\[\frac{n_\alpha}{n_\beta} = \frac{x_\beta - x_0}{x_0 - x_\alpha}\]
含义Meaning
两相区内，两相物质的量之比与体系总组成点到两相组成点的距离成反比，像杠杆平衡一样。用于相图中计算各相的量。
In a two-phase region, the amounts of the two phases are inversely proportional to the distances from the overall composition to each phase’s composition — like a balanced lever.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(x_0\) | 体系总组成overall composition | 1 |
| \(x_\alpha, x_\beta\) | 两相各自的组成（连接线两端）compositions of the two phases (tie-line ends) | 1 |
推导Derivation
物料守恒：\(n x_0 = n_\alpha x_\alpha + n_\beta x_\beta\)，\(n = n_\alpha + n_\beta\)。
Mass balance on component B.
消去 n 整理即得 \(n_\alpha(x_0 - x_\alpha) = n_\beta(x_\beta - x_0)\)。
Eliminate n.
适用条件与局限Assumptions & limitations
组成可用摩尔分数（得物质的量比）或质量分数（得质量比），须一致。
Use mole fractions for amounts or mass fractions for masses, consistently.
例题Worked example
苯–甲苯在某温度下液相 x = 0.30、气相 y = 0.60，总组成 0.40：n(液)/n(气) = (0.60 − 0.40)/(0.40 − 0.30) = 2。
Liquid 0.30, vapour 0.60, overall 0.40: n(l)/n(g) = 2.