Electrolysis Calculator - Mass Deposition (Faraday's Law)

What is an electrolysis calculator?

An electrolysis calculator finds the mass of a metal deposited or dissolved at an electrode during electrolysis. Electrolysis is a process that uses an electric current to force a chemical reaction that would not happen on its own. The calculator applies Faraday's law of electrolysis, using the current, the time, and the properties of the chosen metal.

How to calculate electrolysis mass: Faraday's law formula

Faraday's law states that the mass of a substance produced at an electrode is proportional to the amount of electric charge that passes through it. Charge equals current multiplied by time, so the formula is usually written as:

$m = \frac{I \times t \times M}{z \times F}$

• m — mass of the substance produced or dissolved, in grams
• I — current, in amperes (A)
• t — time, in seconds (s)
• M — molar mass of the substance, in grams per mole (g/mol)
• z — valency, the number of electrons transferred per ion
• F — the Faraday constant, 96,485 coulombs per mole (C/mol)

The Faraday constant is named after the English scientist Michael Faraday. It is the electric charge carried by one mole of electrons.

Why valency matters

Valency depends on the ion's charge. A copper ion, Cu²⁺, needs two electrons to become a copper atom, so its valency is 2. A silver ion, Ag⁺, needs only one electron, so its valency is 1. A gold ion, Au³⁺, needs three electrons, so its valency is 3. A higher valency means more electrons are needed per atom, so less mass is deposited for the same amount of charge.

Molar mass and valency of common metals

Example calculation

A current of 1 ampere passes through a copper sulfate solution for 1 hour (3,600 seconds). How much copper is deposited at the cathode, the electrode where reduction happens?

• I = 1 A
• t = 3,600 s
• M = 63.55 g/mol (copper)
• z = 2 (Cu²⁺)
• F = 96,485 C/mol

$m = \frac{1 \times 3600 \times 63.55}{2 \times 96485} = \frac{228780}{192970} \approx 1.18557 \text{ g}$

About 1.19 grams of copper are deposited.

A second example: a current of 2 amperes passes through a silver nitrate solution for 10 minutes (600 seconds). Silver has a molar mass of 107.87 g/mol and a valency of 1.

$m = \frac{2 \times 600 \times 107.87}{1 \times 96485} \approx 1.34160 \text{ g}$

About 1.34 grams of silver are deposited, more than the copper example, mainly because silver's valency is lower.

How to use the calculator

Enter the current in amperes and the time in seconds, then choose a metal from the list. The result updates automatically. Common time conversions: 1 minute = 60 seconds, 1 hour = 3,600 seconds, 1 day = 86,400 seconds.

Applications of electrolysis

Electroplating coats one metal with a thin layer of another, such as plating jewelry with gold or plating steel parts with nickel to resist corrosion. Metal refining uses electrolysis to purify metals; copper refined this way can reach over 99.9% purity. Electrowinning extracts metals such as zinc and aluminum from dissolved ores. Water electrolysis splits water into hydrogen and oxygen gas, a method used to produce hydrogen fuel.

Faraday's law gives the theoretical maximum mass. Real processes usually deposit slightly less, because some current drives side reactions instead of the main one. This ratio is called current efficiency, and it is typically 90–98% in industrial plating.

History of Faraday's law

In 1800, Alessandro Volta built the first battery, giving scientists a steady source of electric current for the first time. That same year, William Nicholson and Anthony Carlisle used it to split water into hydrogen and oxygen, an early demonstration of electrolysis. Between 1807 and 1808, Humphry Davy used electrolysis to isolate several elements, including potassium and sodium.

Michael Faraday, who had worked as Davy's assistant, ran careful experiments on electrolysis in the early 1830s. In 1832 and 1834 he published two laws describing the exact relationship between electric charge and the mass of substance produced. He also introduced the terms electrode, anode, cathode, and ion, words still used in chemistry today.

Frequently asked questions

How do you calculate the mass deposited during electrolysis? Multiply the current by the time to get the total charge, multiply that by the substance's molar mass, then divide by the valency times the Faraday constant: m = (I × t × M) / (z × F).

What is the Faraday constant? It is the electric charge carried by one mole of electrons, approximately 96,485 coulombs per mole.

What is the difference between the anode and the cathode? The anode is the electrode where oxidation happens and electrons are lost. The cathode is the electrode where reduction happens and electrons are gained. When a metal is deposited from solution, it forms at the cathode.

Does temperature affect the result of the calculation? Temperature does not appear in Faraday's law, so it does not change the calculated mass. It can affect the real efficiency of the process, since higher temperatures often speed up side reactions.

Which metals does this calculator support? Copper, silver, gold, zinc, nickel, iron, and aluminum, each with its standard molar mass and valency built in. For any other metal, the same formula works if the molar mass and valency are known.

Why might the actual deposited mass differ from the calculated value? Faraday's law assumes all the current goes into the main reaction. In practice, some current is lost to side reactions or resistance, so real deposits are usually a little lighter than the calculated value. The ratio of actual to theoretical mass is called current efficiency.

References

1. Faraday, M. (1834). "Experimental Researches in Electricity. Seventh Series." Philosophical Transactions of the Royal Society of London, 124, 77–122.
2. Bard, A. J., & Faulkner, L. R. (2000). Electrochemical Methods: Fundamentals and Applications (2nd ed.). John Wiley & Sons.
3. Atkins, P., & de Paula, J. (2014). Atkins' Physical Chemistry (10th ed.). Oxford University Press.