Faraday's Law of Electrolysis Calculator

About the Faraday's Law of Electrolysis Calculator

Faraday's first law of electrolysis gives the mass of substance deposited at an electrode from the total electric charge passed, the substance's molar mass and the number of electrons per ion.

Enter the current (A), time (s), molar mass (g/mol) and the number of electrons transferred per ion n (e.g. 2 for Cu²⁺). The Faraday constant F = 96485 C/mol. Mass is returned in grams.

How to use this calculator

1. Enter the current, time, molar mass, and charge number for the substance.
2. Make sure the current is in amperes and the time is in seconds, so the calculator can find total charge.
3. Check that the molar mass is in grams per mole and the charge number is the number of electrons transferred per ion.
4. Read the deposited mass from the result, along with the step-by-step calculation.

The formula explained

The formula computes the mass deposited, where total charge is found by \(Q = I t\), then converted into mass with \(m = \frac{Q M}{n F} = \frac{I t M}{n F}\). Here \(F\) is Faraday's constant, about \(96485\,\text{C/mol}\).

• m = mass deposited or released, in grams
• Q = total electric charge passed, in coulombs
• I = current, in amperes
• t = time, in seconds
• M = molar mass of the substance, in grams per mole
• n = charge number, meaning electrons transferred per ion
• F = Faraday's constant, about \(96485\,\text{C/mol}\)

Step by step method

1. Find the total charge using \(Q = I t\).
2. Substitute \(Q\), \(M\), \(n\), and \(F\) into \(m = \frac{Q M}{n F}\).
3. Carry out the division carefully and keep units consistent.
4. Interpret the answer as the mass deposited or produced at the electrode.

Worked example

Problem. A current of \(2.0\,\text{A}\) flows for \(30\,\text{min}\) through a solution of copper(II) ions. If \(M = 63.55\,\text{g/mol}\) and \(n = 2\), how much copper is deposited?

1. Convert time to seconds: \(30\,\text{min} = 1800\,\text{s}\).
2. Find charge: \(Q = I t = 2.0 \times 1800 = 3600\,\text{C}\).
3. Compute mass: \(m = \frac{Q M}{n F} = \frac{3600 \times 63.55}{2 \times 96485} \approx 1.19\,\text{g}\).

Tips and common mistakes

• Always convert time to seconds before calculating, because \(F\) is in coulombs per mole of electrons.
• Use the correct value of \(n\) for the ion, since a wrong charge number gives a wrong mass even if the current and time are correct.

Frequently asked questions