\[m = \frac{QM}{zF} = \frac{ItM}{zF},\qquad n_e = \frac{Q}{F}\]
含义Meaning
电解时电极上析出（溶解）物质的量与通过的电量成正比（第一定律）；通过相同电量时，析出物质的量与离子电荷数成反比（第二定律）。法拉第（1834）。
The amount deposited or dissolved at an electrode is proportional to the charge passed (first law) and, for equal charge, inversely proportional to the ion’s charge number (second law) — Faraday, 1834.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(Q = It\) | 电量charge | C |
| \(F\) | 法拉第常数 96485 C/molFaraday constant | C·mol⁻¹ |
| \(z\) | 电极反应中每个离子转移的电子数electrons per ion in the electrode reaction | 1 |
| \(M\) | 摩尔质量molar mass | g·mol⁻¹ |
推导Derivation
每个 M^{z+} 还原需要 z 个电子；1 mol 电子带电量 \(F = N_Ae\)。
Each M^{z+} needs z electrons; one mole of electrons carries F = N_A e.
电子的物质的量 Q/F，金属的物质的量 Q/(zF)，乘以 M 得质量。
Moles of metal = Q/(zF); multiply by M.
适用条件与局限Assumptions & limitations
假设电流效率 100%；有副反应（如析氢）时实际析出量更少。
Assumes 100 % current efficiency; side reactions (H₂ evolution) reduce yield.
例题Worked example
2.00 A 电流电解 CuSO₄ 溶液 1 h：m(Cu) = 2.00×3600×63.55/(2×96485) = 2.37 g。
2.00 A for 1 h deposits 2.37 g of Cu.