Osmotic pressure calculator
Enter the molar concentration of the solute, its van ’t Hoff factor and the temperature to get the osmotic pressure in four units together with the osmolarity. Or switch to molar mass: enter the mass of solute dissolved, the solution volume and the osmotic pressure you measured.
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How to use it
- Choose osmotic pressure or molar mass.
- Enter the van ’t Hoff factor (1 for non-electrolytes).
- For osmotic pressure, enter the molar concentration. For molar mass, enter the dissolved mass in grams, the solution volume in litres and the measured osmotic pressure with its unit.
- Set the temperature and read the result.
- π = i × M × R × T (M in mol/L, T in K)
- Molar mass = i × m × R × T ÷ (π × V)
- R = 8.314462618 J/(mol·K) = 0.082057 L·atm/(mol·K); 1 atm = 101.325 kPa = 760 mmHg
Worked example
Saline, 0.154 mol/L NaCl, i = 2, at body temperature 37 °C = 310.15 K:
π = 2 × 154 mol/m³ × 8.314462618 × 310.15 = 794,249 Pa = 7.8386 atm (794.249 kPa, 5,957.4 mmHg). Osmolarity: 0.308 osmol/L.
A protein: 1 g dissolved in 0.1 L gives 3.5 mmHg at 25 °C. π = 3.5 × 133.322 = 466.63 Pa, so M = 1 × 8.314462618 × 298.15 ÷ (466.63 × 0.0001 m³) = 53,124.9 g/mol.
Tips
- Litres to cubic metres. If you calculate by hand in SI units, 1 mol/L = 1000 mol/m³ and 1 L = 0.001 m³.
- Dilute solutions only. The van ’t Hoff equation is an ideal-solution law, like PV = nRT for gases.
- Osmolarity vs osmolality. Osmolarity is per litre of solution, osmolality per kilogram of water; in dilute water solutions they are nearly the same.
Frequently asked questions
What is the formula for osmotic pressure?
The van ’t Hoff equation π = i × M × R × T: i is the van ’t Hoff factor, M the molar concentration, R the gas constant and T the absolute temperature. With M in mol/L and R = 0.082057 L·atm/(mol·K), π comes out in atmospheres.
What van ’t Hoff factor should I use?
The number of particles one formula unit gives in solution: 1 for glucose, urea or a protein, 2 for NaCl, 3 for CaCl₂. These are ideal values; real salt solutions behave as if i were somewhat smaller because ions pair up.
How is molar mass found from osmotic pressure?
Moles of solute are n = π × V ÷ (R × T), and the molar mass is the mass divided by n: M = m × R × T ÷ (π × V). Osmotic pressure is large even for dilute solutions, which makes it suited to proteins and polymers with molar masses in the tens of thousands.
Why is 0.9 % saline isotonic?
0.9 % NaCl is about 0.154 mol/L; with i = 2 it gives 0.308 osmol/L, close to the osmolarity of blood plasma. At 37 °C its ideal osmotic pressure is about 7.84 atm.