How to use the faraday electrolysis calculator
- Choose what to find: the mass deposited, the time needed or the current needed.
- Enter the molar mass of the substance and the electrons per ion, such as 2 for copper(II).
- Enter the current and time for a mass, or the mass wanted with the current or the time.
- Read the answer with the charge passed, the moles of electrons and the moles of the substance.
Formula
Charge Q = current x time, in coulombs
Moles of electrons = Q / F, with the Faraday constant F = 96485.33 C/mol
Moles of substance = moles of electrons / z, where z is the electrons per ion
Mass = moles of substance x molar mass
This is Faraday's law of electrolysis in one line: mass = current x time x molar mass / (z x F). It assumes that all the current goes into depositing the substance.
Copper deposited by 2 A in 1 hour
Two amps for an hour is 7200 coulombs. That is 7200 / 96485.33 = 0.074623 mol of electrons, and since each copper ion takes 2 electrons it is 0.037311 mol of copper. The mass is 0.037311 x 63.546 = 2.371 g.
Silver plating with 0.5 A for 30 minutes passes 900 C and deposits 1.006 g of silver (z = 1, molar mass 107.8682). Depositing 5 g of copper with 3 A takes 5061 s, about 84.4 minutes. One gram of aluminum (z = 3) in 2 hours needs a current of about 1.49 A.
Current efficiency
In real plating some of the current goes into side reactions, such as releasing hydrogen, so the actual mass is lower than the calculated one. The ratio of the actual to the calculated mass is the current efficiency. Divide the page's mass by your efficiency to estimate the time needed in practice, or multiply the mass by the efficiency to estimate the result.
To convert between mass and moles for the reaction, use the moles to grams calculator.
Choosing z
The number of electrons per ion depends on the ion in solution. Copper(II) takes 2, copper(I) takes 1, silver takes 1, aluminum takes 3 and zinc(II) takes 2. A wrong value changes the answer by the same factor, so check the ion in your bath.
To find the current in a circuit from the voltage, see the Ohm's law calculator, and for amounts in a general reaction see the limiting reagent calculator.
Assumptions and limits
- The current is steady and all of it goes into the reaction (100 percent current efficiency).
- The molar mass and electrons per ion are those of the species being deposited.
- The Faraday constant is 96485.33212 C/mol.
- The page does not model plating thickness, area or density.
Frequently asked questions
What are Faraday's laws of electrolysis?
The mass of a substance deposited is proportional to the charge passed, and for a given charge the masses of different substances are in proportion to their molar mass divided by the electrons per ion.
How long does it take to plate a given mass?
Choose Time needed. The page divides the charge required for your mass by the current.
Why is my real result lower?
Side reactions use part of the current. The ratio of the real mass to the calculated one is the current efficiency, often below 100 percent.
What is the Faraday constant?
It is the charge carried by one mole of electrons, about 96485 coulombs per mole.