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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.

When to use

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).

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.

Inputs

Parameter	Type	Unit	Required	Description
`molarity_mol_per_l`	number		no	Molar concentration of the solute formula units in mol/L. Leave empty to solve it from osmotic_pressure_atm. Range: > 0, ≤ 100
`van_t_hoff_factor`	number		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). Range: > 0, ≤ 20
`temperature`	number		default 25	Solution temperature in temperature_unit.
`temperature_unit`	enum: celsius \| kelvin		default celsius	Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15).
`osmotic_pressure_atm`	number	atm	no	Measured osmotic pressure in atm; when given and molarity is empty, the molarity is solved. Range: > 0
`mass_concentration_g_per_l`	number	g/L	no	Solute mass per litre of solution; together with the molarity it yields the solute's molar mass (osmometry). Range: > 0

Outputs

Output	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.

Example

0.1 M NaCl (i = 2) at 25 °C: {"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: {"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

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/osmotic-pressure (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/osmotic-pressure · Markdown: https://tttkmbb.com/chemistry/osmotic-pressure.md · JSON definition: https://tttkmbb.com/chemistry/osmotic-pressure.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="osmotic-pressure"
OpenAPI operationId: calculate_osmotic_pressure
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

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 calculators

Colligative Properties Calculator — Freezing-point depression and boiling-point elevation for the same solution.
Molarity Calculator — Compute the molarity from solute mass and volume.
Ideal Gas Law Calculator — The van 't Hoff equation has the same form as PV = nRT.