Cryoscopic constant calculator
Recover a solvent's freezing-point constant from your own measurement: a depression of 0.93 K at 0.5 mol/kg with a van 't Hoff factor of 1 gives a Kf of 1.86 K·kg/mol, the water-like value. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Delta tf
- 0.93
- Molality
- 0.5
- Current (A)
- 1
- Kf
- 1.86 K·kg/mol
- Precision
- 10
This cryoscopic constant calculator returns the solvent-specific freezing-point depression constant Kf from the measured colligative depression ΔTf, the solution molality m, and the van 't Hoff factor i using the closed form Kf equals ΔTf divided by i times m. Freezing-point depression is the colligative drop of the freezing temperature of a solution relative to the pure solvent when a non-volatile solute lowers solvent chemical potential in the liquid phase. Rearranging the linear identity ΔTf equals i times Kf times m lets you recover Kf when a lab or textbook problem already gives depression, concentration, and particle factor. Typical textbook checks include water-like data with ΔTf equals 0.93 K, m equals 0.5 mol/kg, and i equals 1 yielding Kf equals 1.86 K·kg/mol, and the same depression with i equals 2 for a strong 1:1 electrolyte at m equals 0.5 yielding Kf equals 0.93 K·kg/mol. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
What the cryoscopic constant tells you
The cryoscopic constant Kf is a solvent property that multiplies molality and the van 't Hoff factor to give the freezing-point depression of an ideal dilute solution of a non-volatile solute. The standard linear relation is ΔTf equals i times Kf times m, where m is molality in moles of solute per kilogram of solvent, Kf has units K·kg/mol (numerically equal to °C·kg/mol for a temperature difference), and i is the van 't Hoff factor that counts the effective particles produced per formula unit.
Ideal non-electrolytes use i equals one; strong electrolytes approach the stoichiometric ion count in the dilute limit, while weak electrolytes use an effective i between one and that count. Solving for the constant gives Kf equals ΔTf divided by i times m. Zero van 't Hoff factor is likewise rejected.
Where cryoscopic constant recovery fits in study, lab, and software
Students meet the cryoscopic constant when a textbook introduces colligative properties after molality, when a lab report asks for the solvent Kf implied by a measured freezing depression, or when a contest problem gives ΔTf and asks for the constant instead of the temperature drop. Teachers can pre-generate answer keys for modest molalities and integer van 't Hoff factors without trusting opaque calculator apps that silently switch units or drop the particle factor.
Developers call the same contract from scripts to seed deterministic test vectors for chemistry education products, to normalize user-entered colligative inputs before plotting freezing curves, or to satisfy programming-challenge statements that demand Kf rather than a hand-waved estimate. Process and quality workflows sometimes need a fast offline source of cryoscopic values so dilute-solution checks can be validated without reopening a full thermodynamics package.
Product and tutoring tools use the quotient when a learner types depression, molality, and i and the UI must show a clean K·kg/mol constant with a formula echo.
What you can do with it
Homework and lab Kf checks
Recover the solvent cryoscopic constant from measured freezing-point depression, molality, and van 't Hoff factor before writing lab reports or checking textbook answers.
Tutoring and chemistry software
Normalize user-entered ΔTf, m, and i into a stable cryoscopic constant for interactive lessons and solution calculators.
FAQ
What does the cryoscopic constant calculator cost?
It is free in your browser on this page.
What formula does this tool use?
Kf = ΔTf / (i · m), where ΔTf is freezing-point depression (K), m is molality (mol/kg), and i is the van 't Hoff factor.
Is the result in K·kg/mol or °C·kg/mol?
The constant is returned as K·kg/mol. For a temperature-difference basis the numeric value matches °C·kg/mol, so 1.86 K·kg/mol is the same figure as 1.86 °C·kg/mol.
Does this tool look up Kf for common solvents?
No. You supply ΔTf, molality, and i. The calculator only rearranges the colligative identity and returns Kf.
What van 't Hoff factor should I enter for a salt?
For a strong electrolyte, use roughly the number of ions per formula unit, for example 2 for a 1:1 salt. With the same 0.93 K depression at 0.5 mol/kg, a factor of 2 halves the result to 0.93 K·kg/mol.
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/cryoscopic-constant \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"delta_tf":0.93,"molality":0.5,"i":1}'const res = await fetch("https://api.kit.forhosting.com/chem/cryoscopic-constant", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"delta_tf": 0.93,
"molality": 0.5,
"i": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/cryoscopic-constant",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"delta_tf": 0.93,
"molality": 0.5,
"i": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/cryoscopic-constant", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"delta_tf":0.93,"molality":0.5,"i":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"delta_tf":0.93,"molality":0.5,"i":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/cryoscopic-constant", 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_tf": 0.93,
"molality": 0.5,
"i": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.cryoscopic_constant",
"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 the cryoscopic constant means and what the response contains
This calculator returns the normalized delta_tf, molality, and i values, the cryoscopic constant kf rounded to the requested precision, the precision used, the method tag cryoscopic_constant, a short formula reminder, and the unit string K·kg/mol. There is no approximate CAS path and no random sampling: the engine either divides three finite scalars inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing delta_tf, molality, or i, non-finite values, magnitudes above the documented ceiling, and any zero molality, because dividing by zero is non-physical for this definition.
How freezing-point depression, molality, and the van 't Hoff factor are read
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 solvent constant. The van 't Hoff factor must also be non-zero for the same division reason. The depression is a required finite number; you supply the measured or textbook ΔTf rather than relying on a hidden pure-solvent freezing table. The preferred fields are delta_tf for the freezing-point depression, molality for m, and i for the van 't Hoff factor, but aliases deltaTf, dt, depression, freezing_depression, and Delta_Tf for the depression, m, b, and molal for molality, and van_t_hoff, vant_hoff, van_hoff, and factor for i are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Molality must not be zero: if the absolute value is at or below the numerical zero threshold, the request fails with invalid_input because cryoscopic constant recovery divides by molality. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for delta_tf, molality, i, and kf, 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 Kf equals ΔTf over i m yourself.
Where cryoscopic constant recovery fits in study, lab, 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 boiling-point elevation or molar-concentration tools when you need related solution chemistry steps, and with other chem endpoints when you are building a small lab of free, deterministic colligative helpers.
Integration use cases
Deterministic test fixtures
Generate reproducible kf values for unit tests, property checks, and CI assertions on colligative rearrangements.
Technical questions
What happens if molality is zero?
The input is rejected with invalid_input. Cryoscopic constant recovery divides by molality, so m = 0 is undefined.