What this calculator does
Osmotic pressure is the pressure needed to stop solvent flowing across a semipermeable membrane into a solution. A 0.3 mol/L solution of a non-dissociating solute at body temperature exerts 7.635 atm, which is a substantial pressure for such a dilute solution.
What matters is the total particle concentration, not the solute concentration. The van t Hoff factor accounts for dissociation, so 0.3 mol/L of sodium chloride behaves as 0.6 mol/L of particles and doubles the pressure. A factor of 3 at 0.3 mol/L gives exactly the same result as a factor of 1 at 0.9 mol/L.
The formula
The pressure is the van t Hoff factor multiplied by molar concentration, the gas constant and absolute temperature. The form is identical to the ideal gas law, which is not a coincidence: dilute solute particles behave much like a gas occupying the solution volume. Temperature is converted from Celsius to kelvin internally.
| Term | Meaning |
|---|---|
| Osmotic pressure (π) | The pressure opposing solvent flow across a membrane. |
| van t Hoff factor (i) | Particles produced per formula unit. 1 for glucose, about 2 for NaCl, about 3 for CaCl₂. |
| Osmolarity | The particle concentration, which is i times the molarity. |
| Colligative property | One depending on particle count rather than particle identity. |
The inputs explained
| Field | What to enter |
|---|---|
| Van’t Hoff factor | van t Hoff factor. Use 1 for a non-electrolyte such as glucose or urea, about 2 for NaCl, about 3 for CaCl₂. |
| Molar concentration (mol/L) | Molar concentration of the solute before dissociation. |
| Temperature (°C) | Temperature in Celsius. Body temperature is 37. |
When to use it
Preparing an isotonic solution
Intravenous fluids must match the osmotic pressure of blood, which is why saline is prepared at a specific concentration.
Reverse osmosis design
The applied pressure must exceed the osmotic pressure of the feed before any water crosses the membrane.
Determining a molar mass
Osmotic pressure is sensitive enough at low concentration to determine the molar mass of polymers and proteins.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does dissociation change the pressure?
The same solute concentration with different particle counts.
| van t Hoff factor | Osmotic pressure | In kPa | In bar |
|---|---|---|---|
| i = 1 | 7.635 atm | 773.6 | 7.736 |
| i = 2 | 15.270 atm | 1,547.2 | 15.472 |
| i = 3 | 22.905 atm | 2,320.8 | 23.208 |
Questions
What is the van t Hoff factor?
The number of particles a formula unit produces in solution. Glucose stays whole and gives 1. Sodium chloride splits into two ions and gives close to 2. Calcium chloride gives close to 3. Real values fall slightly short of the ideal because of ion pairing at higher concentrations.
Why is osmotic pressure so large for a dilute solution?
Because the relationship is the same as the ideal gas law, and a mole of particles exerts substantial pressure however it is distributed. A 0.3 mol/L solution at body temperature gives over 7 atmospheres, which is why cells rupture in pure water.
What does isotonic mean?
Having the same osmotic pressure as the reference fluid, usually blood plasma at around 7.7 atm. An isotonic solution causes no net water movement across a cell membrane, which is why intravenous fluids must be prepared to that specification.
How does this relate to reverse osmosis?
Reverse osmosis applies pressure greater than the osmotic pressure to push solvent the wrong way through the membrane. Seawater has an osmotic pressure near 27 atm, which is why desalination plants operate at much higher pressures still and use so much energy.
For other colligative properties, see the freezing point depression calculator and the boiling point elevation calculator.