Equilibrium constant from cell potential
See how a cell voltage fixes an equilibrium constant: a Daniell cell at 1.1 V with 2 electrons at 298.15 K has K of about 10³⁷. You also get ln K, log K and the standard Gibbs energy change. Free in your browser.
- Free
- Runs in your browser
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- Your data stays on your device
Run — free
Worked example
- Standard cell potential E°
- 1.1
- N
- 2
- Absolute temperature in kelvin
- 298.15
- K
- 15,406,269,312,702,256,000,000,000,000,000,000,000
- Ln K
- 85.6278378726
- Log10 K
- 37.1876974854
- Log10 K classroom
- 37.1876974854
The standard cell potential is not only a voltage on a multimeter—it fixes the equilibrium constant of the balanced cell reaction through the free-energy bridge ΔG° equals minus n F E° equals minus R T ln of K. Given E° in volts, the electron count n from the half-reactions, and absolute temperature T in kelvin, this capability returns K, ln of K, log ten of K, and ΔG° with a deterministic SI formula—no tables, no network, and no random drift. Students use it to check Daniell-cell and concentration-cell homework; lab software and tutoring platforms pin the same contract for auto-graded electrochemistry drills. Non-positive temperature is rejected as invalid input because the product R T would not define a thermodynamic state.
What you need: standard potential E°, electrons n, and temperature T
Start from a balanced redox cell reaction and three numbers only. First, the standard cell potential E° in volts—the tabulated EMF when every species is at unit activity, often taken from reduction-potential tables at twenty-five degrees Celsius or measured under standard conditions. Second, n, the moles of electrons cancelled between the oxidation and reduction half-reactions; for the classic zinc–copper Daniell cell, n equals two.
Third, absolute temperature T in kelvin for the state you care about; two hundred ninety-eight point one five kelvin is the usual laboratory standard, but any strictly positive value is accepted so isothermal battery models and hot-process estimates stay honest. The engine applies ln of K equals n F E° over R T, then K equals the exponential of that natural log, with gas constant R and Faraday constant F fixed in SI units.
Because ΔG° equals minus n F E° equals minus R T ln of K, a positive E° yields K greater than one and a spontaneous standard reaction, while a negative E° yields K less than one.
FAQ
How do I calculate the equilibrium constant from cell potential?
The response includes K, ln_K, log10_K, and ΔG° from K = exp(nFE°/(RT)).
What happens if temperature is zero or negative?
Non-positive T makes the product RT undefined for the thermodynamic relation, so the engine rejects the input and does not charge.
Which constants R and F does the calculator use?
They are echoed under constants in every successful response for lab-notebook citation.
Is the equilibrium constant from cell potential calculator free?
The browser tool runs free on your device.
How is this different from the Nernst equation calculator?
This capability converts standard EMF into the equilibrium constant K. The Nernst equation calculator converts E°, n, and Q into the non-standard cell potential E. Related electrochemistry, different search intent and outputs.
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/equilibrium-constant-from-emf \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"e0":1.1,"n":2,"T":298.15}'const res = await fetch("https://api.kit.forhosting.com/chem/equilibrium-constant-from-emf", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"e0": 1.1,
"n": 2,
"T": 298.15
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/equilibrium-constant-from-emf",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"e0": 1.1,
"n": 2,
"T": 298.15
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/equilibrium-constant-from-emf", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"e0":1.1,"n":2,"T":298.15}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"e0":1.1,"n":2,"T":298.15}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/equilibrium-constant-from-emf", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"e0": 1.1,
"n": 2,
"T": 298.15
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.equilibrium_constant_from_emf",
"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.
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
What you need: standard potential E°, electrons n, and temperature T
Identical inputs always produce identical JSON: the path is pure arithmetic with no network, no random seed, and no wall clock. Field aliases accept E0, emf, electrons, temperature, and kelvin so homework parsers and SDK demos can keep familiar names without rewriting payloads.
Reading K, logs, free energy, and the classroom log-ten form
When E° and n are so large that exp overflows IEEE double range, K is returned as null with overflow true while ln_K and log10_K remain finite and usable. Missing required fields, non-finite numbers, zero electrons, and non-positive T all fail with invalid_input and are not charged after the engine rejects the request.
API usage, pricing, lab workflows, and practical limits
Call the free in-browser equilibrium constant from cell potential calculator for homework checks, lecture demos, and quick intuition about how millivolts of EMF map to enormous powers of ten in K without installing a spreadsheet or a computer algebra system. Keep T strictly positive and n non-zero; extreme positive E° values may set K to null on overflow, but logarithms remain the reliable scientific-notation channel for display. Authors shipping SDKs can map K, ln_K, log10_K, and delta_G_kJ directly into UI rows that mirror the worked thermodynamic examples students write on paper when they convert a standard cell potential into an equilibrium constant by hand. Send a JSON body with required numeric fields e0, n, and T. Use the prepaid API when a tutoring platform, electrochemistry lab notebook, battery-model microservice, or curriculum generator needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after rejection. Pair this endpoint with the Nernst equation calculator when you later need non-standard cell potential from a measured quotient, or with concentration-based equilibrium constant tools when K is assembled from species lists rather than from EMF.
Integration use cases
Homework and exam verification
Students enter E°, n, and T for Daniell-type or fuel-cell problems, compare K and ΔG° to worked solutions, and get a clear invalid_input error when temperature is zero or negative by mistake.
Lab notebooks and battery models
Electrochemistry labs and lightweight battery simulators call a stable prepaid endpoint for thermodynamic K from measured or tabulated EMF without reimplementing R, F, and exp in every language.
Tutoring platforms and curriculum generators
Lesson builders produce EMF-to-K drills with structured JSON for flashcards and auto-graded quizzes, using the free browser widget for demos and the API for server-side grading.