About the Osmotic Pressure Calculator
This osmotic pressure calculator applies the van 't Hoff equation, Π = iMRT, to find the pressure needed to stop solvent flowing across a semipermeable membrane into a solution. Enter the molar concentration, the temperature and the van ’t Hoff factor (or pick an electrolyte type), and get the result in atm, kPa, bar and mmHg along with the osmolarity.
You can also run it in reverse: enter the mass of solute, the solution volume and a measured osmotic pressure to calculate the solute’s molar mass — the classic method for sizing proteins and polymers, because even tiny concentrations produce easily measured pressures. It is useful for general and physical chemistry students, biology students studying tonicity, and lab work on dialysis and reverse osmosis.
The equation is exact only for ideal, dilute solutions. Real electrolytes form ion pairs, so their effective i is a little below the ideal value — about 1.9 for NaCl at physiological concentrations — and concentrated solutions deviate further. Enter a measured i under Custom for better accuracy.
With the default inputs, the answer is 7.635. Change any value above to recalculate instantly.
How to use the osmotic pressure calculator
- 1Choose whether to find the osmotic pressure or a molar mass.
- 2Pick the solute type, or enter a custom van ’t Hoff factor.
- 3Enter the molarity — or the mass, volume and measured pressure for molar mass.
- 4Enter the temperature and read the result in several pressure units.
Formula and method
The van 't Hoff equation treats dissolved particles like an ideal gas: the osmotic pressure Π equals the particle concentration (i × M) times RT. With M in mol/L, T in kelvin and R = 0.082057 L·atm/(mol·K), Π comes out in atmospheres; the calculator converts to kPa (× 101.325), bar (× 1.01325) and mmHg (× 760).
The van ’t Hoff factor i is the number of particles each formula unit produces: 1 for non-electrolytes such as glucose, 2 for NaCl, 3 for CaCl₂. To find a molar mass, the equation is rearranged to M = Π/(iRT) for the molarity, and molar mass = grams of solute ÷ (liters × M). The model assumes a dilute, ideal solution and a perfectly semipermeable membrane.
- Π
- Osmotic pressure (atm)
- i
- van ’t Hoff factor (particles per formula unit)
- M
- Molar concentration (mol/L)
- R
- Gas constant, 0.082057 L·atm/(mol·K)
- T
- Absolute temperature (K)
- m, V
- Mass of solute (g) and solution volume (L)
Worked examples
0.15 M NaCl at body temperature (37 °C)
With ideal i = 2, Π = 2 × 0.15 × 0.082057 × 310.15 = 7.64 atm (774 kPa). Using the measured i of about 1.9 for saline gives roughly 7.3 atm.
0.30 M glucose at 25 °C
Glucose does not dissociate, so i = 1 and Π = 0.30 × 0.082057 × 298.15 = 7.34 atm.
Molar mass of a protein from 2.0 mmHg
2.0 mmHg = 0.002632 atm, so M = 0.002632 ÷ (0.082057 × 298.15) = 1.076 × 10⁻⁴ mol/L. 1.0 g in 0.100 L is 10 g/L, and 10 ÷ 1.076 × 10⁻⁴ ≈ 93,000 g/mol.
Frequently asked questions
What is the osmotic pressure formula?+
Π = iMRT, the van 't Hoff equation: i is the van ’t Hoff factor, M the molar concentration, R the gas constant (0.082057 L·atm/(mol·K)) and T the absolute temperature in kelvin.
What is the van ’t Hoff factor?+
It is the number of particles a solute produces in solution per formula unit. Sugars and proteins have i = 1, NaCl ideally 2, CaCl₂ ideally 3. Measured values are a little lower because some ions pair up.
What is the osmotic pressure of blood?+
Blood plasma has an osmolality of about 280–300 mOsm/kg, which corresponds to an osmotic pressure of roughly 7.1–7.6 atm at 37 °C. Normal saline (0.9% NaCl) is formulated to match it.
Why is osmotic pressure used to find molar mass?+
Osmotic pressure is large even for very dilute solutions, so it can measure molar masses of proteins and polymers that would produce immeasurably small freezing-point or boiling-point changes.
What is the difference between osmolarity and osmotic pressure?+
Osmolarity (i × M) is the concentration of dissolved particles in osmoles per liter. Osmotic pressure is the pressure that concentration generates across a semipermeable membrane, Π = osmolarity × RT.