Colligative effects: When a non-volatile solute is added to a pure solvent, how do the boiling point and freezing point of the solution change?

Introduction / Context:
Adding a non-volatile solute to a solvent alters phase-change temperatures in ways that depend only on the number of solute particles (colligative properties). This principle underpins antifreeze formulations, de-icing salts, and boiling point adjustments in cooking and industrial processes.

Given Data / Assumptions:

• Solute is non-volatile and does not dissociate (or dissociation is accounted for by the van ’t Hoff factor).
• Solution is dilute and ideal for colligative relations.

Concept / Approach:
Raoult’s law predicts a lowering of the solvent’s vapor pressure when a non-volatile solute is present. Consequently, a higher temperature is required to reach the external pressure for boiling (boiling-point elevation). Conversely, the presence of solute lowers the chemical potential of the liquid relative to the solid, requiring a lower temperature to achieve phase equilibrium (freezing-point depression). The magnitudes follow ΔT_b = K_b m i and ΔT_f = K_f m i, proportional to molality m and the van ’t Hoff factor i.

Step-by-Step Solution:

Verification / Alternative check:
Empirical constants K_b and K_f tabulated for solvents (e.g., water) predict linear changes with molality, confirming the qualitative outcomes.

Why Other Options Are Wrong:

• Increase in freezing point: opposite to observation.
• Increase in boiling point only: incomplete; it also depresses freezing point.
• Both (a) and (b): includes the incorrect increase in freezing point.

Common Pitfalls:
Ignoring electrolyte dissociation (van ’t Hoff factor) which amplifies the effects; confusing non-volatile with volatile solutes where additional vapor-phase behavior applies.

Final Answer:
both (b) and (c)