Osmotic Pressure Calculator
Enter the van't Hoff factor i, molarity M and absolute temperature T; by the van't Hoff equation Π = i·M·R·T the tool instantly computes the osmotic pressure (atm and kPa).
Input Data
Results
At a glance:Osmotic pressure (symbol Π) is a colligative property of a solution — a property that depends only on the 'number' of solute particles, not their kind (the other colligative properties are boiling-point elevation, freezing-point depression and vapour-pressure lowering). To understand osmotic pressure, first understand 'osmosis': when a semipermeable membrane (allowing only solvent like water through, not solute) separates pure solvent from a solution (or two solutions of different concentration), solvent molecules spontaneously flow from the 'side with more solvent (lower concentration)' across the membrane to the 'side with less solvent (higher concentration)', diluting the concentrated side toward equilibrium. Osmotic pressure Π is then defined as the extra pressure that must be applied to the solution side to 'just stop' the net inflow of solvent. The more concentrated the solution, the stronger the osmotic tendency and the larger the osmotic pressure needed. The Dutch chemist van 't Hoff found it obeys a relation strikingly similar to the ideal gas law — the van 't Hoff equation: Π = i·M·R·T, where Π is osmotic pressure, i is the van 't Hoff factor (the number of particles one solute unit dissociates into), M the solute molarity (mol/L), R the gas constant (here 0.08206 L·atm/(mol·K), giving Π in atm) and T the absolute temperature (Kelvin). The van 't Hoff factor i: non-electrolytes (glucose, sucrose, urea) do not dissociate, i = 1; strong electrolytes fully dissociate, i equals the total ions — NaCl → Na⁺ + Cl⁻, i ≈ 2; CaCl₂ → Ca²⁺ + 2Cl⁻, i ≈ 3; Na₂SO₄, i ≈ 3 (actual i is slightly below theoretical due to ion pairing, closer in dilute solution). Using this tool's default: i = 2 (e.g. NaCl), M = 0.1 mol/L, T = 298 K (25°C), Π = 2 × 0.1 × 0.08206 × 298 ≈ 4.89 atm, about 495 kPa — even very dilute solutions produce substantial osmotic pressure. Temperature must be in Kelvin, by the same logic as gas laws. Applications are broad: (1) biology — the cell membrane is a semipermeable membrane; isotonic balance maintains cell shape; red blood cells in hypotonic solution swell and may burst (haemolysis), in hypertonic solution shrink — why IV drips use isotonic 0.9% saline; (2) medicine — kidney dialysis, IV fluid design; (3) botany — root water uptake, turgor pressure; (4) industry — reverse osmosis desalination, applying pressure above the osmotic pressure to force water back across the membrane; (5) determining molar mass of macromolecules (proteins). Notes: first, use Kelvin. Second, choose i by dissociation. Third, concentration in mol/L. Fourth, this equation is for dilute (ideal) solutions. The calculator outputs both atm and kPa (1 atm = 101.325 kPa).
Formula
van 't Hoff equation: Π = i · M · R · T.
R = 0.08206 L·atm/(mol·K), T in Kelvin (K = °C + 273.15).
van 't Hoff factor i: non-electrolyte = 1, NaCl ≈ 2, CaCl₂ ≈ 3.
Conversion: 1 atm = 101.325 kPa.
$$\Pi = i\,M\,R\,T$$How to Use
- Enter the van 't Hoff factor i (glucose i = 1, NaCl ≈ 2, CaCl₂ ≈ 3).
- Enter the solute molarity M (mol/L) and absolute temperature T (Kelvin).
- The right panel instantly shows osmotic pressure in both atm and kPa.
van 't Hoff factor i and osmotic pressure at 0.1 mol/L, 298 K
| Solute | Dissociation | van 't Hoff i | Π (atm) |
|---|---|---|---|
| Glucose C₆H₁₂O₆ | no dissociation | 1 | 2.45 |
| Sodium chloride NaCl | Na⁺ + Cl⁻ | 2 | 4.89 |
| Calcium chloride CaCl₂ | Ca²⁺ + 2Cl⁻ | 3 | 7.34 |
| Sodium sulphate Na₂SO₄ | 2Na⁺ + SO₄²⁻ | 3 | 7.34 |
More dissociated particles (larger i) at the same concentration give higher osmotic pressure; actual i is slightly below theoretical due to ion pairing.
Case Studies
Osmotic pressure of normal saline
0.9% NaCl saline has molarity ≈ 0.154 mol/L, NaCl i ≈ 2, body temperature 37°C (310 K).
Π = 2 × 0.154 × 0.08206 × 310 ≈ 7.83 atm, about 794 kPa.
This is close to human plasma osmotic pressure (isotonic), so IV saline neither bursts nor shrinks red blood cells.
Osmotic pressure of 0.1 mol/L NaCl
NaCl fully dissociates into Na⁺ and Cl⁻, i ≈ 2; 0.1 mol/L at 25°C (298 K).
Π = 2 × 0.1 × 0.08206 × 298 ≈ 4.89 atm ≈ 495 kPa.
Glucose at the same concentration (i = 1) gives only about 2.45 atm, showing dissociation doubles the pressure.
FAQ
How to choose the van 't Hoff factor i?
i is the number of particles one solute unit dissociates into. Non-electrolytes (glucose, sucrose, urea) do not dissociate, i = 1; NaCl → Na⁺ + Cl⁻, i ≈ 2; CaCl₂ → Ca²⁺ + 2Cl⁻, i ≈ 3. In practice i is slightly below the theoretical value due to ion pairing, closer in dilute solutions.
Why is the osmotic-pressure formula so like the ideal gas law?
The van 't Hoff equation Π = iMRT has the same form as PV = nRT (i.e. P = cRT), because in dilute solution solute particles behave like rarefied gas molecules — independent, exerting a pressure-like effect on the membrane. This was van 't Hoff's key insight.
Must temperature be in Kelvin?
Yes. T is the absolute temperature reflecting absolute thermal motion from absolute zero; using Celsius gives wrong or even negative results. Convert K = °C + 273.15, e.g. body temperature 37°C = 310 K.
What are isotonic, hypertonic and hypotonic?
Relative to a cell: isotonic means the external osmotic pressure equals the cell's, so the cell shape is unchanged; hypertonic means the external solution is more concentrated, the cell shrinks; hypotonic means it is more dilute, the cell swells or bursts. Medical IV fluids must be isotonic (e.g. 0.9% saline) to protect blood cells.
What is the relation between osmotic pressure and reverse osmosis?
Reverse osmosis applies external pressure exceeding the solution's osmotic pressure to force the solvent (water) backward across the semipermeable membrane, separating it from solute — used in desalination and pure-water production. You must first know the osmotic pressure to know the minimum pressure needed.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.