Boiling point elevation:\nThe rise in boiling point (ΔT_b) of a dilute solution is directly proportional to which concentration measure?

Introduction / Context:
Boiling point elevation and freezing point depression are classic colligative properties used to determine molar masses and to design antifreeze and coolant formulations. The appropriate concentration basis matters because temperature changes depend on solute amount relative to solvent mass, not solution volume.

Given Data / Assumptions:

• Dilute, non-electrolyte solutions (van’t Hoff factor ~ 1) for simplicity.
• Constant pressure conditions (typically 1 atm).

Concept / Approach:
The empirical relationship is ΔT_b = K_b * m * i, where K_b is the ebullioscopic constant, m is molality (moles solute per kilogram of solvent), and i is the van’t Hoff factor. Thus, ΔT_b is directly proportional to molality for a given solvent and solute dissociation factor. Molarity varies with temperature and volume changes; normality depends on reaction equivalents, not colligative behavior.

Step-by-Step Solution:

Verification / Alternative check:
Freezing point depression similarly follows ΔT_f = K_f * m, reinforcing that solvent-mass-based concentration controls colligative effects.

Why Other Options Are Wrong:

• 1/m, N, M: not the correct direct proportionalities in the standard relation.
• Mass fraction: related but not the standard linear variable in the colligative formula.

Common Pitfalls:
Using molarity for boiling point calculations; since solution volume changes with temperature, molarity is less reliable than molality for thermal properties.

Final Answer:
Molal concentration (molality, m).