Percent ionization of acid calculator
A weak acid at 0.1 mol/L with a Ka of 0.000018 is only a little over 1 % ionized: enter the concentration and Ka and the exact equilibrium is solved for you, with no 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
- Analytical
- 0.1
- Acid dissociation constant Ka
- 0.000018
- Pka
- 4.7447274949
- X
- 0.001332671
- H plus
- 0.001332671
- A minus
- 0.001332671
Percent ionization tells you what fraction of a weak acid’s molecules actually split into ions at equilibrium. For a monoprotic weak acid HA at analytical concentration C with known acid dissociation constant Ka, the equilibrium problem is the standard ICE table: Ka equals x squared over C minus x, where x is the equilibrium hydrogen-ion concentration. Solving the quadratic gives the physical root, and percent ionization is one hundred times x over C. Zero or negative concentration is rejected with a clear invalid input error because the percentage is undefined when you would divide by zero.
What percent ionization means and which inputs to send
Write the monoprotic weak acid equilibrium as HA reverses to H plus and A minus. At analytical concentration C the ICE table sets initial HA equal to C and products to zero, then lets x moles per liter ionize. Charge and mass balance give Ka equals x squared divided by C minus x when water autoionization is neglected, which is the textbook model for pure HA in water when the acid contribution dominates.
Percent ionization is one hundred times the degree of ionization alpha, and alpha is simply x over C. Concentration must be strictly greater than zero: zero concentration makes one hundred times x over C undefined, and negative concentration has no meaning for an analytical stock solution. Ka must also be positive so the quadratic has a physical ionized root.
The engine does not accept measured equilibrium concentrations alone—that is a different product intent served by the percent-dissociation-from-C0-and-Ceq calculator—nor does it invert Ka from a measured pH.
What you can do with it
Homework and exam verification
Students enter C and Ka for acetic acid or similar monoprotic weak acids, check percent ionization and alpha against worked solutions, and get a clear error when concentration is zero or negative.
FAQ
What happens if concentration is zero or negative?
Percent ionization is undefined when C is zero (division by zero), and negative analytical concentration is not accepted.
Is the approximation x ≈ √(Ka·C) used?
No. The calculator always uses the exact physical root of the ICE quadratic so results remain accurate when ionization is not small.
Is the percent ionization of acid calculator free?
The browser tool runs free on your device.
Does this use measured C0 and Ceq instead of Ka?
No. This product takes analytical concentration and Ka. For percent dissociation from initial and equilibrium concentrations, use the dedicated equilibrium-concentration calculator.
Does it show the equilibrium concentrations too?
Yes. Besides the percentage, you get the hydrogen ion and conjugate base concentrations, the acid left undissociated, the degree of ionization alpha, the pKa and an approximate pH, so you can check a whole worked solution.
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/percent-ionization \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"concentration":0.1,"ka":0.000018}'const res = await fetch("https://api.kit.forhosting.com/chem/percent-ionization", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"concentration": 0.1,
"ka": 0.000018
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/percent-ionization",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"concentration": 0.1,
"ka": 0.000018
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/percent-ionization", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"concentration":0.1,"ka":0.000018}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"concentration":0.1,"ka":0.000018}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/percent-ionization", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"concentration": 0.1,
"ka": 0.000018
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.percent_ionization",
"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
This capability runs that calculation deterministically—no approximation shortcut that fails when ionization is large, no network, no random seed—so homework checkers, lab notebooks, and tutoring apps get the same JSON every time for the same inputs.
What percent ionization means and which inputs to send
Send the required field concentration as a positive finite number in mol per liter; aliases c, C, conc, molarity, and acid_concentration are accepted. Send ka as a positive finite acid dissociation constant; aliases Ka, acid_dissociation_constant, and K_a work the same way. Identical JSON inputs always produce identical results because the path is pure arithmetic with no wall clock and no remote call.
How the quadratic is solved and how to read the response
Rearrange Ka equals x squared over C minus x into the monic quadratic x squared plus Ka times x minus Ka times C equals zero. The physical root is x equals negative Ka plus the square root of Ka squared plus four Ka C, all over two; the negative root is discarded. Approximate pH is negative log ten of x so you can cross-check lecture examples without a second tool. When ionization is small the common shortcut x approximately square root of Ka C is close, but this calculator always uses the exact root so large-Ka or dilute cases stay accurate. Missing fields, non-finite numbers, zero or negative concentration, and non-positive Ka all fail the same way and are not charged after the engine rejects the body. The response echoes concentration and ka, reports pka as negative log ten of Ka, and returns x together with h_plus and a_minus equal to that same ionized concentration under the monoprotic ICE assumption. The field ha_eq is C minus x, the undissociated acid left at equilibrium. Alpha and degree_of_ionization are both x over C; percent_ionization is one hundred times that fraction. The formula string documents the quadratic path, and method is always percent_ionization_quadratic so downstream code can branch without sniffing shapes. If the solved x is not strictly less than C, the request fails with invalid_input because the pure weak-acid ICE model would be inconsistent.
API usage, pricing, classroom workflows, and practical limits
Call the free in-browser percent ionization of acid calculator for homework checks, lab pre-lab estimates, and lecture demos without installing a chemistry CAS. Remember the model is monoprotic, ideal, and neglects water; it is the right fit for textbook weak-acid percent ionization problems, not activity-corrected industrial speciation. Send a JSON body with required positive numbers concentration and ka. Use the prepaid API when a tutoring platform, LMS plug-in, lab data pipeline, or curriculum generator needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with a Ka-from-pH tool when you already measured pH and want the constant, or with percent-dissociation-from-equilibrium-concentrations when your data are C0 and Ceq rather than Ka. Authors shipping SDKs can map percent_ionization and alpha into grade-book columns while exposing pH and ha_eq in worked-solution views—the same numbers students compute by hand when they solve the quadratic on paper.
Integration use cases
Tutoring and curriculum generators
Lesson builders produce deterministic weak-acid ionization examples with structured JSON for flashcards, step sheets, and auto-graded drills without embedding a full chemistry stack.
Lab notebooks and LMS pipelines
Scripts that already store analytical concentration and tabulated Ka call a stable prepaid endpoint to attach percent ionization to each sample row for reports and dashboards.
Technical questions
How do I calculate percent ionization of a weak acid?
Send JSON with concentration (analytical C in mol/L) and ka (acid dissociation constant). The response includes percent_ionization = 100×x/C where x is solved from Ka = x²/(C−x) with the exact quadratic.