Common ion effect solubility calculator
Find how far a common ion pushes down a salt's solubility: with a Ksp of 1.8 × 10⁻¹⁰ and 0.1 mol/L of a shared ion, the molar solubility drops to 1.8 × 10⁻⁹ mol/L. The pure-water value is shown alongside. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Ksp
- 0.0000000002
- Common ion
- 0.1
- Ksp
- 0.0000000002
- Common ion concentration
- 0.1
- C
- 0.1
- Unit concentration
- mol/L
A common ion effect solubility calculator turns a solubility product and a shared-ion concentration into the reduced molar solubility of a sparingly soluble salt. Enter Ksp for a 1:1 salt MX and the concentration C of a common ion already present from a fully soluble salt; the tool solves Ksp equals s times (s plus C) with the exact quadratic formula, returns pure-water solubility for comparison, the textbook approximation s approximately Ksp over C when the common ion dominates, a reduction factor, and step-by-step substitution lines. Homework checks, exam prep, precipitation planning, and coding kata expected values all need that same suppressed-solubility number without opening a full equilibrium solver.
What the common-ion effect does to molar solubility
A sparingly soluble salt MX dissolves according to the equilibrium MX solid yields M plus plus X minus, with solubility product Ksp equal to the product of the equilibrium ion concentrations. In pure water each ion concentration equals the molar solubility s, so Ksp equals s squared and s equals the square root of Ksp.
When a fully soluble salt that shares one ion—for example NaX providing extra X minus at concentration C—is already present, Le Chatelier’s principle shifts the dissolution equilibrium left and the amount of MX that can dissolve falls. The equilibrium expression becomes Ksp equals s times (s plus C), because the common ion total is the sum of the dissolved contribution s and the background C.
Solving the quadratic equation s squared plus C s minus Ksp equals zero yields the physical positive root s equals negative C plus the square root of C squared plus four Ksp, all over two. That exact root is always valid; the familiar classroom approximation s approximately Ksp over C applies only when C is much larger than s, so the quadratic term is negligible.
Teachers and automated graders care about rejecting a negative Ksp as much as computing the suppressed value: a student who plugs a negative product into the square root has left the domain of physical constants, and a silent absolute-value fallback would hide that mistake. The check path recomputes the discriminant and the root with the same fixed rounding used for published fields, so a successful response always ships with steps you can assert in tests or worksheets.
Practical tips, limits, and related searches
Keep Ksp and common-ion concentration inside the published absolute range so C squared plus four Ksp cannot overflow into a non-finite square root that the solver must reject. 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. When C is zero the tool reports pure-water solubility without requiring a second calculator, which is handy for side-by-side worksheets.
Prefer this capability when you already have Ksp and a single common-ion concentration for a one-to-one salt; if your salt is AB two or A two B, expand the mass-balance algebra separately. Round-trip checks are easy: recompute negative C plus square root of C squared plus four Ksp over two by hand and confirm it equals the published solubility within the same twelve-decimal rounding, and confirm that setting C to zero recovers the square root of Ksp.
What you can do with it
Homework checks for common-ion solubility
Students enter Ksp and a shared-ion concentration from textbook problems and compare hand-written reduced s, pure-water s0, and the Ksp/C approximation against a deterministic result before submitting.
Precipitation and process screening
Lab pipelines estimate how much extra common ion suppresses residual dissolved MX before designing a wash or precipitation step.
FAQ
What is the common-ion effect on solubility?
Adding an ion that already appears in the dissolution equilibrium of a sparingly soluble salt shifts the equilibrium left (Le Chatelier), lowering the molar solubility compared with pure water.
What formula does this calculator use?
For a 1:1 salt MX with common-ion concentration C it solves Ksp = s(s + C) exactly: s = (−C + √(C² + 4·Ksp)) / 2. It also reports s ≈ Ksp / C when C > 0.
Does this handle salts like CaF₂ (AB₂)?
No. The model is for 1:1 MX salts only. AB₂ / A₂B mass balances need different polynomials and are out of scope.
Is the common ion effect calculator free?
The browser tool is free and runs locally.
When is the shortcut of dividing Ksp by the ion concentration good enough?
When the common ion is far more concentrated than the dissolved salt. The calculator always solves the exact equation and tells you whether the shortcut lands within one percent of that exact answer.
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/common-ion-solubility \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"ksp":1.8e-10,"common_ion":0.1}'const res = await fetch("https://api.kit.forhosting.com/chem/common-ion-solubility", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"ksp": 1.8e-10,
"common_ion": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/common-ion-solubility",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"ksp": 1.8e-10,
"common_ion": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/common-ion-solubility", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"ksp":1.8e-10,"common_ion":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"ksp":1.8e-10,"common_ion":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/common-ion-solubility", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"ksp": 1.8e-10,
"common_ion": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.common_ion_solubility",
"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
When Ksp is negative the API returns a clear invalid_input error instead of inventing a physical constant.
How to call the API and what comes back
The common-ion concentration must also be non-negative. Send a JSON body with two required finite numbers: ksp (aliases Ksp, solubility_product, k_sp, and K_sp) and common_ion (aliases common_ion_concentration, C, c_common, ion_concentration, and common). 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. The solubility product ksp must be non-negative; a negative value is rejected with invalid_input. On success the response echoes rounded ksp and common_ion, sets solubility, molar_solubility, and s to the same reduced molar solubility in mol per litre, pure_water_solubility and s0 to the square root of Ksp, approximation to Ksp over C when C is positive or null when C is zero, approximation_used to true when that approximation lies within one percent of the exact root, reduction_factor to s over s0, formula and reaction to the model strings, 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, negative Ksp, or negative common ion—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: silver chloride with Ksp about one point eight times ten to the minus ten in zero point one molar chloride yields s about one point eight times ten to the minus nine, orders of magnitude below the pure-water root; a zero common-ion case recovers the square root of Ksp exactly; and a deliberately negative Ksp demonstrates the hard invalid_input path. This landing targets people searching for a common ion effect calculator, reduced solubility from Ksp, or sparingly soluble salt with common ion online; it is not a multi-ion speciation solver, not an AB two salt tool for calcium fluoride style stoichiometry, and not a temperature-dependent Ksp table. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send a negative product.
Integration use cases
Unit tests for student equilibrium solvers
Generate known-good common-ion cases plus deliberate negative-Ksp rejections for coding kata expected values and grader fixtures.
Technical questions
What happens when Ksp is negative?
A negative solubility product is not physical. This tool returns invalid_input instead of taking an absolute value or inventing a result.