# Osmotic Pressure Calculator

> Computes the osmotic pressure of a solution from molarity, van 't Hoff factor and temperature with the van 't Hoff equation π = i·M·R·T, or solves the molarity (and the solute's molar mass, given its mass concentration) from a measured osmotic pressure.

- Calculator id: `osmotic-pressure` · Category: Chemistry (`chemistry`) · Tool name: `calculate_osmotic_pressure`
- Canonical page: https://tttkmbb.com/chemistry/osmotic-pressure · This document: https://tttkmbb.com/chemistry/osmotic-pressure.md · JSON definition: https://tttkmbb.com/chemistry/osmotic-pressure.json

## Purpose

Computes the osmotic pressure of a solution from molarity, van 't Hoff factor and temperature with the van 't Hoff equation π = i·M·R·T, or solves the molarity (and the solute's molar mass, given its mass concentration) from a measured osmotic pressure.

**Use when:** You need the osmotic pressure of a solution of known concentration, or the concentration or molar mass of a solute (e.g. a protein or polymer) from an osmometry measurement.

**Do not use when:** You need freezing-point depression or boiling-point elevation (use colligative-properties), or the solution is concentrated enough that activity effects matter (roughly above 0.1–0.5 mol/L for electrolytes).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `molarity_mol_per_l` | number |  | optional | Molar concentration of the solute formula units in mol/L. Leave empty to solve it from osmotic_pressure_atm. (> 0, max 100) |
| `van_t_hoff_factor` | number |  | optional, default 1 | Particles per formula unit in solution: 1 for non-electrolytes (glucose, urea, proteins), 2 for NaCl or KCl, 3 for CaCl2 (ideal values; measured values are somewhat lower). (> 0, max 20) |
| `temperature` | number |  | optional, default 25 | Solution temperature in temperature_unit. |
| `temperature_unit` | enum: celsius \| kelvin |  | optional, default "celsius" | Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15). |
| `osmotic_pressure_atm` | number | atm | optional | Measured osmotic pressure in atm; when given and molarity is empty, the molarity is solved. (> 0) |
| `mass_concentration_g_per_l` | number | g/L | optional | Solute mass per litre of solution; together with the molarity it yields the solute's molar mass (osmometry). (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `osmotic_pressure_atm` | number | atm | π = i·M·R·T. |
| `osmotic_pressure_kpa` | number | kPa | π in kilopascals (1 atm = 101.325 kPa). |
| `osmotic_pressure_bar` | number | bar | π in bar. |
| `osmotic_pressure_mmhg` | number | mmHg | π in mmHg (Torr). |
| `osmolarity_osmol_per_l` | number | osmol/L | i × M: total particle concentration. |
| `molarity_mol_per_l` | number | mol/L | Solute concentration, given or solved. |
| `molar_mass_g_mol` | number | g/mol | mass_concentration / molarity (only when mass_concentration_g_per_l is given). |
| `temperature_k` | number | K | Absolute temperature used. |
| `solved_for` | string |  | osmotic_pressure_atm or molarity_mol_per_l. |

## Formula

`π = i × M × R × T with R = 0.082057366 L·atm/(mol·K) and T in kelvin; M = π / (i × R × T); molar_mass = mass_concentration_g_per_l / M`

The van 't Hoff equation is the ideal-solution limit and is most accurate for dilute solutions; the factor i accounts for dissociation into ions.

## Data Sources

- OpenStax Chemistry 2e – 11.4 Colligative Properties — https://openstax.org/books/chemistry-2e/pages/11-4-colligative-properties (textbook, retrieved 2026-09-24)
- Wikipedia – Osmotic pressure — https://en.wikipedia.org/wiki/Osmotic_pressure (reference, retrieved 2026-09-24)
- NIST – CODATA internationally recommended values of the fundamental physical constants (molar gas constant R = 8.314462618 J/(mol·K), exact) — https://physics.nist.gov/cuu/Constants/index.html (standard, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/osmotic-pressure?`
- `POST https://tttkmbb.com/api/v1/calculate/osmotic-pressure` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/osmotic-pressure · OpenAPI operationId `calculate_osmotic_pressure` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "osmotic-pressure", "inputs": {…}}`

## Example

- 0.1 M NaCl (i = 2) at 25 °C: inputs `{"molarity_mol_per_l":0.1,"van_t_hoff_factor":2,"temperature":25}` → `{"osmotic_pressure_atm":4.8931,"osmotic_pressure_kpa":495.79,"osmolarity_osmol_per_l":0.2,"temperature_k":298.15,"solved_for":"osmotic_pressure_atm"}`
- Protein solution 10 g/L with π = 0.003 atm at 25 °C: inputs `{"osmotic_pressure_atm":0.003,"mass_concentration_g_per_l":10,"temperature":25}` → `{"molarity_mol_per_l":0.00012262,"molar_mass_g_mol":81551,"osmotic_pressure_kpa":0.304,"solved_for":"molarity_mol_per_l"}`

```
GET https://tttkmbb.com/api/v1/calculate/osmotic-pressure?molarity_mol_per_l=0.1&van_t_hoff_factor=2&temperature=25
```

## Limitations

You need freezing-point depression or boiling-point elevation (use colligative-properties), or the solution is concentrated enough that activity effects matter (roughly above 0.1–0.5 mol/L for electrolytes). The van 't Hoff equation is the ideal-solution limit and is most accurate for dilute solutions; the factor i accounts for dissociation into ions. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Which van 't Hoff factor should I use?**

The number of particles one formula unit gives in solution: 1 for molecular solutes, 2 for NaCl, 3 for CaCl2 or Na2SO4. Real electrolytes give slightly lower values (about 1.9 for 0.1 M NaCl) because of ion pairing.

**Why is osmotic pressure so large?**

Even 0.1 mol/L of dissolved particles exerts about 2.4 atm at 25 °C, because π depends on the number of particles like an ideal gas of the same concentration; blood plasma is about 0.3 osmol/L, roughly 7.6 atm.

## Related

- [Colligative Properties Calculator](https://tttkmbb.com/chemistry/colligative-properties.md) — Freezing-point depression and boiling-point elevation for the same solution.
- [Molarity Calculator](https://tttkmbb.com/chemistry/molarity.md) — Compute the molarity from solute mass and volume.
- [Ideal Gas Law Calculator](https://tttkmbb.com/chemistry/ideal-gas-law.md) — The van 't Hoff equation has the same form as PV = nRT.