\[K_a = \frac{\alpha^2c}{1 - \alpha},\qquad \alpha = \frac{\Lambda_m}{\Lambda_m^\circ},\qquad \frac{1}{\Lambda_m} = \frac{1}{\Lambda_m^\circ} + \frac{c\Lambda_m}{K_a(\Lambda_m^\circ)^2}\]
含义Meaning
弱电解质的电离度随稀释而增大，K 保持不变（1888）。由电导测得电离度即可求电离常数。
A weak electrolyte’s degree of dissociation rises on dilution while K stays fixed (1888); conductance gives α and hence K.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\alpha\) | 电离度degree of dissociation | 1 |
| \(c\) | 分析浓度analytical concentration | mol·L⁻¹ |
推导Derivation
HA ⇌ H⁺ + A⁻：平衡浓度 \(c(1-\alpha), c\alpha, c\alpha\)，代入 Ka。
Equilibrium concentrations c(1−α), cα, cα.
阿伦尼乌斯：摩尔电导只来自已电离部分，\(\alpha \approx \Lambda_m/\Lambda_m^\circ\)。
Arrhenius: α ≈ Λ_m/Λ°.
整理得线性式：1/Λ_m 对 cΛ_m 作图，截距 1/Λ°，斜率 1/(KaΛ°²)。
Linearise for plotting.
适用条件与局限Assumptions & limitations
忽略离子间作用（活度、离子氛对迁移率的影响）；精确工作需德拜–休克尔–昂萨格修正。强电解质不适用。
Neglects interionic effects; not for strong electrolytes.
例题Worked example
乙酸 Ka = 1.8×10⁻⁵：c = 0.10 mol/L 时 α = 1.3%，c = 0.0010 mol/L 时 α = 12.5%。
Acetic acid: α = 1.3 % at 0.10 M, 12.5 % at 0.0010 M.