Colligative properties depends upon:

the number of solute particles present in solution.

The correct answer is option 3. the number of solute particles present in solution.

Colligative properties are a set of properties of solutions that depend solely on the ratio of the number of solute particles to the number of solvent particles in a solution, regardless of the nature of the solute particles. These properties are critical in understanding how solutes affect the physical properties of solvents in a solution.

There are four main colligative properties:

i. Lowering of Vapor Pressure

ii. Elevation of Boiling Point

iii. Depression in Freezing Point

iv. Osmotic Pressure

Dependence on the Number of Solute Particles

The defining characteristic of colligative properties is that they depend only on the number of solute particles present in the solution, not on the type or nature of those particles. This means that:

Electrolytes (like NaCl, \( \text{MgCl}_2 \), etc.) dissociate in water to produce multiple particles (ions), so they have a greater impact on colligative properties than non-electrolytes (like glucose, urea) which do not dissociate.

Non-electrolytes remain as single molecules in solution, so the number of particles is equal to the number of molecules dissolved.

Detailed Explanation of Each Colligative Property:

Lowering of Vapor Pressure

When a non-volatile solute is added to a solvent, the solute particles occupy some of the surface area of the solvent. This reduces the number of solvent molecules at the surface that can escape into the vapor phase, thereby lowering the vapor pressure of the solution. Raoult's Law states that the vapor pressure of a solvent in a solution is proportional to the mole fraction of the solvent. The reduction in vapor pressure depends on the number of solute particles and is independent of their nature.

Elevation of Boiling Point

The boiling point of a liquid is the temperature at which its vapor pressure equals the external pressure. Because adding a solute lowers the vapor pressure of the solvent, a higher temperature is required to reach the external pressure, leading to an elevation in the boiling point. The magnitude of boiling point elevation (\( \Delta T_b \)) is directly proportional to the molality of the solution (\( m \)), which is a measure of the number of solute particles per kilogram of solvent.

\(\Delta T_b = K_b \cdot m\)

Where \( K_b \) is the ebullioscopic constant of the solvent.

Depression in Freezing Point

The freezing point is the temperature at which the liquid and solid phases of a substance are in equilibrium. The presence of solute particles disrupts the formation of the solid phase, requiring a lower temperature to reach the freezing point. Similar to boiling point elevation, the decrease in freezing point (\( \Delta T_f \)) is proportional to the molality of the solute.

\(\Delta T_f = K_f \cdot m\)

Where \( K_f \) is the cryoscopic constant of the solvent.

Osmotic Pressure

Osmotic pressure is the pressure required to stop the flow of solvent molecules through a semipermeable membrane into a solution. It depends on the number of solute particles in the solution. The osmotic pressure (\( \pi \)) is given by the equation:

\(\pi = nRT\)

Where:

\( n \) is the number of moles of solute particles,

\( R \) is the gas constant,

\( T \) is the absolute temperature.

Why the Number of Solute Particles Matters:

The colligative properties are influenced by the number of solute particles because these particles cause disruptions in the solvent’s structure, leading to changes in properties like vapor pressure, boiling point, freezing point, and osmotic pressure.

For instance:

Electrolytes like NaCl dissociate into Na\(^+\) and Cl\(^-\) ions in solution, effectively doubling the number of particles in solution compared to a non-electrolyte like glucose.

\( \text{NaCl} \overset{H_2O}{\longrightarrow} \text{Na}^+ + \text{Cl}^- \)  (2 particles per formula unit)

\( \text{MgCl}_2  \overset{H_2O}{\longrightarrow} \text{Mg}^{2+} + 2\text{Cl}^- \)  (3 particles per formula unit)

Non-electrolytes like glucose do not dissociate and remain as one particle per molecule.

\( \text{C}_6\text{H}_{12}\text{O}_6 \) (1 particle per molecule)

The greater the number of solute particles, the more significant the impact on the colligative properties, regardless of the chemical identity of the solute.

Summary:

Colligative properties depend on the number of solute particles present in a solution because these properties are a result of the solute's effect on the solvent's behavior. The physical or chemical nature of the solute is irrelevant—what matters is how many particles (atoms, molecules, ions) are present to interact with the solvent.