\[\sum_i n_i\,d\mu_i = -S\,dT + V\,dp \xrightarrow{T,p\ \text{恒定}} \sum_i x_i\,d\mu_i = 0\]\[\sum_i n_i\,d\mu_i = -S\,dT + V\,dp \xrightarrow{T,p\ \text{const.}} \sum_i x_i\,d\mu_i = 0\]
含义Meaning
多组分体系中各组分的化学势不能独立变化：二组分溶液中一个组分的化学势变化决定了另一个的变化。由此可从溶剂的蒸气压推算溶质的活度，并检验实验数据的热力学一致性。
Chemical potentials in a mixture are not independent: in a binary solution one component’s μ change fixes the other’s. It lets solute activities be obtained from solvent data and checks thermodynamic consistency.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(x_i\) | 摩尔分数mole fraction | 1 |
推导Derivation
G 是广延量，\(G = \sum n_i\mu_i\)（欧拉定理）。
G is extensive, so G = Σnμ (Euler).
全微分 \(dG = \sum n_id\mu_i + \sum\mu_idn_i\)。
Differentiate.
与基本方程 \(dG = -SdT + Vdp + \sum\mu_idn_i\) 比较，得上式。
Compare with the fundamental equation.
适用条件与局限Assumptions & limitations
适用于平衡态的均匀相。
Homogeneous phases at equilibrium.
例题Worked example
二组分 \(x_A\,d\ln a_A + x_B\,d\ln a_B = 0\)：若溶剂服从拉乌尔定律，溶质必服从亨利定律。
If the solvent obeys Raoult’s law, the solute obeys Henry’s law.