Steam distillation of immiscible liquids:\nPure toluene boils at 110.6°C, pure water at 100°C. Toluene and water are immiscible. In a well-agitated equimolar mixture boiling at 1 atm (sum of vapour pressures = 1 atm), the mole fraction of water in the vapour phase (Xw) will satisfy:

Introduction / Context:
When two liquids are immiscible, the total vapour pressure over the mixture equals the sum of the pure-component vapour pressures at the mixture temperature. The mixture boils when this sum reaches the external pressure (here 1 atm). The vapour composition is proportional to the individual vapour pressures, not to liquid mole fractions (which are irrelevant for immiscibles).

Given Data / Assumptions:

• Pboiling: water 100°C, toluene 110.6°C.
• Immiscible and well agitated.
• Boiling at total pressure 1 atm.

Concept / Approach:
At a given temperature below both pure-component boiling points, the more volatile liquid (higher vapour pressure at that T) contributes a larger partial pressure and therefore a larger mole fraction in the vapour. Because water has a lower normal boiling point than toluene, water exhibits a higher vapour pressure than toluene at any T where the mixture boils by combined vapour pressures. Thus, Xw in the vapour must exceed 0.5.

Step-by-Step Solution:
Boiling condition: Pw(T) + Ptoluene(T) = 1 atm.Relative volatility: at the same T, Pw(T) > Ptoluene(T) since Tb(water) < Tb(toluene).Vapour mole fraction: Xw = Pw / (Pw + Ptoluene) > 0.5.Therefore select 0.5 < Xw < 1.0.

Verification / Alternative check:
Steam distillation principles confirm that immiscible mixtures boil below either pure component’s normal boiling point, with the more volatile component dominating the vapour.

Why Other Options Are Wrong:
Xw ≤ 0.5 contradicts relative volatility; Xw = 1.0 would require Ptoluene = 0, which is false; “indeterminate” is incorrect because qualitative ordering suffices.

Common Pitfalls:
Applying Raoult’s law with liquid mole fractions—irrelevant for immiscible pairs; here, each liquid contributes as if pure.

Final Answer:
0.5 < Xw < 1.0