Ideal solutions and Raoult’s law: For an ideal binary solution, how does the total vapor pressure vary with composition (mole fraction)?

Introduction / Context:Understanding vapor–liquid equilibrium (VLE) begins with ideal solutions, where Raoult’s law applies. This provides a linear dependence of partial pressures, and hence total pressure, on composition.

Given Data / Assumptions:

• Ideal solution behavior: each component obeys Raoult’s law.
• Binary mixture at fixed temperature.

Concept / Approach:Raoult’s law states p_i = x_i * p_i^sat(T). The total pressure is P_total = Σ p_i = x_1 p_1^sat + x_2 p_2^sat. Because x_2 = 1 − x_1, P_total is a linear function of x_1 (and of x_2).

Step-by-Step Solution:

Verification / Alternative check:Graphical VLE diagrams for ideal pairs (e.g., benzene–toluene) show linear total pressure lines at constant temperature.

Why Other Options Are Wrong:

• Inverse, exponential, parabolic, or negligible change: Do not match Raoult’s law behavior for ideal solutions.

Common Pitfalls:Mixing up ideal solution (Raoult) with ideal gas behavior; forgetting temperature must be held constant for the linear relation.

Final Answer:Linearly