Degree of dissociation calculator
Turn an equilibrium constant and a starting concentration into the share that splits apart: Kc 0.05 with 0.1 mol/L gives α 0.5, so 50 % dissociates. It solves the exact equilibrium equation rather than the square-root shortcut. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Kc
- 0.05
- C0
- 0.1
- Alpha
- 0.5
- Percent dissociation
- 50
- Precision
- 10
This degree of dissociation calculator recovers the fraction of undissociated molecules that split at equilibrium from the concentration equilibrium constant Kc and the initial concentration of the parent species. For the binary dissociation A equilibrates to B plus C — the pattern behind many weak-acid and gas-phase monomer–dimer style problems written with unit stoichiometry — an ICE table at constant volume gives Kc equals c0 times alpha squared over one minus alpha. The engine solves that relation with a stable closed form so alpha lands between zero and one for any non-negative Kc and positive c0, with no network calls, no sampling, and no date-dependent shortcuts. Quick checks you may already know include Kc equals 0.05 with c0 equals 0.1 giving alpha equals 0.5, and Kc equals zero giving alpha equals zero.
Where dissociation from Kc fits in study, lab work, and software
Students meet degree of dissociation from Kc when a textbook gives the equilibrium constant and the starting concentration of a weak electrolyte or a gas that dissociates into two fragments and asks for alpha or percent dissociation, when they check the dilute approximation alpha approximately square root of Kc over c0 against the exact root, or when exam problems demand the ICE-table solution without a graphing calculator.
Teachers can pre-generate answer keys for a grid of Kc and c0 pairs without trusting opaque calculator apps that silently apply the square-root approximation even when alpha is not small. Developers call the same contract from scripts to seed deterministic test vectors for equilibrium widgets, to normalize user-entered Kc and concentration pairs before dissociation demos, or to satisfy programming-challenge statements that demand alpha rather than a hand-waved percentage.
Lab write-ups often need a fast, offline check that a measured Kc at a stated analytical concentration matches the expected alpha before reporting percent dissociation. Product and education tools use the closed form when a learner types Kc and c0 and the UI must show alpha and percent dissociation without a server-side chemistry database.
What you can do with it
Homework and equilibrium checks
Convert a textbook Kc and initial concentration into degree of dissociation α and percent ionization for A ⇌ B + C exercises.
Lab report support
Turn experimentally fitted Kc values and analytical c0 into reproducible α for equilibrium lab write-ups without manual quadratic errors.
FAQ
What does the degree of dissociation from Kc calculator cost?
It is free in your browser on this page.
How is degree of dissociation defined here?
For A ⇌ B + C with initial concentration c0 and no products initially, Kc = c0·α²/(1−α). The engine returns α and percent dissociation as 100 × α.
What happens if Kc is negative?
A negative concentration equilibrium constant is non-physical for this binary dissociation model.
Does this tool use the dilute approximation α ≈ √(Kc/c0)?
No. It always solves the exact relation Kc = c0·α²/(1−α) with a stable closed form. The square-root approximation is not applied.
What stoichiometry is assumed?
Binary dissociation A ⇌ B + C (or HA ⇌ H⁺ + A⁻). Reactions such as A ⇌ 2B use a different mass-action expression and are not covered here.
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/dissociation-from-kc \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"kc":0.05,"c0":0.1}'const res = await fetch("https://api.kit.forhosting.com/chem/dissociation-from-kc", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"kc": 0.05,
"c0": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/dissociation-from-kc",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"kc": 0.05,
"c0": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/dissociation-from-kc", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"kc":0.05,"c0":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"kc":0.05,"c0":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/dissociation-from-kc", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"kc": 0.05,
"c0": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.dissociation_from_kc",
"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 degree of dissociation from Kc means and what the response contains
Degree of dissociation alpha answers a classic equilibrium question: of the formula units present at the start, what fraction have dissociated when the system reaches equilibrium under the given Kc. For A going to B plus C with no products present initially, the equilibrium concentrations are c0 times one minus alpha for A and c0 times alpha for each product, so the mass-action expression collapses to Kc equals c0 alpha squared over one minus alpha. Solving for alpha is a quadratic that always admits a unique physical root in the unit interval when Kc is non-negative and c0 is positive. This calculator returns the normalized Kc and c0, the dimensionless alpha rounded to the requested precision, percent_dissociation as one hundred times alpha, a method tag dissociation_from_kc, the precision used, and a short formula reminder. There is no Ka lookup table, no activity-coefficient model, and no temperature conversion from Kp: the engine either solves the closed form inside the supported numeric range or rejects the input with invalid_input. Rejected cases include missing kc or c0, non-finite values, magnitudes above the documented ceiling, non-positive initial concentration, and any negative Kc, because a negative concentration equilibrium constant is non-physical for this dissociation model.
How Kc and c0 are read and how alpha stays 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 degree of dissociation. A Kc of zero with positive c0 is valid and simply yields alpha zero, meaning no measurable dissociation under the mass-action model. The c0 field must be strictly positive: zero or negative initial concentration is rejected as non-physical for this setup. The preferred fields are kc for the equilibrium constant and c0 for the initial concentration of A, but aliases Kc, K_c, equilibrium_constant, and K for kc, and c, C0, initial_concentration, concentration, and conc for c0 are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Negative Kc fails with invalid_input because the defining relation Kc equals c0 alpha squared over one minus alpha cannot produce a negative constant for real alpha between zero and one. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for kc, c0, alpha, and percent_dissociation, 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 root yourself.
Where dissociation from Kc 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 degree of dissociation from van 't Hoff factor, Kp from partial pressures, and related equilibrium endpoints when you are building a small lab of free, deterministic chemistry helpers.
Integration use cases
Deterministic test fixtures
Generate stable α and percent_dissociation outputs for unit tests, tutoring software, and CI assertions on dissociation math.