Q.[Note: two or more options may be correct] Relative lowering of vapour pressure is a colligative property because _____________.

Concept: Colligative properties depend solely on the number of solute particles in solution, not their chemical identity.

Relative lowering of vapour pressure follows Raoult's law for dilute solutions:

This ratio depends only on the mole fraction (i.e., the count of particles), whether the solute is molecular or ionic.

For non-electrolytes: Each molecule counts as one particle. The lowering depends on concentration but not on whether the solute is sugar, urea, or any other non-electrolyte — option (i) is correct. …

The term "colligative" comes from the Latin colligatus, meaning "bound together"—these properties are tied to the collective effect of solute particles, regardless of what those particles actually are. A mole of sugar molecules and a mole of urea molecules lower vapour pressure by the same amount in an ideal solution, even though their chemical structures are completely different.

Raoult's law captures this beautifully. For an ideal solution, the vapour pressure of the solvent is:

where $P_0$ is the vapour pressure of the pure solvent and $x_{\text{solvent}}$ is its mole fraction. The relative lowering is:

For dilute solutions where $n_{\text{solvent}} \gg n_{\text{solute}}$, this simplifies to being directly proportional to the number of moles (or concentration) of solute particles. Notice: nowhere does the chemical nature of the solute appear—only the count of particles matters.

Now let's examine each option:

1. Option (i): Non-electrolyte solutes

   For non-electrolytes like glucose or urea, one molecule remains one particle in solution. The relative lowering depends on concentration (number of particles) and is independent of the solute's nature. This is the textbook definition of a colligative property. Option (i) is correct.

2. Option (ii): Electrolyte solutes …

Method: Conceptual Analysis of Colligative Properties

Step 1 — Recall the definition of a colligative property

A colligative property depends only on the number of solute particles in solution, not on their identity or nature.

Examples:

• Relative lowering of vapour pressure
• Elevation of boiling point
• Depression of freezing point
• Osmotic pressure

Step 2 — Apply this to relative lowering of vapour pressure

For a non-electrolyte solute, the relative lowering of vapour pressure is given by Raoult’s law:

where

• $P^0$ = vapour pressure of pure solvent
• $P$ = vapour pressure of solution
• $n$ = moles of solute
• $N$ = moles of solvent

This depends only on the mole fraction (concentration) of the solute, not on its chemical nature.

Step 3 — Extend to electrolyte solutes

For an electrolyte solute, the number of particles increases due to dissociation. The property still depends only on the total number of particles (via van’t Hoff factor $i$), not on the specific identity of the ions.

Step 4 — Evaluate each option

| Option | Statement | Correct? |

|--------|-----------|----------| …

Here are the common mistakes students make with this question and how to avoid them.

Mistake 1: Confusing "Colligative" with "Concentration-Only"

The Mistake:

Students often think a colligative property depends only on the concentration of the solute particles, regardless of whether the solute is an electrolyte or non-electrolyte. This leads them to pick option (ii) as the only correct answer.

Why it’s wrong:

Option (ii) is correct for electrolytes (like NaCl), which dissociate into ions. The property depends on the number of particles (ions), not the nature of the solute. However, the question asks for the relative lowering of vapour pressure in general. For a non-electrolyte (like glucose), the property depends on the concentration of molecules, not the number of particles (since they don't dissociate).

How to Avoid:

• Remember the definition: A colligative property depends on the number of solute particles in solution, irrespective of their nature.
• Distinguish between solute types:
  • For non-electrolytes: number of particles = concentration of molecules.
  • For electrolytes: number of particles = concentration × van't Hoff factor ($i$).
• Read the options carefully: Option (i) says "concentration of a non-electrolyte" – this is correct for non-electrolytes. Option (ii) says "number of particles of electrolyte" – this is correct for electrolytes. Both are valid statements of the colligative property.

Correct approach: Both (i) and (ii) are correct because they correctly describe the colligative nature for the two types of solutes.

Mistake 2: Thinking "Nature of Solute" Always Matters

The Mistake:

Students believe that because Henry's Law constant ($K_H$) depends on the nature of the gas and solvent, the relative lowering of vapour pressure must also depend on the nature of the solute. This leads them to pick options (iii) or (iv).

Why it’s wrong:

Henry's Law ($P = K_H \cdot x$) describes the solubility of a gas in a liquid. The constant $K_H$ does depend on the nature of the gas and solvent. However, relative lowering of vapour pressure ($\frac{P^0 - P}{P^0} = x_{solute}$) is a different colligative property. For a non-volatile solute, it depends only on the mole fraction of the solute ($x_{solute}$), not on what the solute is.

How to Avoid:

• Separate the concepts: Henry's Law is about gas solubility. Relative lowering of vapour pressure is about non-volatile solutes in a liquid.
• Recall Raoult's Law: For a non-volatile solute, $\frac{P^0 - P}{P^0} = x_{solute}$. This equation has no term for the nature of the solute.
• Test with an example: If you dissolve 1 mole of glucose or 1 mole of urea in 100 moles of water, the relative lowering is the same ($\frac{1}{101}$). The nature of the solute doesn't matter.

Correct approach: Options (iii) and (iv) are wrong because they incorrectly state that the property depends on the nature of the solute molecules.

Mistake 3: Ignoring the "Non-Electrolyte" vs "Electrolyte" Distinction

The Mistake: …