# Faraday's Law of Electrolysis Calculator

> Applies Faraday's laws of electrolysis: from current and time it computes the charge passed, moles of electrons, moles and mass of substance deposited or evolved (m = Q·M / (z·F)), or, for a target mass, the electrolysis time required at the given current.

- Calculator id: `faraday-electrolysis` · Category: Chemistry (`chemistry`) · Tool name: `calculate_faraday_electrolysis`
- Canonical page: https://tttkmbb.com/chemistry/faraday-electrolysis · This document: https://tttkmbb.com/chemistry/faraday-electrolysis.md · JSON definition: https://tttkmbb.com/chemistry/faraday-electrolysis.json

## Purpose

Applies Faraday's laws of electrolysis: from current and time it computes the charge passed, moles of electrons, moles and mass of substance deposited or evolved (m = Q·M / (z·F)), or, for a target mass, the electrolysis time required at the given current.

**Use when:** You need how much metal is plated or gas is evolved by a current over a time, or how long an electrolysis must run at a given current to produce a target mass.

**Do not use when:** The current efficiency is well below 100% (side reactions such as hydrogen evolution reduce the real yield), or you need the cell voltage rather than the amount of product (use nernst-equation).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `current_a` | number | A | required | Constant electrolysis current in amperes. (> 0) |
| `time` | number |  | optional | Duration of electrolysis in time_unit. Leave empty to solve it from target_mass_g. (> 0) |
| `time_unit` | enum: seconds \| minutes \| hours |  | optional, default "seconds" | Unit of the time input. |
| `electrons_per_ion` | integer |  | required | Moles of electrons per mole of product: Ag⁺ → Ag 1, Cu²⁺ → Cu 2, Al³⁺ → Al 3, 2H⁺ → H2 2, 2H2O → O2 4, 2Cl⁻ → Cl2 2. (min 1, max 12) |
| `formula` | string |  | optional | Formula of the substance deposited or evolved (Ag, Cu, Al, H2, O2, Cl2) for its molar mass. Alternative to molar_mass_g_mol. |
| `molar_mass_g_mol` | number | g/mol | optional | Molar mass of the substance; use instead of formula when it is already known. (> 0, max 10000000) |
| `target_mass_g` | number | g | optional | Mass of product wanted; when given, the calculator solves the time needed at current_a (the time input is ignored). (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `charge_c` | number | C | Q = I × t. |
| `moles_electrons` | number | mol | Q / F (F = 96 485.33 C/mol). |
| `moles_substance` | number | mol | moles_electrons / z. |
| `mass_g` | number | g | moles_substance × molar mass. |
| `gas_volume_stp_l` | number | L | moles_substance × 22.414 L/mol; meaningful only for gaseous products such as H2, O2 or Cl2. |
| `time_s` | number | s | Electrolysis time in seconds. |
| `time_min` | number | min | Electrolysis time in minutes. |
| `time_h` | number | h | Electrolysis time in hours. |
| `molar_mass_g_mol` | number | g/mol | Molar mass of the product used. |
| `solved_for` | string |  | mass_g (from current and time) or time_s (from target mass). |

## Formula

`Q = I × t; n_e = Q / F; n = n_e / z; m = n × M = I × t × M / (z × F) with F = 96485.33212 C/mol; time for a target mass: t = m × z × F / (M × I)`

Assumes 100% current efficiency (all charge goes into the stated product) and a constant current; real plating baths typically run at 90–98% efficiency.

## Data Sources

- OpenStax Chemistry 2e – 17.7 Electrolysis — https://openstax.org/books/chemistry-2e/pages/17-7-electrolysis (textbook, retrieved 2026-09-24)
- Wikipedia – Faraday's laws of electrolysis — https://en.wikipedia.org/wiki/Faraday%27s_laws_of_electrolysis (reference, retrieved 2026-09-24)
- NIST – CODATA internationally recommended values of the fundamental physical constants (Faraday constant F = 96 485.33212 C/mol, exact) — https://physics.nist.gov/cuu/Constants/index.html (standard, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/faraday-electrolysis?current_a=…&electrons_per_ion=…`
- `POST https://tttkmbb.com/api/v1/calculate/faraday-electrolysis` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/faraday-electrolysis · OpenAPI operationId `calculate_faraday_electrolysis` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "faraday-electrolysis", "inputs": {…}}`

## Example

- Silver plating at 10.23 A for 1 hour: inputs `{"current_a":10.23,"time":1,"time_unit":"hours","electrons_per_ion":1,"formula":"Ag"}` → `{"charge_c":36828,"moles_electrons":0.381695,"moles_substance":0.381695,"mass_g":41.1735,"time_s":3600,"molar_mass_g_mol":107.87,"solved_for":"mass_g"}`
- Time to deposit 10.0 g of copper at 5.0 A: inputs `{"current_a":5,"electrons_per_ion":2,"formula":"Cu","target_mass_g":10}` → `{"moles_substance":0.157366,"moles_electrons":0.314733,"charge_c":30367.08,"time_s":6073.42,"time_min":101.224,"time_h":1.68706,"solved_for":"time_s"}`

```
GET https://tttkmbb.com/api/v1/calculate/faraday-electrolysis?current_a=10.23&time=1&time_unit=hours&electrons_per_ion=1&formula=Ag
```

## Limitations

The current efficiency is well below 100% (side reactions such as hydrogen evolution reduce the real yield), or you need the cell voltage rather than the amount of product (use nernst-equation). Assumes 100% current efficiency (all charge goes into the stated product) and a constant current; real plating baths typically run at 90–98% efficiency. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How do I choose z?**

z is the number of electrons per atom or molecule of product in the half-reaction: the ion charge for metals (Cu²⁺ + 2e⁻ → Cu gives 2), 2 for H2 or Cl2, 4 for O2 from water.

**What if the current is not constant?**

Use the total charge instead: enter the average current and the total time, since Q = ∫I dt; a coulometer reading divided by any time gives the equivalent constant current.

## Related

- [Moles to Grams Calculator](https://tttkmbb.com/chemistry/moles-mass.md) — Convert the moles of product to atoms or check the mass.
- [Nernst Equation Calculator](https://tttkmbb.com/chemistry/nernst-equation.md) — Cell potential of the same electrochemical reaction.
- [Electric Power Calculator](https://tttkmbb.com/physics/electric-power.md) — Energy consumed from current, voltage and time.