含义Meaning
稀电解质溶液中，离子平均活度系数的对数与离子强度的平方根成正比下降。
In dilute electrolyte solutions the log of the mean activity coefficient falls in proportion to √I.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\gamma_\pm\) | 平均离子活度系数mean ionic activity coefficient | 1 |
| \(A\) | 常数（25 °C 水中 0.509 (mol/kg)^{-1/2}）constant (0.509 in water at 25 °C) | (mol·kg⁻¹)^{-1/2} |
| \(a\) | 离子最近接近距离distance of closest approach | m |
推导Derivation
每个离子周围形成电荷相反的“离子氛”，其电荷分布由泊松方程 \(\nabla^2\phi = -\rho/\varepsilon\) 与玻尔兹曼分布联立。
Each ion is surrounded by an oppositely charged ‘ionic atmosphere’; combine Poisson’s equation with a Boltzmann distribution.
线性化后得屏蔽库仑势 \(\phi = \frac{ze}{4\pi\varepsilon r}e^{-r/r_D}\)，\(r_D\) 为德拜长度，\(1/r_D \propto \sqrt I\)。
Linearising gives a screened Coulomb potential with Debye length \(r_D\), \(1/r_D \propto \sqrt I\).
离子氛使中心离子能量降低 \(\Delta\mu = -\frac{z^2e^2N_A}{8\pi\varepsilon r_D} = RT\ln\gamma\)，所以 \(\ln\gamma \propto -z^2\sqrt I\)。
The atmosphere lowers the ion’s energy by \(\Delta\mu = RT\ln\gamma \propto -z^2\sqrt I\).
阳、阴离子取几何平均并用电中性条件得到 \(|z_+z_-|\)。
Averaging cation and anion with electroneutrality gives \(|z_+z_-|\).
适用条件与局限Assumptions & limitations
极限定律只在 I < 约 0.01 mol/kg 时准确；更高浓度用扩展式、戴维斯或皮策方程。
The limiting law holds below I ≈ 0.01 mol/kg; use extended, Davies or Pitzer equations beyond.
把溶剂视为连续介质、离子视为点电荷，忽略离子缔合。
Continuum solvent, point ions, no ion pairing.