What osmotic pressure is
When a solution and pure water are separated by a membrane that lets water through but not the dissolved particles, water flows toward the solution. The osmotic pressure is the pressure you would have to apply to the solution to stop that flow. It depends on the number of dissolved particles, not on what they are.
The van ’t Hoff equation
For dilute solutions, Jacobus van ’t Hoff, winner of the first Nobel Prize in Chemistry in 1901, showed that osmotic pressure behaves like the pressure of a gas:
π = i × M × R × T
- i: the van ’t Hoff factor, the number of particles each formula unit gives: 1 for sugar, about 2 for NaCl, about 3 for CaCl₂;
- M: the molar concentration in mol/L;
- R: the gas constant, 0.082057 L·atm/(mol·K) or 8.314 L·kPa/(mol·K);
- T: the absolute temperature in kelvin.
The calculator also gives the osmolarity, i × M, in milliosmoles per liter.
Worked example: normal saline
0.9% saline contains 9 g of NaCl per liter, or 0.154 mol/L. At body temperature, 37 °C, with i = 2:
| Result | Value |
|---|---|
| Osmotic pressure | 7.84 atm |
| In kilopascals | 794 kPa |
| In bar | 7.94 bar |
| In mmHg | 5,957 mmHg |
| Ideal osmolarity | 308 mOsm/L, close to blood plasma |
In reality, Na⁺ and Cl⁻ ions interact, so the effective factor is about 1.86 instead of 2 and the measured osmolality of saline is about 286 mOsm/kg.
Why it matters
- Medicine: IV fluids must be close to the osmolarity of plasma, about 275 to 295 mOsm/kg, or red blood cells swell or shrink. 5% dextrose is about 278 mOsm/L.
- Reverse osmosis: to make fresh water from seawater, pumps must push above its osmotic pressure, about 27 atm, so plants run at 55 to 80 bar.
- Biology: osmotic pressure moves water into plant roots and keeps cells firm.
- Chemistry: measuring the osmotic pressure of a dilute solution gives the molar mass of large molecules such as proteins.
Tips
- The equation is an ideal-solution approximation: it works best below about 0.1 mol/L.
- Temperature must be in kelvin; the calculator converts from degrees Celsius.
- Osmolarity is per liter of solution, osmolality per kilogram of water. For dilute aqueous solutions, they are nearly equal.