Raoult’s law application at room conditions:\nA saturated aqueous solution of benzene (liquid mole fraction of benzene = xB) is in equilibrium with an air–vapor mixture at room temperature. If the pure-component vapor pressures at these conditions are pvB for benzene and pvw for water, what is the partial pressure of benzene in the gas mixture?

Introduction / Context:
Determining partial pressures of volatile components above solutions is fundamental in vapor–liquid equilibrium, environmental emissions estimation, and absorber/stripper design. For ideal or near-ideal solutions at low solute concentrations, Raoult’s law provides a simple, widely used relation between the liquid composition and the partial pressure of a volatile solvent/solute in the gas phase.

Given Data / Assumptions:

• Temperature is fixed (room temperature).
• Liquid phase: water containing dissolved benzene; liquid mole fraction of benzene is xB.
• Gas phase: air plus water vapor plus benzene vapor.
• Pure-component vapor pressures at the same temperature: pvB (benzene), pvw (water).
• Ideal solution approximation for benzene in water at low xB.

Concept / Approach:
Raoult’s law states: partial pressure of component i above a liquid solution is p_i = x_i · p_i^sat, where x_i is the mole fraction of i in the liquid, and p_i^sat is the pure-component saturated vapor pressure at the same temperature. The presence of other gases (air, water vapor) affects the total pressure but does not change the direct proportionality p_B = xB · pvB under the ideal assumption.

Step-by-Step Solution:
Identify benzene as the volatile component of interest.Apply Raoult’s law: p_B = xB * pvB.Therefore, the benzene partial pressure equals xB·pvB.

Verification / Alternative check:
Dalton’s law governs the gas mixture: P_total = p_air + p_w + p_B. Even though water contributes pvw (or close to it), benzene’s contribution is still xB·pvB if the liquid behaves ideally for benzene. Nonideality would introduce an activity coefficient γB (p_B = xB·γB·pvB), but γB ≈ 1 is assumed here.

Why Other Options Are Wrong:
pvB: ignores dilution in the liquid; only valid for pure benzene.(Patm − pvw)·xB: incorrectly scales by the “dry-air” pressure, not Raoult’s law.xB·Patm: total pressure is irrelevant to Raoult’s proportionality.

Common Pitfalls:
Confusing Raoult’s law (liquid-based) with Dalton’s law (gas-based), or forgetting that dissolved benzene’s partial pressure drops in proportion to its liquid mole fraction.

Final Answer:
xB·pvB