Electrolysis Calculation: Faraday’s Law Explained

An electrolysis calculation uses electric current and time to estimate how much chemical substance an electrolytic cell produces or consumes. Enter the current in amperes, time in seconds, and the substance’s molar mass and electron requirement; the calculator returns the theoretical mass deposited or released in grams.

Formula

Faraday’s law relates electrical charge to the amount of chemical change. For a product formed by transferring z electrons per formula unit, the theoretical mass is:

m = I × t × M ÷ (z × F)

• m is theoretical product mass, in grams (g).
• I is current, in amperes (A), equivalent to coulombs per second.
• t is electrolysis time, in seconds (s).
• M is the product’s molar mass, in grams per mole (g/mol).
• z is the number of moles of electrons needed per mole of product, taken from the balanced electrode reaction.
• F is the Faraday constant, approximately 96,485.33212 coulombs per mole of electrons (C/mol).

The calculator also reports charge, Q = I × t, in coulombs, and substance amount, n = m ÷ M, in moles. The mass equation follows from n = Q ÷ (zF): each mole of electrons carries one Faraday of charge, and forming one mole of product requires z moles of electrons.

Worked Example

Using the calculator’s defaults, a current of 2 A passes for 3,600 s, producing copper from Cu²⁺. Copper’s molar mass is 63.546 g/mol, and the reaction requires two electrons per copper atom: Cu²⁺ + 2e⁻ → Cu.

1. Find charge: Q = I × t = 2 A × 3,600 s = 7,200 C.
2. Find the theoretical mass: m = (2 × 3,600 × 63.546) ÷ (96,485.33212 × 2) = 2.3695 g, rounded to four decimal places.
3. Find amount: n = m ÷ M = 2.3695 g ÷ 63.546 g/mol ≈ 0.0373 mol. Using unrounded values gives 0.0373 mol to four decimal places.

Thus, the headline result is 2.3695 g of copper theoretically deposited. It is a prediction for ideal current efficiency, not a guarantee that a real experiment collects exactly that mass.

How to Choose the Reaction and Inputs

The calculation is only as sound as the reaction and inputs. Use current in amperes and time in seconds; convert milliamperes by dividing by 1,000 and hours by multiplying by 3,600. Use the molar mass of the actual product, not automatically the mass of the ion or starting compound.

Most importantly, determine z from the balanced half-reaction at the electrode of interest. For silver deposition, Ag⁺ + e⁻ → Ag, so z = 1. For aluminum deposition from Al³⁺, the formal reduction requires three electrons, so z = 3. If the products, ion charge, or reaction conditions are uncertain, first identify the likely electrode reaction; the calculator cannot choose it for you.

When the Calculation Is Useful

Faraday’s law is useful for estimating electrodeposition, electrolysis product quantities, and the charge or time needed for a theoretical target. Rearranging the mass equation gives t = m z F ÷ (I M) for the required time at a steady current, or I = m z F ÷ (t M) for the required current. These rearrangements assume the same ideal reaction and efficiency as the mass calculation.

In practical terms, the result scales directly with current and time: doubling either doubles the predicted amount if the other conditions stay unchanged. Increasing z reduces the amount formed for the same charge, because more electrons are required per product unit.

Theoretical Yield and Real-World Limits

The calculation gives a Faraday-law theoretical yield. Actual yield can be lower because some current may drive competing reactions, such as gas formation, rather than producing the desired material. Other influences include electrode condition, solution composition, temperature, concentration changes, and uneven current distribution. The fraction of current that produces the target is called current efficiency or Faradaic efficiency.

If a known efficiency is available as a decimal fraction, a simple estimate is theoretical mass multiplied by that fraction. For example, 90% efficiency corresponds to multiplying by 0.90. This calculator deliberately does not assume an efficiency: without measured or otherwise justified data, inserting a value would imply accuracy the inputs do not support. Efficiency can also vary during a run, so one fixed factor may only be an approximation.

Common Calculation Mistakes

• Mixing time units: entering 1 for one hour means one second to this calculator. Enter 3,600 seconds instead.
• Using the wrong electron count: z comes from the balanced reaction, not simply from current or time. A two-electron metal-ion reduction needs twice the charge per mole as a one-electron reduction.
• Confusing product mass and moles: m is in grams, while n is in moles. Molar mass converts between them.
• Overstating precision: the displayed digits are rounding, not proof that current, time, reaction, and efficiency are known that accurately.

Frequently Asked Questions

What is the formula for electrolysis calculations?
For constant current, use m = I t M ÷ (zF), where m is mass, I is amperes, t is seconds, M is grams per mole, z is electrons per product unit, and F is Faraday’s constant.

How do I calculate electrolysis time?
For a desired theoretical mass, use t = m z F ÷ (I M). Keep mass and molar mass in compatible units, use current in amperes, and interpret the answer in seconds.

How much copper is deposited by 1 amp for 1 hour?
For Cu²⁺ reduction, use z = 2 and M = 63.546 g/mol. The theoretical result is about 1.185 g; actual deposition may be lower if current efficiency is below 100%.

Why is my actual electrolysis yield lower than calculated?
The equation assumes all charge produces the selected product. Competing electrode reactions, changing conditions, and current inefficiency divert some charge, reducing collected yield.

What value of z should I use?
Use the electron coefficient in the balanced half-reaction for the product. For Cu²⁺ + 2e⁻ → Cu, z = 2; for Ag⁺ + e⁻ → Ag, z = 1.

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in I | Current | A | 2 | 0
in t | Time | s | 3600 | 0
in M | Molar mass | g/mol | 63.546 | 0
in z | Electrons per ion | - | 2 | 1
out m | Theoretical mass | g | I * t * M / (96485.33212 * z) | 4
out Q | Charge passed | C | I * t | 0
out n | Substance amount | mol | m / M | 4