\[\ln K = \frac{nFE^\circ}{RT},\qquad \lg K = \frac{nE^\circ}{0.05916\ \mathrm V}\ (25\,{}^\circ\mathrm C)\]
含义Meaning
由标准电动势可直接算出氧化还原反应的平衡常数；E° 只要 0.3 V（n = 2），K 就达 10¹⁰，反应可视为完全。也可用于求溶度积、配合物稳定常数和 Kw。
Standard EMFs give equilibrium constants directly; just 0.3 V (n = 2) gives K ≈ 10¹⁰. Also used for solubility products, stability constants and Kw.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(K\) | 平衡常数equilibrium constant | 1 |
推导Derivation
平衡时 E = 0、Q = K，代入能斯特方程：\(0 = E^\circ - (RT/nF)\ln K\)。
At equilibrium E = 0 and Q = K.
或由 \(\Delta G^\circ = -nFE^\circ = -RT\ln K\)。
Equivalently from ΔG° = −nFE° = −RT ln K.
适用条件与局限Assumptions & limitations
K 对 E° 极其敏感：E° 误差 10 mV（n = 1）使 K 误差约 50%。
K is very sensitive: 10 mV error changes K by ~50 % (n = 1).
例题Worked example
Ag⁺ + e⁻ → Ag（0.799 V）与 AgCl + e⁻ → Ag + Cl⁻（0.222 V）：lg Ksp = (0.222 − 0.799)/0.05916 = −9.75，Ksp(AgCl) = 1.8×10⁻¹⁰。
From the Ag⁺/Ag and AgCl/Ag potentials: Ksp(AgCl) = 1.8×10⁻¹⁰.