Cell potential from Gibbs free energy
Turn a standard Gibbs energy change into a cell voltage: −212300 J/mol with 2 electrons transferred gives 1.100167224278 V, the Daniell zinc-copper cell. A positive voltage marks a spontaneous cell as written. Free in your browser.
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Worked example
- Delta g
- -212,300
- N
- 2
- Gibbs
- -212,300 V
- DG
- -212,300
- Delta G
- -212,300
- Electrons
- 2
A cell potential from Gibbs free energy calculator turns the standard free-energy change of a redox reaction into the standard cell voltage electrochemists write as E° cell. Enter ΔG° in joules per mole and the number of electrons transferred n; the tool returns E° equals negative ΔG° over n times Faraday constant, mirrored field names for Gibbs energy and electron count, the fixed Faraday value used, a formula string, a spontaneity label from the sign of E°, and step-by-step substitution you can paste into notebooks, homework, or automated tests. Classic classroom cases—the Daniell zinc-copper cell near one point one volts from a strongly negative ΔG°, a nonspontaneous reverse cell with positive free energy, or equilibrium when ΔG° is zero—all reduce to the same closed formula once ΔG° and n are known.
What E° = −ΔG°/(nF) means for electrochemical cells
In introductory electrochemistry, the standard Gibbs free energy change of a cell reaction is linked to the standard cell potential by the exact relation ΔG° equals negative n F E°, where n is the number of moles of electrons transferred in the balanced equation and F is the Faraday constant (charge per mole of electrons). Solving for the voltage yields the closed formula E° equals negative ΔG° over n F.
A negative free-energy change therefore produces a positive standard cell potential, meaning the cell reaction is thermodynamically spontaneous as written under standard conditions and can drive electrical work; a positive ΔG° produces a negative E° and favors the reverse direction; ΔG° near zero means E° near zero and equilibrium with no net driving force. Units must be consistent—ΔG° in joules per mole with F in coulombs per mole yields E° in volts—because the calculator does not silently convert kilojoules to joules.
The check path recomputes −ΔG°/(nF) with the same fixed rounding used for published fields, so a successful response always ships with steps you can assert in tests, lab reports, or electrochemistry worksheets about standard cell potential from Gibbs free energy.
Practical tips, limits, and related electrochemistry searches
Keep energy units consistent with SI volts: if your textbook lists ΔG° in kilojoules per mole, multiply by one thousand before sending so the input is in joules per mole; otherwise the reported potential will be off by a factor of one thousand. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern.
Prefer this capability when you already have ΔG° and n and only need E°; if your goal is free energy from a known voltage, evaluate ΔG° equals negative n F E offline. Round-trip checks are easy: recompute −ΔG divided by n times F by hand and confirm it equals the published E within the same twelve-decimal rounding for electrochemistry report verification.
What you can do with it
Homework checks for E° from tabulated ΔG°
Students enter ΔG° and n from textbook redox problems and compare hand-written standard cell potentials and spontaneity labels against a deterministic result before submitting.
Lab report cell voltages from free-energy estimates
Convert measured or computed reaction free energies into the standard cell potential expected under the ΔG° = −nFE° relation for report tables.
FAQ
What is the cell potential from Gibbs free energy formula?
E° = −ΔG° / (n F), where n is electrons transferred and F is the Faraday constant (96485.3321 C/mol). With ΔG° in J/mol, E° is in volts.
Should I enter ΔG° in kJ/mol or J/mol?
Use joules per mole (J/mol) for SI consistency with F so E° is in volts. If your source lists kJ/mol, multiply by 1000 first.
Does a positive E° always mean a spontaneous cell?
Under standard conditions, yes for the reaction as written: E° > 0 implies ΔG° < 0. Nonstandard concentrations need the Nernst equation, which this tool does not apply.
Is the cell potential from Gibbs calculator free?
The browser tool is free and runs locally.
What does a negative cell potential mean?
That the standard Gibbs energy change is positive and the reaction favours the reverse direction under standard conditions. A Gibbs energy change of zero gives zero volts: equilibrium, with no net driving force.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/chem/cell-potential-from-gibbs \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"delta_g":-212300,"n":2}'const res = await fetch("https://api.kit.forhosting.com/chem/cell-potential-from-gibbs", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"delta_g": -212300,
"n": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/cell-potential-from-gibbs",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"delta_g": -212300,
"n": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/cell-potential-from-gibbs", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"delta_g":-212300,"n":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"delta_g":-212300,"n":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/cell-potential-from-gibbs", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"delta_g": -212300,
"n": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.cell_potential_from_gibbs",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Zero electron count is rejected with a clear invalid_input error because dividing by nF would be undefined and would hide a stoichiometry mistake.
What E° = −ΔG°/(nF) means for electrochemical cells
Teachers and automated graders care about the zero-n rejection as much as the success path: a learner who leaves electron count at zero after a half-reaction error should see an explicit invalid_input message instead of Infinity or NaN.
How to call the API and what comes back
Electron count must be non-zero; values whose absolute value is at or below one times ten to the minus fifteen are treated as zero and rejected. Send a JSON body with two required finite numbers: delta_g (aliases gibbs, dG, deltaG, G, gibbs_free_energy, dg, Delta_G, DG, delta_G, and free_energy) and n (aliases electrons, electrons_transferred, n_e, ne, z, electron_count, and moles_electrons). Absolute values must stay within the published limit of one trillion so the quotient remains finite in IEEE double precision on the Worker and in the browser. On success the response echoes rounded delta_g and n, mirrors them as gibbs, dG, delta_G, and electrons, sets faraday and F to the fixed Faraday constant, sets E, E_cell, cell_potential, and potential_V to the same rounded volt result, formula to the string E° equals negative ΔG° over n F, equation to a filled substitution string, unit to V, spontaneity and note to sign-based classification labels, message to a short English summary, and steps to an ordered array of calculation lines. Failed validation—missing fields, non-finite numbers, values outside absolute limits, or zero electrons—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related electrochemistry searches
When teaching electrochemistry, pair examples: a Daniell-style case with ΔG° equals negative two hundred twelve thousand three hundred joules per mole and n equals two recovers a positive E° near one point one volts and spontaneity spontaneous; the reverse free-energy sign shows nonspontaneous with a negative voltage; ΔG° equals zero yields equilibrium; and deliberately send n equals zero to demonstrate the hard invalid_input path that guards against undefined division. This landing targets people searching for a cell potential from Gibbs calculator, E equals negative delta G over nF, standard electrode potential from free energy, or chemistry homework help online; it is not a Nernst equation solver at nonstandard concentrations, not a half-cell table lookup by species name, and not a converter from tabulated E° values back to ΔG°. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send zero electrons.
Integration use cases
Unit tests for student electrochemistry solvers
Generate known-good E° = −ΔG°/(nF) cases plus deliberate zero-electron rejections for coding kata expected values in chemistry tools.
Technical questions
What happens when the number of electrons is zero?
Division by zero is undefined. This tool returns invalid_input instead of Infinity or NaN when n is zero or near-zero.