Ideal solutions and Raoult’s law: For an ideal binary solution, how does the total vapor pressure vary with composition (mole fraction)?
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AInversely
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BExponentially
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CLinearly
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DNegligibly (no change)
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EParabolically
Answer
Correct Answer: Linearly
Explanation
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:
Write P_total(x_1) = x_1 p_1^sat + (1 − x_1) p_2^sat.Rearrange: P_total = p_2^sat + x_1 (p_1^sat − p_2^sat).This is a straight line in x_1 with slope (p_1^sat − p_2^sat).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