含义Meaning
理想溶液中，每个组分的蒸气分压等于其纯态蒸气压乘以它在液相中的摩尔分数。
In an ideal solution each component’s vapour pressure equals its pure vapour pressure times its liquid mole fraction.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(p_\mathrm{A}\) | 组分 A 的平衡蒸气分压partial vapour pressure of A | Pa |
| \(p_\mathrm{A}^*\) | 纯 A 的饱和蒸气压vapour pressure of pure A | Pa |
| \(x_\mathrm{A}\) | A 在液相中的摩尔分数mole fraction of A in the liquid | 1 |
推导Derivation
直观图像：液面上 A 分子所占比例为 \(x_\mathrm{A}\)，逸出速率按比例降低，而凝结速率正比于 \(p_\mathrm{A}\)。
Picture: only a fraction \(x_\mathrm{A}\) of the surface is A, so escape is reduced proportionally; condensation is proportional to \(p_\mathrm{A}\).
热力学：平衡时 \(\mu_\mathrm{A}(l) = \mu_\mathrm{A}(g)\)；理想溶液 \(\mu_\mathrm{A}(l) = \mu_\mathrm{A}^*(l) + RT\ln x_\mathrm{A}\)，理想气体 \(\mu_\mathrm{A}(g) = \mu^\circ + RT\ln(p_\mathrm{A}/p^\circ)\)。
Thermodynamically, equate \(\mu_\mathrm{A}(l) = \mu_\mathrm{A}^*(l) + RT\ln x_\mathrm{A}\) with \(\mu^\circ + RT\ln(p_\mathrm{A}/p^\circ)\).
纯液体时 \(x_\mathrm{A} = 1\) 给出 \(p_\mathrm{A}^*\)，两式相减即 \(p_\mathrm{A} = x_\mathrm{A}p_\mathrm{A}^*\)。
For the pure liquid \(x_\mathrm{A} = 1\) gives \(p_\mathrm{A}^*\); subtracting yields \(p_\mathrm{A} = x_\mathrm{A}p_\mathrm{A}^*\).
二组分理想溶液总压 \(p = p_\mathrm{B}^* + (p_\mathrm{A}^* - p_\mathrm{B}^*)x_\mathrm{A}\)，是 x 的直线。
Total pressure of a binary ideal solution is linear in x.
适用条件与局限Assumptions & limitations
严格适用于理想溶液（A–A、B–B、A–B 作用相同，如苯–甲苯）；对稀溶液的溶剂近似成立。
Exact for ideal solutions (e.g. benzene–toluene); approximately for the solvent of dilute solutions.
正偏差（如乙醇–水）、负偏差（如丙酮–氯仿）体系需引入活度系数 \(p_\mathrm{A} = \gamma_\mathrm{A}x_\mathrm{A}p_\mathrm{A}^*\)，可形成共沸物。
Positive (ethanol–water) or negative (acetone–chloroform) deviations need activity coefficients and can form azeotropes.