Kc from degree of dissociation calculator
Turn a degree of dissociation into an equilibrium constant: with α of 0.1 at a starting 0.1 mol/L, Kc is 0.001111111111 mol/L, leaving 0.09 mol/L of A and 0.01 mol/L each of B and C at equilibrium. Free in your browser.
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Worked example
- Degree of dissociation α
- 0.1
- Concentration
- 0.1
- Degree of dissociation
- 0.1
- C0
- 0.1
- Unit concentration
- mol/L
- Kc
- 0.0011111111
A Kc from degree of dissociation calculator turns two classroom numbers—the fraction of molecules that have dissociated and the starting molarity—into the concentration equilibrium constant for a binary dissociation. Enter the degree of dissociation α (between zero and one) and the initial concentration c₀ in mol/L; the tool returns Kc equals c₀ times alpha squared over one minus alpha, the equilibrium concentrations of undissociated A and products B and C, a readable reaction model A reversible B plus C, and ordered substitution steps you can check by hand. Homework checks, Ostwald dilution law exercises, weak-electrolyte Ka estimates, and coding kata expected values all need that same closed form without opening a computer-algebra system.
What degree of dissociation means for Kc
The degree of dissociation α is the fraction of the original undissociated species that has split into products at equilibrium. For a monomeric binary dissociation written A goes to B plus C, if the initial concentration of A is c₀ and a fraction α has dissociated, the equilibrium amounts are [A] equals c₀ times one minus α, and [B] equals [C] equals c₀ times α, assuming one-to-one stoichiometry and no other sources of B or C.
The concentration equilibrium constant is then Kc equals [B] times [C] over [A], which simplifies algebraically to Kc equals c₀ times α squared over one minus α. That identity is the concentration form of Ostwald’s dilution law and is the same closed form students use when estimating Ka for a weak monoprotic acid from measured α at a known initial concentration.
When α is much smaller than one the denominator is nearly one and Kc is approximately c₀ α squared, which is why dilute weak electrolytes often look “more dissociated” even though Kc is fixed. When α approaches one the denominator shrinks and Kc becomes very large—consistent with a reaction that lies far toward products—until α equals one, where the undissociated concentration is zero and the mass-action expression for this model is undefined.
Teachers and automated graders care about the out-of-range rejection as much as the numerical answer: a student who reports α equals 1.2 or a negative fraction has left the domain of the definition, and a silent clamp would hide that mistake.
Practical tips, limits, and related searches
Keep α inside the open-closed interval used by the formula and keep c₀ positive so the mass-action quotient stays finite and physically interpretable for dilute solutions. 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.
Remember that this landing targets people searching for a Kc from degree of dissociation calculator, equilibrium constant from alpha, or Ostwald dilution law online; it is not a gas-phase Kp converter, not a multi-step polyprotic solver, and not a full ICE-table tool for arbitrary stoichiometry such as A goes to two B (which would need a different prefactor).
Prefer this capability when you already have measured or assigned α and c₀ and only need Kc and the matching equilibrium concentrations; if your source is percent dissociation, convert percent to a fraction first by dividing by one hundred. Round-trip checks are easy: recompute c₀ times alpha times alpha over one minus alpha by hand and confirm it equals the published kc within the same twelve-decimal rounding, and confirm that equilibrium A plus either product equals c₀ within that same rounding.
What you can do with it
Homework checks for Ostwald’s dilution law
Students enter α and c₀ from textbook weak-electrolyte problems and compare hand-written Kc and equilibrium concentrations against a deterministic result before submitting.
FAQ
What formula does this calculator use for Kc?
For binary dissociation A ⇌ B + C, Kc = c₀ · α² / (1 − α), where α is the degree of dissociation and c₀ is the initial concentration of A in mol/L (Ostwald dilution law).
What values of α are allowed?
α must satisfy 0 ≤ α < 1.
Does this work for A ⇌ 2B?
No. This tool uses the one-to-one product stoichiometry of A ⇌ B + C. A dissociation that produces two identical particles would need a different prefactor (4c₀α²/(1−α)).
Is Kc the same as Ka?
For a monoprotic weak acid HA ⇌ H⁺ + A⁻ in dilute solution with concentrations in mol/L, the same algebraic form is used for Ka. This response labels the result Kc for the general binary model.
Is the Kc from degree of dissociation calculator free?
The browser tool is free and runs locally.
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/kc-from-dissociation \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"alpha":0.1,"concentration":0.1}'const res = await fetch("https://api.kit.forhosting.com/chem/kc-from-dissociation", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"alpha": 0.1,
"concentration": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/kc-from-dissociation",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"alpha": 0.1,
"concentration": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/kc-from-dissociation", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"alpha":0.1,"concentration":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"alpha":0.1,"concentration":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/kc-from-dissociation", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"alpha": 0.1,
"concentration": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.kc_from_dissociation",
"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
Values of α outside the interval from zero to one are rejected with a clear invalid_input error, and complete dissociation (α equals one) is rejected because the factor one minus alpha is zero and the Ostwald formula is singular.
How to call the API and what comes back
The degree of dissociation must satisfy zero less than or equal to alpha and alpha strictly less than one; values outside zero to one, and the singular case alpha equals one, are rejected. The initial concentration must be strictly positive. Send a JSON body with two required finite numbers: alpha (aliases degree, degree_of_dissociation, dissociation, dissociation_degree, and a) and concentration (aliases c0, c_initial, initial_concentration, c, and molarity). Absolute values must stay within the published limit of one trillion so intermediate products remain finite in IEEE double precision on the Worker and in the browser. On success the response echoes rounded alpha and concentration, sets degree_of_dissociation and c0 as mirrors, unit_concentration and unit_kc to mol/L, kc and Kc to the same rounded equilibrium constant, formula to the string Kc equals c₀ · α² / (1 − α), reaction to A ⇌ B + C, equilibrium to an object with undissociated, A, B, and C concentrations, message to a short English summary, and steps to an ordered array of substitution lines. Failed validation—missing fields, non-finite numbers, values outside absolute limits, alpha outside zero to one, alpha equals one, non-positive concentration, or a non-finite Kc—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 searches
When teaching, pair examples: alpha equals zero point one with c₀ equals zero point one yields Kc equals about zero point zero zero one one one; alpha equals zero point five with c₀ equals zero point two yields Kc equals zero point one; and alpha equals one point five or alpha equals negative zero point one demonstrates the hard invalid_input path for out-of-range dissociation. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send alpha greater than one.
Integration use cases
Unit tests for student equilibrium solvers
Generate known-good Kc values from α and c₀ plus deliberate out-of-range dissociation rejections for coding kata expected values.
Quick Ka estimates from measured α
Lab notebooks that report percent dissociation at a known initial concentration convert to α and call this API to get Kc (or Ka for monoprotic HA) without rebuilding an ICE table.