Part of JPC-05 — Solutions: Raoult's Law & Colligative Properties

Raoult's Law for Ideal Solutions

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Raoult's law states that the partial vapour pressure of each volatile component in an ideal solution is proportional to its mole fraction: PAP_A = xAx_A * P_A_{std} and PBP_B = xBx_B * P_B_{std}. Total pressure: PtotalP_{total} = xAx_AP_A_{std} + xBx_BP_B_{std} = P_B_{std} + (P_A_{std} - P_B_{std})xAx_A, which is linear in xAx_A. The vapour composition: yAy_A = PAPtotal\frac{P_A}{P_total} = xAx_AP_A_{std}/PtotalP_{total} (Dalton's law). The more volatile component (higher PstdP_{std}) is enriched in the vapour phase — this is the principle behind fractional distillation. Ideal solutions satisfy: delta_H_{mix} = 0 noheatabsorbedreleased\frac{no heat absorbed}{released}, delta_V_{mix} = 0 (no volume change), and A-B interactions ≈ average of A-A and B-B. Examples: benzene + toluene, n-hexane + n-heptane, chlorobenzene + bromobenzene — all pairs with similar molecular structures. PtotalP_{total} vs xAx_A is a straight line for ideal solutions. PtotalP_{total} vs yAy_A gives a curve. On T-x and T-y diagrams, the liquid line (bubble curve) and vapour line (dew curve) enclose the two-phase region. The lever rule gives the ratio of liquid to vapour phases at any point in this region. Understanding ideal solutions provides the baseline for analysing deviations.

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