For a solution formed by dissolving a nonvolatile solute in a volatile solvent, how does the vapor pressure compare with that of the pure solvent at the same temperature?

Introduction / Context:
Vapor pressure lowering is one of the colligative properties of solutions. It underpins practical operations like evaporation, distillation, and humidity control. Knowing the qualitative trend helps in quickly diagnosing process behavior when solutes are present.

Given Data / Assumptions:

• Solute is nonvolatile (it does not contribute to the vapor).
• Solvent is volatile and obeys Raoult’s law approximately at low solute concentrations.
• Temperature is fixed and uniform.

Concept / Approach:
Raoult’s law for an ideal solution states that the partial pressure of the solvent over the solution equals its mole fraction in the liquid times the pure-solvent vapor pressure: Psolution = xsolvent * P°solvent. Since xsolvent < 1 when a solute is present, Psolution < P°solvent. This reduction is independent of the solvent’s identity to first order and depends mainly on the solute mole fraction (a colligative effect).

Step-by-Step Solution:
Assume a nonvolatile solute so the vapor is essentially pure solvent.Apply Raoult’s law: Psolution = xsolvent * P°solvent.Because 0 < xsolvent < 1, conclude Psolution < P°solvent.Therefore, vapor pressure is “less than” that of the pure solvent.

Verification / Alternative check:
Experimental data for aqueous salt solutions show decreasing water activity (and thus lower vapor pressure) with increasing solute concentration, aligning with the law.

Why Other Options Are Wrong:
“More than” or “equal to” would require volatile solutes raising total pressure or pure solvent, which contradicts the stated nonvolatile condition.“Depends on the solvent” ignores the colligative nature of the effect for ideal solutions.

Common Pitfalls:
Confusing nonvolatile with volatile solutes; forgetting that strong nonideality or electrolytes need activity coefficients but still show vapor pressure lowering.

Final Answer:
Less than