The one equation, and what each term does
The mass deposited on the electrode equals the molar mass M (g/mol) times the total charge Q (coulombs), divided by the electrons transferred n and Faraday's constant 96485 C/mol. Charge is just current in amps times time in seconds, so a bigger current or a longer run both add mass in direct proportion.
Common plating metals
The value of n comes from the metal's half-reaction, and it changes the answer as much as the molar mass does.
| Metal | Molar mass M | Electrons n | Half-reaction |
|---|---|---|---|
| Silver (Ag) | 107.87 g/mol | 1 | Ag+ + e− → Ag |
| Copper (Cu) | 63.55 g/mol | 2 | Cu2+ + 2e− → Cu |
| Nickel (Ni) | 58.69 g/mol | 2 | Ni2+ + 2e− → Ni |
| Zinc (Zn) | 65.38 g/mol | 2 | Zn2+ + 2e− → Zn |
| Chromium (Cr) | 52.00 g/mol | 3 | Cr3+ + 3e− → Cr |
| Gold (Au) | 196.97 g/mol | 3 | Au3+ + 3e− → Au |
Worked example: silver-plating at 0.5 A for 2 hours (7200 s) gives Q = 3600 C, so m = (107.87 × 3600) ÷ (1 × 96485) ≈ 4.0 g of silver.
Solving for the other variables
- Time. To hit a target mass, rearrange to t = (m × n × F) ÷ (M × I).
- Current. For a fixed run time, I = (m × n × F) ÷ (M × t).
- Moles of electrons. The charge alone gives this: mol e− = Q ÷ F, independent of which metal you plate.
Common questions
What is Faraday's constant?
It is the charge carried by one mole of electrons: 96485 coulombs per mole. Every electrolysis mass calculation runs through it, because it links the number of electrons pushed through the cell to the amount of substance deposited.
What does n mean in the electrolysis formula?
n is the number of electrons transferred per ion in the half-reaction. Copper is Cu2+ plus 2 electrons, so n is 2. Silver is Ag+ plus 1 electron, so n is 1. A larger n means less metal deposited for the same charge.
Why is the deposited mass less than the formula predicts?
The formula assumes every electron does the intended job. In practice current efficiency is often 80 to 98 percent because side reactions, resistance and impurities consume some of the charge. Multiply the result by the efficiency to get a realistic figure.
