Electrolysis drives a non-spontaneous redox reaction with an external power supply: metal ions are reduced and deposited at the cathode, while something is oxidised at the anode. Michael Faraday showed in 1833–34 that the amount of substance produced is proportional to the electric charge passed (first law), and that for the same charge the masses of different substances are proportional to their molar masses divided by the number of electrons each particle needs (second law).
Both laws collapse into one equation: moles of electrons = Q/F, and moles of product = Q/(nF). Multiplying by the molar mass gives the mass. The quantity M/(nF) is the electrochemical equivalent Z – for copper it is 0.3293 mg per coulomb, for silver 1.118 mg/C – so the deposit is simply Z times the charge.
Real plating baths rarely use every electron for the wanted reaction: hydrogen evolution and other side reactions steal part of the current. The current efficiency field scales the result – about 95–100% for acid copper, but only 10–25% for hard chromium. The same calculation sizes electrorefining, electrowinning, anodising, hydrogen electrolysers and chlor-alkali cells.
How to use the Electrolysis Calculator
- Calculate
- Electrode reaction
- Molar mass
- Electrons per particle (n)
- Current
- Time
- Charge passed
- Target mass
- Current efficiency
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Pick the electrode reaction (or enter your own molar mass and electrons), choose what you want to find, and enter current and time or the charge directly. The calculator converts charge to moles of electrons with the Faraday constant, divides by n, multiplies by the molar mass and applies the current efficiency; for gases it also gives the volume at 0 °C and 25 °C.
Worked example
Copper plating at 2 A for 30 min, 100% efficiency: Q = 2 × 1800 = 3600 C → 3600 / 96 485.33 = 0.037311 mol e⁻ → 0.037311 / 2 = 0.018656 mol Cu → 0.018656 × 63.546 = 1.1855 g of copper.
Water electrolysis from a 4000 mAh charge (14 400 C): 0.14925 mol e⁻ give 0.074623 mol H₂ (0.1504 g, 1.69 L at 0 °C and 1 bar) and 0.037311 mol O₂ (1.194 g).
Electrochemical equivalents
| Reaction | M (g/mol) | n | Z (mg/C) | g per A·h |
|---|---|---|---|---|
| Copper – Cu²⁺ + 2e⁻ → Cu | 63.5460 | 2 | 0.32930 | 1.1855 |
| Silver – Ag⁺ + e⁻ → Ag | 107.8682 | 1 | 1.11798 | 4.0247 |
| Nickel – Ni²⁺ + 2e⁻ → Ni | 58.6934 | 2 | 0.30416 | 1.0950 |
| Gold – Au³⁺ + 3e⁻ → Au | 196.9666 | 3 | 0.68047 | 2.4497 |
| Gold – Au⁺ (cyanide bath) + e⁻ → Au | 196.9666 | 1 | 2.04141 | 7.3491 |
| Iron – Fe²⁺ + 2e⁻ → Fe | 55.8450 | 2 | 0.28940 | 1.0418 |
| Zinc – Zn²⁺ + 2e⁻ → Zn | 65.3800 | 2 | 0.33881 | 1.2197 |
| Tin – Sn²⁺ + 2e⁻ → Sn | 118.7100 | 2 | 0.61517 | 2.2146 |
| Lead – Pb²⁺ + 2e⁻ → Pb | 207.2000 | 2 | 1.07374 | 3.8655 |
| Chromium – from Cr(VI), 6e⁻ per Cr (hard chrome) | 51.9961 | 6 | 0.08982 | 0.3233 |
| Aluminium – Al³⁺ + 3e⁻ → Al (Hall–Héroult) | 26.9815 | 3 | 0.09321 | 0.3356 |
| Sodium – Na⁺ + e⁻ → Na (molten NaCl) | 22.9898 | 1 | 0.23827 | 0.8578 |
| Potassium – K⁺ + e⁻ → K | 39.0983 | 1 | 0.40523 | 1.4588 |
| Hydrogen gas – 2H⁺ + 2e⁻ → H₂ | 2.0159 | 2 | 0.01045 | 0.0376 |
| Oxygen gas – 2H₂O → O₂ + 4H⁺ + 4e⁻ | 31.9988 | 4 | 0.08291 | 0.2985 |
| Chlorine gas – 2Cl⁻ → Cl₂ + 2e⁻ | 70.9060 | 2 | 0.36744 | 1.3228 |
Tips
- Standard potentials are reduction potentials at 25 °C, 1 M and 1 bar.
- n is the number of electrons transferred in the balanced reaction.
- Faraday constant: 96 485 C per mole of electrons.
- Everything is calculated in your browser.
Common mistakes to avoid
- Flipping the sign of a potential and also subtracting it (counting the reversal twice).
- Multiplying a standard potential by the coefficient of the half-reaction – potentials are intensive.
- Using log base e where the Nernst equation uses log₁₀ (or the other way round).
Inputs explained
| Field | What to enter |
|---|---|
| Calculate | Choose one: Mass deposited (from current and time), Mass deposited (from charge), Time needed for a mass, Current needed for a mass |
| Electrode reaction | Choose one: Copper – Cu²⁺ + 2e⁻ → Cu, Silver – Ag⁺ + e⁻ → Ag, Nickel – Ni²⁺ + 2e⁻ → Ni, Gold – Au³⁺ + 3e⁻ → Au … |
| Molar mass | Units: g/mol, kg/mol, Da (u), kDa |
| Electrons per particle (n) | A number |
| Current | Units: A, mA, µA, kA |
| Time | Units: min, s, h, days |
| Charge passed | Units: C, mAh, Ah, kC, F (mol e⁻) |
| Target mass | Units: g, mg, µg, kg, oz, lb |
| Current efficiency | In % |
What each result means
- Electrochemical equivalent Z = [Molar mass used]÷([Electrons per particle n]×96485.33212)×1000
- Time needed = [Charge passed Q]÷[Current]
- Current needed = [Charge passed Q]÷[Time]
- Moles of electrons = [Charge passed Q]÷96485.33212
- Moles of substance = [Mass deposited ÷ produced]÷[Molar mass used]
- Gas volume at STP (0 °C, 1 bar) = ([Mass deposited ÷ produced]÷[Molar mass used])×22.71095
- Gas volume at 25 °C, 1 atm = ([Mass deposited ÷ produced]÷[Molar mass used])×24.4654
Formula
Q = I·t · m = (Q·M)/(n·F) × efficiency · Z = M/(n·F) · t = m·n·F/(M·I) · I = m·n·F/(M·t)Worked example
Inputs — Calculate: Mass deposited (from current and time); Electrode reaction: Copper – Cu²⁺ + 2e⁻ → Cu; Current: 2 A; Time: 30 min; Current efficiency: 100 %.
Results — Molar mass used = 63.546 g/mol; Electrons per particle n = 2; Electrochemical equivalent Z = 0.3293 mg/C; Charge passed Q = 3,600 C; Mass deposited / produced = 1.18549 g; Moles of electrons = 0.037311 mol; Moles of substance = 0.018656 mol.
Key terms
- Electrolysis
- Using electric current to drive a non-spontaneous chemical reaction.
- Electrochemical equivalent Z
- Mass deposited per coulomb, M/(nF).
- Current efficiency
- Fraction of the charge that goes into the wanted reaction.
- Coulomb
- Charge carried by 1 ampere in 1 second; 1 A·h = 3600 C, 1 mAh = 3.6 C.
Frequently asked questions
How do you calculate the mass deposited in electrolysis?
m = I·t·M/(n·F). For copper at 2 A for 30 minutes: Q = 3600 C, moles of e⁻ = 0.03731, moles of Cu = 0.01866, mass = 1.186 g.
What are Faraday's two laws of electrolysis?
First: the mass produced is proportional to the charge passed. Second: for the same charge, masses of different substances are proportional to M/n (their equivalent weights).
What is the Faraday constant?
96 485.332 C/mol – the charge on one mole of electrons (Avogadro constant × elementary charge).
How long does it take to plate 1 g of silver at 0.5 A?
t = m·n·F/(M·I) = 1 × 1 × 96 485 / (107.87 × 0.5) = 1789 s, just under 30 minutes.
How much hydrogen does 1 A·h of charge make?
3600 C ÷ 96 485 = 0.0373 mol e⁻ → 0.01866 mol H₂ = 0.0376 g, about 0.42 L at 0 °C and 1 bar.
Why is my plated mass lower than calculated?
Current efficiency below 100% (hydrogen evolution, side reactions), loose deposit lost in rinsing, or a current that was not constant over the run.
Is this the same as Faraday's law of induction?
No. Faraday's law of induction relates a changing magnetic flux to an induced voltage; the laws of electrolysis relate charge to the amount of chemical change.
What formula does the Electrolysis Calculator use?
Q = I·t · m = (Q·M)/(n·F) × efficiency · Z = M/(n·F) · t = m·n·F/(M·I) · I = m·n·F/(M·t).