Colligative properties of dilute solutions depend entirely on what fundamental factor?

Introduction / Context:
Colligative properties include boiling point elevation, freezing point depression, relative lowering of vapor pressure, and osmotic pressure. They are central to solution thermodynamics and analytical determinations like molar mass measurements of solutes.

Given Data / Assumptions:

• Dilute, ideal (or nearly ideal) solutions.
• Solute is non-volatile for vapor pressure considerations.
• Electrolytes may dissociate, thus changing the effective number of particles.

Concept / Approach:
Colligative effects are proportional to the number of solute particles in a given amount of solvent, not their identity. This is why electrolytes, which dissociate into multiple ions, show larger effects than nonelectrolytes at the same molality. The van ’t Hoff factor accounts for dissociation/association when necessary.

Step-by-Step Solution:

Verification / Alternative check:
Compare a 0.1 m glucose solution with a 0.1 m NaCl solution (near complete dissociation, i ≈ 2). The NaCl solution exhibits roughly twice the colligative effect, illustrating the role of particle number, not chemical nature.

Why Other Options Are Wrong:

• (a), (b), and (e) relate to identity and interactions; in the ideal dilute limit, colligative properties ignore identity and depend only on count.
• (d) is invalid because a correct general statement exists in (c).

Common Pitfalls:
Ignoring dissociation/association (van ’t Hoff factor i) or using molarity instead of molality when temperature changes are involved in freezing/boiling problems.

Final Answer:
Number of solute molecules present per given amount of solvent