Vapor pressure molar mass calculator
A relative vapor-pressure lowering of 0.02 with 5 mol of solvent and 10 g of solute points to a molar mass of 98 g/mol. Enter the relative lowering, the solvent moles and the solute mass to identify an unknown non-volatile solute with Raoult's law. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Relative lowering
- 0.02
- Solvent moles
- 5
- Solute grams
- 10
- Solute moles
- 0.1020408163 g/mol
- Molar mass
- 98
- Mole fraction solute
- 0.02
- Precision
- 10
This vapor pressure molar mass calculator returns the solute molar mass M in grams per mole from the relative vapor-pressure lowering χ equals (P° minus P) over P°, the amount of solvent in moles, and the mass of non-volatile solute in grams using Raoult’s law rearrangement M equals g times (1 minus χ) divided by χ times n1. Relative lowering equals the mole fraction of solute for an ideal solution of a non-volatile solute, so the same identity that links measured vapor pressures to composition also yields the unknown molar mass without a molecular formula. The same path appears in general chemistry labs that compare manometer or isoteniscope readings of pure solvent and solution, in identification of unknowns from colligative vapor-pressure data, and in homework that gives χ and solvent moles instead of moles of solute. Typical textbook checks include χ equals 0.02 with five moles of solvent and ten grams of solute yielding about ninety-eight grams per mole, and a smaller lowering with the same masses yielding a larger M. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
Where inverse vapor-pressure lowering fits in study, lab, and software
Students meet molar mass from relative vapor-pressure lowering when a lab compares the vapor pressure of pure solvent with that of a solution of unknown organic solute, when a textbook gives χ and solvent moles instead of moles of solute, or when a contest problem asks for M from Raoult data without a molecular formula. Teachers can pre-generate answer keys for modest relative lowerings and known solvent amounts without trusting opaque calculator apps that silently switch between the dilute approximation χ equals n2 over n1 and the exact mole-fraction form.
Developers call the same contract from scripts to seed deterministic test vectors for chemistry education products, to normalize user-entered colligative inputs before reporting molar mass, or to satisfy programming-challenge statements that demand M rather than a hand-waved estimate. Process and quality workflows sometimes need a fast offline source of molar-mass checks so dilute-solution vapor-pressure data can be validated without reopening a full thermodynamics package.
Product and tutoring tools use the inverse product when a learner types relative lowering, solvent moles, and solute grams and the UI must show a clean g/mol result with a formula echo. Pair it with boiling-point elevation and freezing-point depression molar-mass helpers when you are building a small lab of free, deterministic colligative tools that share the same validation style and precision contract.
What you can do with it
Lab unknown molar mass
Convert measured relative vapor-pressure lowering, solvent moles, and solute grams into solute molar mass for lab reports and unknown identification.
Tutoring and chemistry software
Normalize user-entered χ, solvent moles, and grams into a stable g/mol result for interactive lessons and solution calculators.
FAQ
What does the vapor pressure molar mass calculator cost?
It is free in your browser on this page.
What formula does this tool use?
M = g·(1−χ)/(χ·n1), from Raoult’s law χ = (P°−P)/P° = n2/(n1+n2). M is returned in g/mol.
What happens if relative vapor-pressure lowering is zero?
Zero relative lowering makes molar mass undefined (division by zero).
Does this use the dilute approximation χ ≈ n2/n1?
No. It uses the exact Raoult mole-fraction form χ = n2/(n1+n2), so M = g·(1−χ)/(χ·n1). For very small χ the two forms nearly agree.
How do I get the relative lowering from my measurements?
Subtract the solution's vapor pressure from the pure solvent's vapor pressure and divide the difference by the pure solvent's value. The result has no unit and must lie strictly between zero and one.
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/vapor-pressure-molar-mass \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"relative_lowering":0.02,"solvent_moles":5,"solute_grams":10}'const res = await fetch("https://api.kit.forhosting.com/chem/vapor-pressure-molar-mass", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"relative_lowering": 0.02,
"solvent_moles": 5,
"solute_grams": 10
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/vapor-pressure-molar-mass",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"relative_lowering": 0.02,
"solvent_moles": 5,
"solute_grams": 10
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/vapor-pressure-molar-mass", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"relative_lowering":0.02,"solvent_moles":5,"solute_grams":10}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"relative_lowering":0.02,"solvent_moles":5,"solute_grams":10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/vapor-pressure-molar-mass", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"relative_lowering": 0.02,
"solvent_moles": 5,
"solute_grams": 10
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.vapor_pressure_molar_mass",
"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 vapor-pressure molar mass means and what the response contains
Relative vapor-pressure lowering is a colligative property grounded in Raoult’s law: for an ideal solution of a non-volatile solute, the vapor pressure of the solvent above the mixture is the pure-solvent vapor pressure times the solvent mole fraction. Equivalently, the dimensionless relative lowering χ equals (P° minus P) over P° equals the mole fraction of solute n2 over n1 plus n2. When you know χ, the solvent amount n1 in moles, and the solute mass g in grams, moles of solute equal χ times n1 over one minus χ, and the inverse formula for molar mass is M equals g times (1 minus χ) divided by χ times n1. This calculator returns the normalized relative_lowering, solvent_moles, and solute_grams values, the recovered solute_moles, the molar_mass in g/mol, the mole_fraction_solute echo of χ, the precision used, the method tag vapor_pressure_molar_mass, a short formula reminder, and the unit string g/mol. There is no approximate CAS path and no random sampling: the engine either rearranges three finite scalars inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing relative_lowering, solvent_moles, or solute_grams, non-finite values, magnitudes above the documented ceiling, zero relative lowering because division by zero makes M undefined, relative lowering equal to one because one minus χ vanishes, and zero solvent moles for the same reason.
How relative lowering, solvent moles, and solute grams 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 molar mass. Relative lowering must also not equal one, and solvent moles must be non-zero. You supply the measured or problem-statement relative lowering and the solvent mole count rather than relying on a hidden table of pure-solvent vapor pressures. The preferred fields are relative_lowering for χ equals (P° minus P) over P°, solvent_moles for the solvent amount n1, and solute_grams for the solute mass, but aliases chi, delta_p_over_p0, vapor_pressure_lowering, rel_lowering, x_solute, and lowering for the relative lowering, n_solvent, n1, moles_solvent, and solvent_mol for the solvent moles, and grams, mass_solute, solute_mass, w, and g_solute for the solute mass are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Relative lowering must not be zero: if the absolute value is at or below a tiny epsilon, the request fails with invalid_input because M is undefined when χ is zero. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for the inputs, solute_moles, molar_mass, and mole_fraction_solute, 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 M equals g times (1 minus χ) over χ times n1 yourself.
Where inverse vapor-pressure lowering 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.
Integration use cases
Deterministic test fixtures
Generate reproducible molar_mass and solute_moles values for unit tests, property checks, and CI assertions on Raoult inverse formulas.
Technical questions
Is solvent amount entered in moles or grams?
Solvent amount is in moles (solvent_moles). Solute mass is in grams (solute_grams), matching the usual Raoult rearrangement for unknown M.