Faraday’s Law Calculator
Calculate electrolysis mass, charge, time, or current with ion presets, efficiency checks, visuals, and step-by-step solutions.
Background
Faraday’s law connects electric charge to the amount of substance deposited or consumed at an electrode. This upgraded calculator helps students move between current, time, charge, electrons transferred, molar mass, moles, and deposited mass.
How to use this calculator
- Choose whether to solve for mass, charge, time, or current.
- Enter the molar mass and electrons transferred, or use a quick ion preset.
- Enter either total charge or current and time.
- Use the result, table, and electrolysis visual to check the setup.
Formula & Equations Used
Faraday’s law of electrolysis: m = (Q · M · η) / (n · F)
Charge from current and time: Q = I · t
Charge required for a mass: Q = (m · n · F) / (M · η)
Moles deposited: mol = m / M
Faraday constant: F ≈ 96485 C/mol e⁻
Electroplating note: mass increases at the cathode for metal deposition.
Example Problems & Step-by-Step Solutions
Example 1: Mass of copper deposited
Given: Cu²⁺, n = 2, M = 63.546 g/mol, I = 2.50 A, and t = 30.0 min = 1800 s.
Step 1: Q = I · t = 2.50 × 1800 = 4500 C.
Step 2: m = (Q · M)/(n · F) = (4500 × 63.546)/(2 × 96485.33212).
Answer: m ≈ 1.48 g Cu.
Example 2: Time needed to plate silver
Given: Ag⁺, n = 1, M = 107.8682 g/mol, m = 0.500 g, and I = 0.750 A.
Step 1: Q = (m · n · F)/M.
Step 2: t = Q/I.
Answer: The calculator finds the charge first, then divides by current to get time.
Example 3: Efficiency correction
Given: A process has 80% current efficiency.
Step 1: Convert efficiency to a decimal: η = 0.80.
Step 2: For the same charge, only 80% contributes to the desired product.
Answer: The deposited mass is smaller than the ideal 100% efficiency result.
Common mistakes to avoid
- Do not forget to convert minutes or hours into seconds before using Q = I · t.
- Do not use the ion charge as the molar mass. n and M are different inputs.
- Do not use n = 1 for every ion. For example, Cu²⁺ uses n = 2.
- Do not confuse molar mass M with deposited mass m.
- Do not ignore current efficiency when a problem says the process is not 100% efficient.
Frequently Asked Questions
What does Faraday’s law calculate?
It calculates how much substance is deposited or consumed at an electrode from the electric charge passed through an electrolysis cell.
What is n in Faraday’s law?
The value n is the number of electrons transferred per ion or formula unit in the half-reaction.
Can I use current and time instead of charge?
Yes. The calculator uses Q = I · t when charge is not entered but current and time are provided.
What does current efficiency mean?
Current efficiency is the fraction of charge that actually produces the desired electrolysis product.
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