\[\mu_i = \left(\frac{\partial G}{\partial n_i}\right)_{T,p,n_{j\ne i}},\qquad \mu_i = \mu_i^\circ + RT\ln a_i\]
气体gases
\[\mu = \mu^\circ + RT\ln\frac{p}{p^\circ}\ (\text{理想气体}),\qquad \mu = \mu^\circ + RT\ln\frac{f}{p^\circ}\ (\text{真实气体，逸度 } f)\]\[\mu = \mu^\circ + RT\ln\frac{p}{p^\circ}\ (\text{ideal gas}),\qquad \mu = \mu^\circ + RT\ln\frac{f}{p^\circ}\ (\text{real gas , fugacity} f)\]含义Meaning
偏摩尔吉布斯能，衡量物质“逃逸”某相的倾向。物质总是从化学势高处向低处转移；相平衡、化学平衡的条件都是化学势相等（或计量组合为零）。
The partial molar Gibbs energy — a substance’s escaping tendency. Matter moves from high to low μ; phase and chemical equilibria both require equal (or stoichiometrically balanced) chemical potentials.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\mu_i\) | 组分 i 的化学势chemical potential of i | J·mol⁻¹ |
| \(a_i\) | 活度activity | 1 |
| \(f\) | 逸度fugacity | Pa |
推导Derivation
理想气体 \((\partial\mu/\partial p)_T = V_m = RT/p\)，从 p° 积分到 p 得 \(\mu = \mu^\circ + RT\ln(p/p^\circ)\)。
For an ideal gas integrate V_m = RT/p from p°.
溶液中类比写成活度形式，非理想性全部归入活度系数。
In solutions use activities by analogy.
多相平衡：同一物质在各相中 μ 相等；化学平衡：\(\sum\nu_i\mu_i = 0\)。
Phase equilibrium: equal μ; chemical equilibrium: Σνμ = 0.
适用条件与局限Assumptions & limitations
标准态的选择（纯物质、无限稀释、1 mol/L 等）决定 μ° 和 a 的数值，必须一致。
μ° and a depend on the chosen standard state.