Equilibrium constant at new temperature
Find how an equilibrium constant shifts with temperature: a K of 0.05 at 298.15 K with a reaction enthalpy of −58000 J/mol falls to 0.0015616472 at 350 K, as an exothermic reaction should. Free in your browser.
- Free
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- Your data stays on your device
Run — free
Worked example
- K1
- 0.05
- Delta h
- -58,000
- T1
- 298.15
- T2
- 350
- Gas constant
- 8.314
- K2
- 0.0015616472
- Ln k2 over k1
- -3.4662818736
- K2 over k1
- 0.0312329431
This equilibrium constant at new temperature calculator applies the integrated van't Hoff equation to predict how a reaction’s equilibrium constant changes when you move from one absolute temperature to another. You supply a known equilibrium constant K1 at reference temperature T1, the standard reaction enthalpy change ΔH, and the target temperature T2; the engine returns K2, the logarithmic shift ln(K2/K1), and the ratio K2/K1 so you can see whether products become more or less favored as temperature rises or falls. The arithmetic is fully deterministic: two temperature reciprocals, one scaled enthalpy term, and one exponential, with no network calls, no formation-table lookups, and no date-dependent shortcuts. Keep energy units consistent before you call—if ΔH is in joules per mole, leave the default gas constant R at 8.314 joules per mole-kelvin; if ΔH is in kilojoules per mole, set R to 0.008314.
What the van't Hoff shift tells you
Chemical equilibrium constants are not fixed numbers stamped on a reaction forever: they depend on temperature through the enthalpy of reaction. The integrated van't Hoff relation, under the usual constant-ΔH assumption over the interval of interest, links two temperatures and two constants by ln of K2 over K1 equals minus ΔH over R times the difference of the reciprocals of T2 and T1. Exponentiating both sides yields the working form used here: K2 equals K1 times exp of that same scaled reciprocal difference.
An exothermic reaction (negative ΔH) loses equilibrium product favor as temperature rises; an endothermic reaction (positive ΔH) gains product favor as temperature rises—exactly the qualitative Le Chatelier picture students already know, now quantified. This calculator implements that closed form only.
Where K at a new temperature fits in study, lab work, and software
Students meet the van't Hoff equation when a general-chemistry unit moves from Le Chatelier’s principle to quantitative K versus T problems, when a physical-chemistry course integrates d ln K over dT equals ΔH over R T squared, or when an exam problem gives K at twenty-five degrees Celsius and asks for K at a new kelvin temperature with a stated reaction enthalpy.
Teachers can pre-generate answer keys for modest K1, ΔH, and temperature pairs without trusting opaque calculator apps that silently switch from joules to kilojoules or invert the reciprocal difference. Developers call the same contract from scripts to seed deterministic test vectors for thermo dashboards, to normalize user-entered reaction parameters before process demos, or to satisfy programming-challenge statements that demand K2 rather than a hand-waved increases or decreases label.
Lab and process work often needs a fast, offline source of equilibrium-constant temperature checks so report numbers can be verified against the stated formula under time pressure. Product and education tools use the evaluation when a learner types a known K, an enthalpy, and two temperatures and the UI must show the new constant plus the ratio that quantifies the shift.
What you can do with it
Homework and exam van't Hoff drills
Plug textbook K1, ΔH, T1, and T2 into the integrated van't Hoff equation and check whether K2 rises or falls with temperature.
Lab reports and process demos
Normalize user-entered equilibrium data into a new-temperature K for worksheets, dashboards, and interactive thermo lessons.
FAQ
What does the equilibrium constant at new temperature calculator cost?
It is free in your browser on this page.
How is K2 defined from K1, ΔH, T1, and T2?
ln(K2/K1) = −(ΔH/R)·(1/T2 − 1/T1), so K2 = K1·exp(−(ΔH/R)·(1/T2 − 1/T1)). ΔH is the reaction enthalpy, T1 and T2 are absolute kelvin temperatures, and R is the gas constant in energy units matching ΔH.
What happens if a temperature is zero?
Zero or negative absolute temperature is non-physical here because the van't Hoff formula uses the reciprocal 1/T.
Does this tool compute K from Gibbs free energy at one temperature?
No. It only shifts a known K1 to a new temperature using ΔH. Use the equilibrium-from-Gibbs calculator if you need K = exp(−ΔG°/RT) at a single T.
Why must energy units of ΔH and R match?
The ratio ΔH/R must be dimensionless times kelvin. If ΔH is in J/mol use R ≈ 8.314 J/(mol·K); if ΔH is in kJ/mol use R ≈ 0.008314 kJ/(mol·K). Mixed units produce a wrong exponent and a wrong K2.
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/k-at-new-temperature \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"k1":0.05,"delta_h":-58000,"t1":298.15,"t2":350}'const res = await fetch("https://api.kit.forhosting.com/chem/k-at-new-temperature", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"k1": 0.05,
"delta_h": -58000,
"t1": 298.15,
"t2": 350
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/k-at-new-temperature",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"k1": 0.05,
"delta_h": -58000,
"t1": 298.15,
"t2": 350
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/k-at-new-temperature", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"k1":0.05,"delta_h":-58000,"t1":298.15,"t2":350}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"k1":0.05,"delta_h":-58000,"t1":298.15,"t2":350}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/k-at-new-temperature", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"k1": 0.05,
"delta_h": -58000,
"t1": 298.15,
"t2": 350
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.k_at_new_temperature",
"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_value | 1000000000000000 |
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 the van't Hoff temperature shift means and what the response contains
It returns the normalized k1, delta_h, t1, t2, and gas_constant you supplied, the new equilibrium constant k2 rounded to the requested precision, ln_k2_over_k1 and k2_over_k1 for log-scale and ratio checks, the precision used, the method tag van_t_hoff, the formula string for the integrated equation, and a short unit_note reminding you to keep energy scales consistent between ΔH and R. There is no approximate CAS path and no random sampling of conditions: the engine either builds a finite or representable K2 inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing k1, delta_h, t1, or t2, non-finite values, magnitudes above the documented ceiling, a gas constant of zero, a non-positive K1, and any temperature that is zero or strictly negative on the absolute kelvin scale.
How K1, ΔH, T1, T2, and R are read and stay reproducible
Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong K2. Zero enthalpy is valid and yields K2 equal to K1 for any T2. K1 itself must be strictly positive because the logarithmic form uses the ratio of two constants. The preferred fields are k1 for the reference equilibrium constant, delta_h for the reaction enthalpy, t1 for the reference absolute temperature in kelvin, and t2 for the new absolute temperature in kelvin, but aliases such as K1, K, and equilibrium_constant for K1, dH, deltaH, enthalpy, and reaction_enthalpy for ΔH, T1, temp1, and temperature_1 for T1, and T2, temp2, new_temperature, and temperature_2 for T2 are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Optional gas_constant defaults to 8.314 joules per mole-kelvin when omitted; aliases R, r, and gasConstant let you pass a matching R when ΔH is in kilojoules or calories. Both temperatures must be strictly positive: if T1 or T2 is zero or less than zero, the request fails with invalid_input because division by T is undefined and negative absolute temperature is non-physical for this relation. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for all finite numeric fields, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the temperature-shift formula yourself.
Where K at a new temperature fits in study, lab work, and software
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split—free interactive exploration and a priced, identical API—matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with the equilibrium-from-Gibbs helper when you need K at a single T from free energy, and with other chemistry endpoints when you are building a small lab of free, deterministic reaction helpers.
Integration use cases
Deterministic test fixtures
Generate reproducible K2, ln(K2/K1), and K2/K1 ratios for unit tests, property checks, and CI assertions.