Molar mass from freezing point depression calculator
2.5 g of an unknown in 0.05 kg of water that freezes 0.465 °C lower, with a Kf of 1.86, has a molar mass of 200 g/mol. Turn a cryoscopy reading into a molecular weight, with the molality and moles shown. Free in your browser.
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Worked example
- Delta tf
- 0.465
- Cryoscopic
- 1.86
- Solute grams
- 2.5
- Solvent kg
- 0.05
- Molar mass
- 200
- Molality
- 0.25
- Moles solute
- 0.0125
Freezing-point depression cryoscopy is a classic laboratory route to the molar mass of an unknown non-electrolyte: dissolve a weighed sample in a known mass of solvent, measure how far the freeze point falls below that of the pure solvent, and invert the colligative relation. For ideal dilute non-electrolytes the depression delta Tf equals Kf times molality, and molality is grams of solute divided by molar mass divided by kilograms of solvent, so rearranging gives M equals Kf times grams of solute divided by delta Tf times kilograms of solvent. Students use the inversion for organic unknown labs and colligative-property homework; teaching labs grade freeze-point molar-mass experiments against the same closed form; formulation and quality teams sanity-check reported molecular weights when only freeze-point data are on hand. This calculator accepts freezing-point depression, cryoscopic constant, solute mass in grams, and solvent mass in kilograms, returns the molar mass with intermediate molality and moles, unit labels, and the formula string for audit, and rejects zero depression so a pure-solvent measurement is never inverted into a silent infinity.
How molar mass is recovered from freezing-point depression
Start from the dilute-solution colligative relation for an ideal non-electrolyte: the freezing point of the solution is lower than that of the pure solvent by an amount delta Tf equal to Kf times m, where m is molality in moles of solute per kilogram of solvent and Kf is the cryoscopic constant of the solvent in degrees Celsius times kilogram per mole.
Molality itself is the amount of solute in moles divided by the solvent mass in kilograms, and the amount of solute is the weighed solute mass in grams divided by the unknown molar mass M in grams per mole. Substituting and solving for M produces the working formula M equals Kf times grams of solute divided by delta Tf times kilograms of solvent. The temperature interval of the depression may be reported in degrees Celsius or kelvin; the size of the interval is the same either way.
Kf is a tabulated material property of the solvent—about one point eight six for water, higher for solvents such as camphor or cyclohexane used in historical Rast-type determinations. Solvent mass must likewise be non-zero because it sits in the denominator.
Where cryoscopy molar-mass calculators show up in real work
Secondary-school and introductory university chemistry courses assign colligative-property problems that invert a measured freeze-point drop into a molecular weight; a single trusted oracle speeds grading and demo setup without hand-waving floating-point noise. Organic teaching laboratories still run cryoscopic molar-mass determinations on unknowns dissolved in water, benzene, or cyclohexane and compare experimental M to the expected formula weight, so students need the same closed form their report cites.
Process and quality teams sometimes receive only freeze-point depression data for a dilute product stream and need a quick estimate of average solute molar mass before commissioning a full analytical suite. Research groups validating new solvent Kf values against known standards also invert the same relation as a consistency check.
If you later need the forward freezing-point depression from molality, boiling-point elevation molar mass with Kb, osmotic-pressure molar mass, automatic Kf lookup tables, or an explicit van 't Hoff factor for electrolytes, treat those as separate search intents and landings rather than overloading this molar mass from freezing point depression calculator page.
What you can do with it
Cryoscopy lab molar-mass unknowns
Invert measured ΔTf, tabulated Kf, solute grams, and solvent kilograms into M for teaching-lab unknowns and formula-weight checks.
Homework and exam answer keys
Generate M = (Kf × g) / (ΔTf × kg) for textbook cryoscopy sets so students and auto-graders share one closed-form ground truth.
Dilute-stream average molecular weight estimates
Estimate average solute molar mass from freeze-point depression data when only cryoscopic measurements are available.
FAQ
What formula does this molar mass from freezing point depression calculator use?
The ideal non-electrolyte inversion M = (Kf × g) / (ΔTf × kg), where ΔTf is freezing-point depression, Kf is the cryoscopic constant, g is solute mass in grams, and kg is solvent mass in kilograms.
Does this include a van 't Hoff factor?
For electrolytes, scale ΔTf by i externally or use a dedicated electrolyte landing when available.
What units should I use for solvent mass?
Kilograms of solvent (kg). That matches the SI definition of molality (mol/kg). Convert grams of solvent by dividing by 1000 before calling the calculator.
What does it cost?
The browser tool is free and runs locally.
What Kf value should I use for water?
About 1.86 °C·kg/mol. Kf is a property of the solvent, so camphor or cyclohexane have higher values. The calculator does not look it up for you; enter the value from your table or textbook.
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/molar-mass-from-fp-depression \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"delta_tf":0.465,"cryoscopic_constant":1.86,"solute_grams":2.5,"solvent_kg":0.05}'const res = await fetch("https://api.kit.forhosting.com/chem/molar-mass-from-fp-depression", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"delta_tf": 0.465,
"cryoscopic_constant": 1.86,
"solute_grams": 2.5,
"solvent_kg": 0.05
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/molar-mass-from-fp-depression",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"delta_tf": 0.465,
"cryoscopic_constant": 1.86,
"solute_grams": 2.5,
"solvent_kg": 0.05
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/molar-mass-from-fp-depression", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"delta_tf":0.465,"cryoscopic_constant":1.86,"solute_grams":2.5,"solvent_kg":0.05}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"delta_tf":0.465,"cryoscopic_constant":1.86,"solute_grams":2.5,"solvent_kg":0.05}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/molar-mass-from-fp-depression", 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": 0.465,
"cryoscopic_constant": 1.86,
"solute_grams": 2.5,
"solvent_kg": 0.05
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.molar_mass_from_fp_depression",
"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
How molar mass is recovered from freezing-point depression
Delta Tf must be finite and non-zero: a measured depression of zero means no colligative shift was observed, so the inversion is undefined and fails validation with a clear invalid_input message rather than returning infinity or NaN. The capability evaluates the closed form in deterministic floating-point arithmetic: no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical inputs always produce identical JSON. It does not look up solvent Kf tables for you, apply a van 't Hoff factor other than the implicit non-electrolyte case of one, compute the forward depression from a known molar mass, or return the absolute freezing temperature of the mixture; those are separate search intents with their own landings when product coverage grows.
What you send and what you get back
Classic textbook checks include two point five grams of solute in zero point zero five kilograms of water with delta Tf of zero point four six five and Kf of one point eight six giving two hundred grams per mole, and one point five grams in zero point zero two five kilograms of benzene with delta Tf of zero point seven five and Kf of five point one two giving four hundred nine point six grams per mole. Send four required finite numbers under the fields delta_tf, cryoscopic_constant, solute_grams, and solvent_kg. delta_tf is the measured freezing-point depression in degrees Celsius or kelvin and must be non-zero; a value of zero fails because molar mass cannot be recovered without a colligative shift. cryoscopic_constant is Kf for your solvent—about one point eight six degrees Celsius kilogram per mole for water, different for benzene, acetic acid, camphor, and other laboratory solvents. solute_grams is the mass of the unknown (or known) solute in grams. solvent_kg is the mass of solvent in kilograms and must be non-zero. Missing fields, non-numeric strings, NaN, Infinity, zero depression, and zero solvent mass fail with invalid_input and are not charged. On success the response echoes cleaned delta_tf, cryoscopic_constant, solute_grams, and solvent_kg, provides molar_mass as the primary result in grams per mole, includes derived molality equal to delta Tf over Kf and moles_solute equal to grams over M, includes a units hint object, sets method to molar_mass_from_freezing_point_depression, and formula to M equals Kf times g over delta Tf times kg so lab reports can cite the same expression. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where cryoscopy molar-mass calculators show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Technical questions
What happens if freezing-point depression is zero?
The request fails with invalid_input. When ΔTf = 0 there is no colligative shift to invert, so molar mass is undefined rather than infinite.