Raoult’s law and vapor pressure: For a solution, the vapor pressure is proportional to which mole fraction? (Sv = mole fraction of solvent, St = mole fraction of solute)

Introduction / Context:
Raoult’s law governs vapor pressure lowering in ideal solutions. It states that the partial pressure of a volatile solvent over a solution equals the pure-solvent vapor pressure multiplied by the solvent mole fraction in the liquid. Understanding which composition term controls vapor pressure is essential in distillation, evaporation, and humidity calculations.

Given Data / Assumptions:

• Ideal solution behavior (low to moderate solute concentration).
• Solvent is volatile; solute may be nonvolatile or less volatile.
• Temperature is fixed.

Concept / Approach:
Raoult’s law in its basic form is P_solvent = x_solvent * P°_solvent. Here x_solvent = Sv. Thus, the vapor pressure contributed by the solvent is directly proportional to Sv, not St. As solute is added (Sv decreases), the solvent’s vapor pressure falls proportionally, which underpins colligative properties like boiling point elevation and freezing point depression.

Step-by-Step Solution:
Write Raoult’s law: P = Sv * P°.Identify proportionality: P ∝ Sv at constant P° and T.Therefore, vapor pressure scales with solvent mole fraction, Sv.Select option “Sv”.

Verification / Alternative check:
Activity-coefficient models reduce to Raoult’s law when γ ≈ 1. In that limit, changing Sv changes the solvent chemical potential and thus the equilibrium vapor pressure linearly.

Why Other Options Are Wrong:
St is for the solute; Raoult’s proportionality references the solvent fraction.Inverse forms 1/St and 1/Sv are not part of the basic Raoult relation.

Common Pitfalls:
Confusing mole fraction of solvent vs. solute; applying Raoult’s law to highly non-ideal or associating systems without activity corrections; forgetting temperature dependence of P°.

Final Answer:
Sv