Electrolysis Calculator: Faraday’s Law Explained

An electrolysis calculator estimates how much substance an electric current can produce, or how long electrolysis must run, using Faraday’s law. Enter current, time, the substance’s molar mass, and the number of electrons transferred per ion; the calculator returns the theoretical deposited mass and charge passed.

Formula

The calculation uses Faraday’s law of electrolysis:

m = I × t × M / (z × F)

• m is the theoretical mass deposited, in grams (g).
• I is current, in amperes (A).
• t is elapsed time, in seconds (s).
• M is the substance’s molar mass, in grams per mole (g/mol).
• z is the number of electrons transferred per ion in the electrode reaction.
• F is the Faraday constant, approximately 96,485 coulombs per mole of electrons (C/mol).

The calculator also reports charge, Q = I × t, in coulombs, and the amount produced, n = Q / (z × F), in moles. One ampere is one coulomb per second, so the input time must be converted to seconds before using the formula. The fixed value of F is built into the calculator.

Worked Example

With the default values—2 A for 3,600 s, copper molar mass 63.546 g/mol, and two electrons per copper ion—the steps are:

1. Find the charge: Q = 2 × 3,600 = 7,200 C.
2. Find the amount of copper: n = 7,200 / (2 × 96,485) ≈ 0.03731 mol.
3. Find the theoretical mass: m = 2 × 3,600 × 63.546 / (2 × 96,485) ≈ 2.370 g.

The calculator therefore displays a theoretical deposited mass of 2.370 g, a charge of 7,200 C, and an amount of 0.0373 mol. The mass is an ideal prediction, not a promise that an experiment will collect exactly that amount.

What an Electrolysis Calculator Is For

Electrolysis uses electrical energy to drive a chemical reaction that would not proceed spontaneously in the same way. At the cathode, reduction occurs: positive ions may gain electrons and form a solid deposit. Faraday’s law links the total charge delivered to the amount of chemical change, making it useful for estimating electrodeposition, electrolysis yields, or the time needed to pass a target charge.

For a target mass, the same equation can be rearranged to estimate time: t = m × z × F / (I × M). For example, this is a theoretical estimate of how long a steady current must flow to deposit a chosen mass. The calculator above is set up to calculate mass from current and time, rather than accept a target mass directly.

Choosing the Right Chemical Values

Use the molar mass and electron count for the actual electrode reaction, not simply the element’s name or its most familiar ion. For copper deposited from Cu²⁺, each ion gains two electrons, so z = 2. For silver deposited from Ag⁺, z = 1. Molar mass is usually given in g/mol on a periodic table or chemical reference.

The value z comes from the balanced half-reaction at the electrode. For instance, Cu²⁺ + 2e⁻ → Cu has z = 2. If the reaction involves a polyatomic ion, gas production, or several possible products, identify the specific product and balance its half-reaction first. Do not enter the full balanced equation’s total electron count if it applies to multiple product units; use the electrons needed to make one mole of the substance being calculated.

Efficiency, Units, and Real-World Results

Faraday’s law gives the theoretical yield when all relevant current drives the chosen reaction. In a real cell, some current may produce side reactions, and deposits may not adhere or may be lost during rinsing and handling. If the current efficiency is known, an approximate actual yield can be estimated by multiplying theoretical mass by efficiency as a decimal—for example, 90% becomes 0.90. Do not assume an efficiency value without experimental data or a reliable source for the specific setup.

Keep units consistent. Enter current in amperes and time in seconds. If a power supply is described in milliamperes, divide by 1,000 to convert to amperes; if duration is in minutes, multiply by 60 to obtain seconds. Mass output is in grams, not milligrams. To convert grams to milligrams, multiply by 1,000; to convert grams to ounces, multiply by approximately 0.035274. The underlying calculation is independent of whether a reader prefers metric or US customary mass units, but the calculator’s inputs and output use metric chemical units.

Results are rounded for display. More displayed digits do not make uncertain input values more precise, and small differences from a measured mass are expected. For a changing current, use the total charge delivered rather than one current reading multiplied by the full duration; if current varies, charge is the integral of current over time, or an appropriate measured average multiplied by time.

Common Errors and Limits

• Using the wrong z: Electron count depends on the actual half-reaction and oxidation state.
• Mixing seconds and hours: The formula requires time in seconds. One hour is 3,600 seconds.
• Confusing current and voltage: Faraday’s law uses current in amperes. Voltage alone does not determine the amount deposited.
• Treating predicted mass as measured yield: Side reactions, changing conditions, and material loss can lower the collected amount.
• Assuming every reaction deposits a solid: Electrolysis may produce gases or dissolved products; choose a product with a meaningful molar mass and reaction stoichiometry.

The calculator does not determine which reactions occur, the cell voltage, current efficiency, electrode area, or electrolyte concentration. Those depend on the chemistry and apparatus. It is a stoichiometric estimate, not a complete electrochemical cell model.

Frequently Asked Questions

How do you calculate electrolysis mass?
Multiply current in amperes by time in seconds and molar mass in g/mol, then divide by the electron count per ion times 96,485 C/mol: m = I t M / (zF).

What does z mean in Faraday’s law?
It is the number of electrons required by the electrode reaction for each ion or product unit. Determine it from the balanced half-reaction; for Cu²⁺ becoming copper metal, z is 2.

Can I use minutes or hours in the calculator?
Convert time to seconds first: multiply minutes by 60 or hours by 3,600. The formula’s current is in amperes, equivalent to coulombs per second.

Why is the actual deposited mass lower than the calculator result?
The calculation assumes all current makes the chosen product. Side reactions, incomplete deposition, and loss during handling can reduce the amount collected.

Does voltage affect the calculated mass?
Voltage is not directly in Faraday’s mass equation. The charge passed—current multiplied by time—sets the theoretical amount; voltage can affect the current and whether the reaction proceeds in a real cell.

Related

• Lattice Energy Calculation: Formula and Examples
• Moles Calculation: Formulas and Worked Examples
• Calculating Zeff for an Atom: Formula and Examples

in i | Current | A | 2 | 0
in t | Time | s | 3600 | 0
in m | Molar mass | g/mol | 63.546 | 0
in z | Electrons transferred per ion | - | 2 | 1
out mass | Theoretical deposited mass | g | i * t * m / (z * 96485) | 3
out charge | Electric charge | C | i * t | 0
out amount | Amount of substance | mol | i * t / (z * 96485) | 4