Osmotic pressure from molarity calculator
A 0.1 mol/L non-electrolyte at 298.15 K exerts about 2.446 atm when you use the litre-atmosphere gas constant; left at its default, the SI constant gives pascals from mol/m³. Zero molarity correctly gives zero pressure. Free in your browser.
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Worked example
- Molarity
- 0.1
- Creativity
- 298.15
- Van t hoff factor
- 1
- Universal gas constant R
- 0.08205746
- Osmotic pressure
- 2.4465431699
Osmotic pressure is the colligative hydrostatic head that develops when a semi-permeable membrane separates a solution from pure solvent: solvent tends to flow into the solution until the opposing pressure balances the chemical-potential difference. For ideal dilute solutions the classical van 't Hoff equation states that this pressure equals the product of the van 't Hoff factor, the molar concentration of solute, the gas constant, and absolute temperature—written compactly as pi equals i M R T. Students meet the formula when predicting the osmotic pressure of sugar or salt solutions at a stated lab temperature; clinical and pharmacy courses use it when comparing isotonic IV fluids and plasma-like concentrations; process engineers sketch reverse-osmosis feed pressures before running a full membrane model. This calculator takes molarity, absolute temperature, and the van 't Hoff factor, optionally a gas constant for non-SI unit systems, returns the osmotic pressure with unit hints and the formula string for audit, and rejects zero or negative temperature so a non-physical absolute scale never becomes a silent nonsense product.
How osmotic pressure is defined from molarity
Start from the van 't Hoff colligative relation taught in general and physical chemistry for ideal dilute solutions: the osmotic pressure pi that balances solvent flow across a perfect semi-permeable membrane equals the product of the van 't Hoff factor i, the molar concentration M of the solute, the gas constant R, and the absolute temperature T. Write pi equals i times M times R times T.
The van 't Hoff factor accounts for dissociation or association—i equals one for non-electrolytes such as glucose or sucrose, about two for ideal strong one-to-one salts such as sodium chloride, and higher for salts that release more ions—while M is the analytical molarity of formula units before counting particles.
The gas constant must match your concentration and pressure unit system—default SI uses R about eight point three one four joules per mole per kelvin with concentration in moles per cubic meter, which yields pressure in pascals; textbook problems that quote atmospheres often pass R about zero point zero eight two zero five seven liters atmospheres per mole per kelvin with molarity in moles per liter to obtain pressure in atmospheres.
Where osmotic-pressure-from-molarity calculators show up in real work
Secondary-school and introductory university chemistry courses assign colligative-property drills that compute pi equals i M R T for a stated concentration, temperature, and dissociation factor; a single trusted oracle speeds grading and demo setup without hand-waving floating-point noise. Laboratory courses prepare aqueous sugar or salt solutions, measure osmotic pressure with membrane cells, and compare experimental pi to the ideal i M R T prediction, so students need the same closed form their report cites.
Clinical and pharmacy teaching labs discuss isotonic saline, dextrose, and plasma-like concentrations against colligative estimates, and process engineers estimate design osmotic pressure for reverse-osmosis or forward-osmosis sketches before committing to a full simulation package. If you later need concentration from measured pressure, freezing-point depression from molality, boiling-point elevation, Raoult vapor-pressure lowering, or automatic unit conversion between pascals and atmospheres without choosing R yourself, treat those as separate search intents and landings rather than overloading this osmotic-pressure-from-molarity calculator page.
What you can do with it
Homework and exam answer keys
Compute π = i·M·R·T for textbook SI and atm/R sets so students and auto-graders share one closed-form ground truth.
Membrane lab osmotic-pressure predictions
Predict ideal osmotic pressure from prepared molarity, bath temperature, and van 't Hoff factor before comparing to cell measurements.
RO and process sketching
Estimate design osmotic pressure from feed molarity and operating temperature for reverse-osmosis or osmotic-power back-of-envelope work.
FAQ
What formula does this osmotic pressure from molarity calculator use?
The van 't Hoff relation: π = i · M · R · T, where M is molarity, T is absolute temperature in kelvin, i is the van 't Hoff factor, and R is the gas constant in consistent units.
What happens if temperature is zero or negative?
Absolute temperature must be greater than zero; T ≤ 0 is non-physical for osmotic pressure π = i·M·R·T.
What van 't Hoff factor should I use?
Partial dissociation uses an effective i between 1 and the ideal limit.
Which gas constant R should I use?
For textbook problems in atmospheres, pass R ≈ 0.08205746 L·atm/(mol·K) with M in mol/L to get π in atm.
What does it cost?
The browser tool is free and runs locally.
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/osmotic-pressure-from-molarity \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"molarity":0.1,"temperature":298.15,"van_t_hoff_factor":1}'const res = await fetch("https://api.kit.forhosting.com/chem/osmotic-pressure-from-molarity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"molarity": 0.1,
"temperature": 298.15,
"van_t_hoff_factor": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/osmotic-pressure-from-molarity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"molarity": 0.1,
"temperature": 298.15,
"van_t_hoff_factor": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/osmotic-pressure-from-molarity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"molarity":0.1,"temperature":298.15,"van_t_hoff_factor":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"molarity":0.1,"temperature":298.15,"van_t_hoff_factor":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/osmotic-pressure-from-molarity", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"molarity": 0.1,
"temperature": 298.15,
"van_t_hoff_factor": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.osmotic_pressure_from_molarity",
"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 osmotic pressure is defined from molarity
Temperature must be absolute and strictly positive: zero kelvin and negative values are non-physical for this equation and fail validation with a clear invalid_input message rather than producing a silent nonsense result. 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 convert Celsius to kelvin for you, invert pressure back to concentration, look up membrane rejection tables, or compute freezing-point depression—those remain separate search intents with their own landings.
What you send and what you get back
Classic textbook checks include zero point one molar non-electrolyte at two hundred ninety-eight point one five kelvin with R equals zero point zero eight two zero five seven four six giving about two point four four six atmospheres, and a pure-solvent limit of zero molarity yielding zero pressure. Send three required finite numbers under the fields molarity, temperature, and van_t_hoff_factor, and optionally gas_constant when you are not using SI defaults. molarity is M in your chosen unit system—moles per liter when you supply the liter-atmosphere form of R, or moles per cubic meter when you rely on the default SI R—and must be non-negative; negative molarity fails as non-physical. temperature is absolute temperature in kelvin and must be greater than zero; zero and negative values fail because the colligative product is non-physical on a non-absolute scale. van_t_hoff_factor is the dimensionless i and must be a positive finite number; non-positive i fails validation. gas_constant is optional: omit it to use eight point three one four four six two six one eight joules per mole per kelvin, or pass a positive finite value that matches your molarity and desired pressure units. Missing fields, non-numeric strings, NaN, Infinity, non-positive temperature, negative molarity, non-positive van 't Hoff factor, and non-positive gas constant fail with invalid_input and are not charged. On success the response echoes cleaned molarity, temperature, van_t_hoff_factor, and gas_constant, flags gas_constant_defaulted when the SI default was applied, provides osmotic_pressure as the primary result, includes a units hint object, sets method to van_t_hoff_osmotic_pressure, and formula to pi equals i M R T so homework write-ups 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 osmotic-pressure-from-molarity 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.