Faraday’s Law for Electrolysis
This calculator uses Faraday’s law of electrolysis to estimate how much material is deposited at an electrode. It is commonly used for electroplating, metal deposition, and electrochemical mass-transfer calculations.
Here, m is deposited mass, I is current, t is time, M is molar mass, η is current efficiency, n is the number of electrons per ion, and F is the Faraday constant.
What Current Efficiency Means
Current efficiency is the percentage of charge that actually goes into the desired deposition reaction. If side reactions occur, such as gas evolution or unwanted reactions, the real deposited mass is lower than the ideal value.
Why Valency Matters
Valency tells you how many electrons are required to deposit one atom or ion of the material. For example, Cu²⁺ requires 2 electrons per copper atom, while Ag⁺ requires 1 electron per silver atom.
| Reaction | n | Meaning |
|---|---|---|
| Ag⁺ + e⁻ → Ag | 1 | 1 mole of electrons deposits 1 mole of silver. |
| Cu²⁺ + 2e⁻ → Cu | 2 | 2 moles of electrons deposit 1 mole of copper. |
| Al³⁺ + 3e⁻ → Al | 3 | 3 moles of electrons deposit 1 mole of aluminum. |
Optional Electroplating Thickness
If density and plated area are known, the calculator estimates average plating thickness.
This is an average thickness estimate. Real plating thickness can vary across the surface because of current distribution, edge effects, geometry, agitation, and bath chemistry.
Example: Copper Deposition
Suppose you pass 2 A through a copper plating cell for 1 hour at 100% current efficiency.
I = 2 A t = 1 h = 3600 s M = 63.546 g/mol n = 2 F = 96485.33212 C/mol m = I t M / (nF) m = 2 × 3600 × 63.546 / (2 × 96485.33212) m ≈ 2.37 g
Common Mistakes
- Using minutes or hours as if they were seconds.
- Forgetting current efficiency.
- Using the wrong valency for the ion being reduced.
- Assuming all current goes into plating when side reactions are present.
- Using average thickness as if plating were perfectly uniform.
Frequently Asked Questions
What is Faraday’s law of electrolysis?
Faraday’s law states that the mass deposited is proportional to the electric charge passed through the electrolyte.
How do I calculate charge?
Charge is current multiplied by time: Q = I × t. Current must be in amperes and time must be in seconds.
Why is current efficiency included?
Because not all charge necessarily produces the desired deposited metal. Some charge may go into side reactions.
Can I calculate required time?
Yes. Choose “Calculate required time” and enter the target mass and current.
Can I calculate plating thickness?
Yes. Enter density and plated area. The calculator estimates average thickness from mass, density, and area.