Molar mass from osmotic pressure
1.2 g of solute in 0.25 L showing 0.52 atm at 298.15 K has a molar mass of 225.834754144615 g/mol. Turn an osmometry reading into molecular weight, with the moles, the molarity and an optional van't Hoff factor. Free in your browser.
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Run — free
Worked example
- Pressure
- 0.52
- Mass
- 1.2
- Volume
- 0.25
- Creativity
- 298.15
- Current (A)
- 1
- R
- 0.08205746
- R unit
- L·atm·mol⁻¹·K⁻¹
- Molar mass
- 225.8347541446
Osmotic pressure is a colligative property that depends on how many solute particles are present in a solution, not on their chemical identity. For ideal dilute solutions the van't Hoff relation connects measured osmotic pressure to molar concentration, absolute temperature, and the gas constant, so rearranging for molar mass turns a laboratory pressure reading into the molecular weight of an unknown non-volatile solute. This capability implements that rearrangement deterministically: send osmotic pressure in atmospheres, solute mass in grams, solution volume in liters, and temperature in kelvin, optionally with a van't Hoff factor for electrolytes, and receive molar mass in grams per mole plus supporting moles and molarity fields. Non-positive pressure or temperature fails with a clear invalid input error so homework checkers and instrument pipelines never silently invent a mass.
What inputs mean and which units the formula expects
The ideal dilute van't Hoff equation writes osmotic pressure π equal to i times molarity times R times T. Molarity is moles of solute per liter of solution, and moles equal mass divided by molar mass, so solving for molar mass yields M equals i times m times R times T, all over π times V. This calculator fixes the unit system so every field is unambiguous: pressure is in atmospheres, mass of pure solute is in grams, solution volume is in liters, and temperature is absolute kelvin.
The gas constant is the textbook-compatible value zero point zero eight two zero five seven four six liter atmosphere per mole per kelvin, returned in the response so you can audit the arithmetic. Optional field i is the van't Hoff factor, defaulting to one for nonelectrolytes such as sugars and many polymers; electrolytes that dissociate should send the effective i you already measured or estimated. Pressure and temperature must be strictly positive; zero or negative values raise invalid input because the rearranged formula is undefined or non-physical.
Mass and volume must also be positive finite numbers.
What you can do with it
Unknown solute homework and exams
Students enter measured osmotic pressure, dissolved mass, flask volume, and bath temperature to obtain molar mass and check intermediate molarity without spreadsheet formulas that silently use the wrong R.
Polymer and biomolecule lab notes
Teaching labs and LIMS connectors convert membrane osmometry readings into g/mol estimates with a fixed unit contract and optional van't Hoff factor for charged solutes.
FAQ
What happens if pressure or temperature is zero or negative?
Non-positive osmotic pressure or non-positive absolute temperature make the rearranged van't Hoff formula undefined or non-physical and are not charged.
When should I set the van't Hoff factor i?
Leave i at the default 1 for nonelectrolytes.
Is the molar mass from osmotic pressure calculator free?
The browser tool runs free on your device.
What molar mass do 1.2 g in 0.25 L give at 0.52 atm and 298.15 K?
With a van't Hoff factor of 1, the molar mass is 225.834754144615 g/mol. That corresponds to 0.005313619706 mol of solute and a molarity of 0.021254478824 mol/L.
Which units do I need to enter?
Osmotic pressure in atmospheres, the solute mass in grams, the solution volume in litres and the temperature in kelvin. The gas constant used is 0.08205746 L·atm per mole per kelvin, and it is shown with the result.
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-osmotic-pressure \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"pressure":0.52,"mass":1.2,"volume":0.25,"temperature":298.15}'const res = await fetch("https://api.kit.forhosting.com/chem/molar-mass-from-osmotic-pressure", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"pressure": 0.52,
"mass": 1.2,
"volume": 0.25,
"temperature": 298.15
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/molar-mass-from-osmotic-pressure",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"pressure": 0.52,
"mass": 1.2,
"volume": 0.25,
"temperature": 298.15
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/molar-mass-from-osmotic-pressure", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"pressure":0.52,"mass":1.2,"volume":0.25,"temperature":298.15}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"pressure":0.52,"mass":1.2,"volume":0.25,"temperature":298.15}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/molar-mass-from-osmotic-pressure", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"pressure": 0.52,
"mass": 1.2,
"volume": 0.25,
"temperature": 298.15
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.molar_mass_from_osmotic_pressure",
"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
What inputs mean and which units the formula expects
Aliases such as pi, osmotic_pressure, m, solute_mass, V, solution_volume, T, and kelvin are accepted so lab notebooks and JSON from other tools map without renaming. Identical inputs always produce identical JSON because the path is pure arithmetic with no network, no random seed, and no wall clock.
Reading molar mass, moles, molarity, and error cases
Supporting fields moles and molarity show intermediate quantities consistent with the same M, which helps graders verify that concentration and particle count line up with the reported pressure. On success the response echoes pressure, mass, volume, temperature, and i, plus the R value and its unit string. The primary result is molar_mass in g per mol, with molar_mass_unit set explicitly for UI labels. The formula string restates M equals open parenthesis i times m times R times T close parenthesis over open parenthesis π times V close parenthesis, and method is always vant_hoff_osmotic_pressure so downstream code can branch without sniffing shapes. Missing required fields, non-finite numbers, non-positive pressure, non-positive temperature, non-positive mass or volume, and non-positive i all fail with invalid_input and are not charged after the engine rejects the request. Use molar_mass alone when you only need the molecular weight; use moles and molarity when lab reports must show concentration steps; pin formula and R when teaching the derivation beside the numerical answer.
API usage, pricing, lab workflows, and practical limits
Call the free in-browser molar mass from osmotic pressure calculator for homework checks, lecture demos, and quick instrument sanity checks without installing a spreadsheet or a CAS. Remember the model assumes ideal dilute behavior; very concentrated solutions, membrane imperfections, and non-ideal activity coefficients are outside this product promise. Send a JSON body with required pressure, mass, volume, and temperature, and optional i when electrolytes or incomplete dissociation matter. Use the prepaid API when a laboratory information system, tutoring platform, polymer characterization pipeline, or colligative-property curriculum 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 van't Hoff factor calculator when you first need i from ions and degree of dissociation, then feed that i here to finish the molar-mass step. Authors shipping SDKs can map molar_mass, moles, and molarity directly into result tables that match what students write when they rearrange the van't Hoff equation by hand.
Integration use cases
Tutoring and colligative pipelines
Curriculum generators and auto-graders call a stable prepaid endpoint instead of reimplementing M = i m R T / (π V) in every language or notebook kernel.
Technical questions
How do I calculate molar mass from osmotic pressure?
Send JSON with pressure (atm), mass (g of solute), volume (L of solution), and temperature (K). The response molar_mass uses M = (i·m·R·T)/(π·V) with optional i defaulting to 1.
Which units does the calculator use?
Pressure in atmospheres, solute mass in grams, solution volume in liters, temperature in kelvin, and R = 0.08205746 L·atm·mol⁻¹·K⁻¹. Molar mass is returned in g/mol.