Enthalpy scaled by coefficients calculator
Rescale the enthalpy of a thermochemical equation when you multiply its coefficients: doubling a step of −92.2 kJ gives −184.4 kJ, still exothermic. It is the usual move before adding steps in a Hess's law cycle. Free in your browser.
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Worked example
- Delta h
- -92.2
- Factor
- 2
- Delta h scaled
- -184.4
- Process
- exothermic
When you multiply every stoichiometric coefficient in a balanced thermochemical equation by the same positive factor, Hess's law requires that the reaction enthalpy multiplies by that same factor. If a formation step is written with Delta H equal to negative ninety two point two kilojoules and you double every coefficient so the equation shows two moles of product, the scaled enthalpy becomes negative one hundred eighty four point four kilojoules for the equation as rewritten. This calculator takes a reference reaction enthalpy and a non-negative scaling factor, returns the scaled enthalpy with an endothermic, exothermic, or thermoneutral process label, and rejects a negative factor because coefficient multipliers in this tool are defined to be greater than or equal to zero. Reverse a reaction by flipping the sign of the reference enthalpy rather than sending a negative factor. Keep energy units consistent with how you wrote the reference step.
How reaction enthalpy scales with stoichiometric coefficients
Thermochemical equations carry both stoichiometry and an intensive enthalpy change for the reaction as written. Hess's law states that enthalpy is a state function, so if you multiply every species coefficient by a constant factor k greater than or equal to zero, the new equation represents k times the original extent of reaction and the enthalpy change becomes k times Delta H of the reference step.
Classic textbook drills include doubling the Haber process equation, tripling a combustion half-step before adding it into a Hess cycle, or taking one-half of a formation equation so a single mole of product appears on the right-hand side. If the reference enthalpy is negative ninety two point two and the factor is two, the scaled enthalpy is negative one hundred eighty four point four and remains exothermic.
If the reference is positive one hundred seventy eight point three and the factor is one half, the scaled enthalpy is about eighty nine point one five and remains endothermic. A factor of zero is the mathematical limit of writing no reaction at all and yields a scaled enthalpy of zero labeled thermoneutral.
The sign convention is the system convention of chemical thermodynamics: heat absorbed by the reacting system is positive, so endothermic reactions show positive Delta H and positive scaled results, while exothermic reactions show negative values when heat released is carried as a negative number. The arithmetic is a single multiply after validating that both fields are finite numbers and that the factor is not negative. Entries of NaN or Infinity are rejected early.
Where coefficient-scaled enthalpy shows up in real work
Secondary-school and college general chemistry courses constantly assign Hess's-law problems that ask students to multiply a tabulated formation or combustion step by one half, two, or three before summing enthalpies; a single trusted oracle that returns the scaled Delta H and the endothermic or exothermic label speeds grading and demo setup. Process chemists building heat-of-reaction tables for alternate stoichiometric bases need a transparent multiply step so plant sheets stay auditable when the written equation is doubled for convenience.
Outreach labs that rewrite a thermochemical equation so coefficients match a measured sample size still need the factor times Delta H step for student notebooks. Quality and CAPA teams that already know a literature Delta H still need a deterministic coefficient scaling step when batch documentation uses a different stoichiometric multiple.
If you later need total heat for a stated amount of substance Q equals n times Delta H, reaction enthalpy from standard heats of formation, or Gibbs free energy from Delta H and Delta S, treat those as separate search intents and landings rather than overloading this enthalpy scaled by coefficients calculator page.
What you can do with it
Hess's law homework and exam keys
Multiply a tabulated formation or combustion step by one half, two, or three and get the scaled ΔH with a clear process label for consistent grading.
Alternate stoichiometric bases
Rewrite plant or lab thermochemical equations with doubled or halved coefficients and keep the matching enthalpy for heat-balance sheets.
FAQ
How is scaled reaction enthalpy calculated from a coefficient factor?
Keep energy units consistent with the reference step as written.
How is this different from reaction heat for amount (Q = n·ΔH)?
Coefficient scaling multiplies the written thermochemical equation under Hess's law. Amount scaling converts molar ΔH to extensive heat for moles reacted. Different search intents and different landings.
What does it cost?
The browser tool is free and runs locally.
How do I reverse a reaction instead of scaling it?
Flip the sign of the reference enthalpy and keep the factor positive. Negative factors are rejected on purpose, because a coefficient multiplier here must be zero or more; reversing is a sign change, not a negative scale.
What happens to the enthalpy if I halve an equation?
It is halved as well. A step of +178.3 kJ with a factor of 0.5 becomes about 89.15 kJ and stays endothermic, which is how you rewrite a formation equation so one mole of product appears.
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/enthalpy-coefficient-scaling \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"delta_h":-92.2,"factor":2}'const res = await fetch("https://api.kit.forhosting.com/chem/enthalpy-coefficient-scaling", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"delta_h": -92.2,
"factor": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/enthalpy-coefficient-scaling",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"delta_h": -92.2,
"factor": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/enthalpy-coefficient-scaling", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"delta_h":-92.2,"factor":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"delta_h":-92.2,"factor":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/enthalpy-coefficient-scaling", 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_h": -92.2,
"factor": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.enthalpy_coefficient_scaling",
"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 reaction enthalpy scales with stoichiometric coefficients
There is no random seed, no wall-clock timestamp, no network call, and no model drift, so identical delta_h and factor always produce identical JSON. A negative factor fails with a message that the stoichiometric scaling coefficient cannot be below zero, so clients can reverse the reaction by flipping the sign of delta_h rather than inventing a negative multiplier.
What you send and what you get back
Send two fields. The field factor is a finite non-negative number for the stoichiometric multiplier applied to every coefficient in that equation. Both fields are required. Classic textbook checks include factor two at negative ninety two point two to obtain negative one hundred eighty four point four (exothermic), and factor zero point five at one hundred seventy eight point three to obtain eighty nine point one five (endothermic). The field delta_h is a finite number for the reference reaction enthalpy Delta H sub ref of the thermochemical equation as written, in any consistent energy unit such as kilojoules or kilojoules per mole of reaction. Missing fields, empty strings, non-numeric strings, NaN, Infinity, and negative factors fail with invalid_input and are not charged. When factor is negative the request fails with a clear message that the scaling coefficient cannot be below zero for Delta H scaled equals factor times Delta H ref, and that reverse reactions should flip the sign of delta_h instead. Zero factor is accepted and returns delta_h_scaled equal to zero with a thermoneutral process label. On success the response echoes the cleaned delta_h and factor, the scaled enthalpy field delta_h_scaled, a process label of endothermic, exothermic, or thermoneutral, the formula string Delta H scaled equals factor times Delta H ref, and the method enthalpy_coefficient_scaling. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where coefficient-scaled enthalpy shows up in real work
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
Curriculum and auto-grader fixtures
Bulk-produce ΔH_scaled values from reference enthalpies and factors so browser demos and API answer keys never diverge.
Technical questions
What happens if factor is negative?
The request fails with invalid_input. Provide factor ≥ 0; reverse a reaction by flipping the sign of delta_h instead of using a negative multiplier.
Is zero factor allowed?
Yes. Zero factor yields delta_h_scaled = 0 and process = thermoneutral, the limit when the equation is scaled to nothing.