na\(^+\) and Cl\(^-\)).

\(C\) is the molar concentration of the solute.

\(R\) is the universal gas constant (approximately 0.0821 L·atm/(K·mol)).

\(T\) is the absolute temperature in Kelvin.

From the equation, it is clear that osmotic pressure (\(\pi\)) is directly proportional to the concentration (\(C\)) of the solute. This means that if the concentration of the solute doubles, the osmotic pressure will also double, assuming that temperature and the van't Hoff factor remain constant.

In summary, the direct proportionality between osmotic pressure and solute concentration means that:

\(\pi \propto C\)

Therefore, the correct answer to the relationship between osmotic pressure and concentration is: \(\pi \propto c\)