Gibbs energy from equilibrium constant calculator
An equilibrium constant of 15000 at 298.15 K gives ΔG° of −23.8371685897 kJ/mol, so products are favoured. Enter K and the temperature in kelvin to get ΔG° in joules and kilojoules per mole, with ln K and RT shown. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Thermodynamic equilibrium constant K
- 15,000
- Temperature k
- 298.15
- R j per mol k
- 8.314462618
- Ln k
- 9.6158054801
- Rt
- 2,478.95702956
- Delta g j mol
- -23,837.1685897
The thermodynamic equilibrium constant K and the standard Gibbs free energy change are two faces of the same standard-state driving force. At absolute temperature T the exact link is Delta G° equals minus R T times the natural logarithm of K: when K is larger than one the logarithm is positive and Delta G° is negative so products are favored under standard conditions; when K is smaller than one Delta G° is positive and reactants are favored; when K equals one the free energy change is zero and the standard state sits at equilibrium. This calculator takes a finite positive equilibrium constant and a temperature in kelvin, applies the CODATA molar gas constant in joules per mole per kelvin, and returns Delta G° in both joules per mole and kilojoules per mole together with ln(K), the product R T, and a clear favorability label. Zero or negative K is rejected with an explicit invalid input error because the logarithm is undefined there; negative kelvin is likewise rejected.
How ΔG° is computed from the equilibrium constant
Start from the fundamental relation that connects the standard reaction Gibbs energy to the thermodynamic equilibrium constant at temperature T: Delta G° equals minus R times T times ln(K). Here K is dimensionless and is the true thermodynamic equilibrium constant at that temperature, R is the molar gas constant fixed at eight point three one four four six two six one eight joules per mole per kelvin, and T is absolute temperature on the kelvin scale.
Taking the natural logarithm maps K greater than one to a negative free energy, K less than one to a positive free energy, and K equal to one to zero free energy, which matches the textbook statement that large equilibrium constants mean product-favored standard states. The same identity can be written with common logarithms as minus two point three zero three R T log ten of K; this implementation uses the natural form with Math.log for numerical stability and clarity.
Because R is expressed in joules, the primary result is reported in joules per mole and a second field divides by one thousand for kilojoules per mole without changing the underlying arithmetic. Absolute temperature must not be negative; kelvin values below zero fail validation. Zero kelvin is accepted as a mathematical edge case and yields Delta G° equal to zero for any finite positive K.
Missing fields, non-numeric strings, NaN, and Infinity fail validation before any arithmetic runs, and K less than or equal to zero fails with a clear message that the logarithm is undefined.
Where equilibrium-to-Gibbs calculations show up in real work
General chemistry and physical chemistry courses assign endless tables that convert published equilibrium constants into standard free energies and ask whether products or reactants are favored at a stated temperature; a single trusted oracle that returns both the number and the favorability class speeds grading and demo setup. Process chemists screening candidate reactions at fixed temperature estimate the standard driving force from measured or estimated K before investing in kinetics or catalyst studies.
Environmental and geochemistry models turn tabulated mineral solubility products into free-energy affinities using the same isothermal logarithm once activity conventions are consistent. If you later need Gibbs free energy from enthalpy and entropy, van't Hoff temperature dependence of K, or tabulated formation free energies from databases, treat those as separate search intents and landings rather than overloading this equilibrium-constant calculator page.
What you can do with it
Homework and exam answer keys
Convert textbook equilibrium constants and kelvin temperatures into ΔG° (J/mol and kJ/mol) with a shared products/reactants favorability label for teachers and auto-graders.
Reaction screening from measured K
Turn an experimental or estimated equilibrium constant at process temperature into a standard free-energy driving force before kinetic or scale-up work.
FAQ
What happens if the equilibrium constant is zero or negative?
The natural logarithm is undefined for K ≤ 0, so zero or negative equilibrium constants are rejected before any arithmetic runs.
How is favorability decided?
Kinetics and non-standard activities are out of scope.
What does it cost?
The browser tool is free and runs locally.
Why is the result given in both J/mol and kJ/mol?
The gas constant is used in joules, 8.314462618 J per mole per kelvin, so the main result comes out in joules per mole. The same value divided by 1000 is shown in kilojoules per mole for tables that use kJ.
What does an equilibrium constant of exactly 1 mean?
The natural logarithm of 1 is zero, so ΔG° is zero and the standard state sits at equilibrium. Above 1 the products are favoured, and below 1 the reactants are.
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/gibbs-from-equilibrium \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"k":15000,"temperature_k":298.15}'const res = await fetch("https://api.kit.forhosting.com/chem/gibbs-from-equilibrium", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"k": 15000,
"temperature_k": 298.15
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/gibbs-from-equilibrium",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"k": 15000,
"temperature_k": 298.15
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/gibbs-from-equilibrium", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"k":15000,"temperature_k":298.15}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"k":15000,"temperature_k":298.15}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/gibbs-from-equilibrium", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"k": 15000,
"temperature_k": 298.15
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.gibbs_from_equilibrium",
"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
How ΔG° is computed from the equilibrium constant
The entire pipeline is deterministic floating-point arithmetic with no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical numbers always produce identical JSON.
What you send and what you get back
The formula and method strings document the closed form for audits and teaching slides. Classic checks include room-temperature values near two hundred ninety-eight point one five kelvin with K much larger than one, endothermic product-scarce cases with K much smaller than one, and the equilibrium edge where K equals one exactly so Delta G° is zero. Send two finite numbers under the fields k and temperature_k. Both fields are required. k is the thermodynamic equilibrium constant and must be strictly greater than zero; any zero or negative value fails with invalid_input and a message that the equilibrium constant cannot be zero or negative because ln(K) is undefined for K less than or equal to zero. temperature_k is absolute temperature in kelvin and must be greater than or equal to zero; any negative value fails with invalid_input. On success the response echoes the cleaned inputs, reports r_j_per_mol_k as the fixed gas constant, reports ln_k as the natural logarithm of K, reports rt as the product R times T in joules per mole, reports delta_g_j_mol as minus R T ln(K) in joules per mole, reports delta_g_kj_mol as the same quantity in kilojoules per mole, and sets favorability to products_favored when Delta G° is negative, reactants_favored when positive, or equilibrium when Delta G° is numerically zero within a tiny floating-point tolerance. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where equilibrium-to-Gibbs calculations show up in real work
Laboratory notebooks that already report K from titration endpoints or spectroscopic plateaus can convert those constants into Delta G° without re-deriving the gas constant or risking unit mix-ups between joules and kilojoules. Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Product-favored versus reactant-favored cases
Compare large-K and small-K outcomes at the same temperature to see when ΔG° flips sign around K = 1.
Technical questions
What formula does this calculator use?
The standard relation ΔG° = −R T ln(K) with R = 8.314462618 J/(mol·K). You supply the equilibrium constant K and absolute temperature in kelvin; the response returns ΔG° in J/mol and kJ/mol plus a favorability label.
What units are used for ΔG°?
Primary result is joules per mole (delta_g_j_mol) using R in J/(mol·K). The same value is also reported in kilojoules per mole as delta_g_kj_mol (divided by 1000).