Osmotic Pressure Calculator (van t Hoff)
Calculate osmotic pressure using the van t Hoff equation.
Enter solute concentration, temperature, and van t Hoff factor to get pressure in atm, kPa, and mmHg.
The van ’t Hoff equation
Jacobus van ’t Hoff (1885, Nobel Prize 1901) showed that dilute solutions follow a remarkably ideal-gas-like pressure equation:
π = i × M × R × T
Where:
- π: osmotic pressure (atm)
- i: van ’t Hoff factor (dimensionless, number of particles a solute dissociates into)
- M: molar concentration (mol/L)
- R: ideal gas constant = 0.08206 L·atm/(mol·K)
- T: absolute temperature (Kelvin = °C + 273.15)
The equation looks identical in form to PV = nRT — and that’s not a coincidence. Dissolved particles in a dilute solution behave statistically like gas molecules in a container, exerting pressure on a semipermeable membrane the same way gas molecules exert pressure on a container wall.
The van ’t Hoff factor (i) — dissociation matters
The osmotic pressure depends on the total number of dissolved particles, not the formula units of solute. Most ionic compounds dissociate fully in water:
| Solute | Dissociation | i (theoretical) | i (actual, ~0.1 M) |
|---|---|---|---|
| Glucose, sucrose, urea | None (covalent) | 1 | 1.00 |
| Acetic acid (weak) | ~1% | 1.01 | 1.01 |
| NaCl | Na⁺ + Cl⁻ | 2 | 1.85-1.93 |
| KCl | K⁺ + Cl⁻ | 2 | 1.85-1.93 |
| HCl, NaOH | Full | 2 | ~1.95 |
| MgSO₄ | Mg²⁺ + SO₄²⁻ | 2 | 1.3-1.5 (significant ion pairing) |
| CaCl₂ | Ca²⁺ + 2 Cl⁻ | 3 | 2.6-2.8 |
| Na₂SO₄ | 2 Na⁺ + SO₄²⁻ | 3 | 2.4-2.6 |
| K₃PO₄ | 3 K⁺ + PO₄³⁻ | 4 | ~3.2 |
| Al₂(SO₄)₃ | 2 Al³⁺ + 3 SO₄²⁻ | 5 | ~3.0 (heavy ion pairing) |
Real i values are slightly lower than theoretical because some ions form transient pairs in solution rather than acting fully independent. The deviation grows with charge product and concentration — divalent + divalent ions (Mg²⁺ + SO₄²⁻) pair more than monovalent + monovalent (Na⁺ + Cl⁻).
Osmolarity vs molarity
Osmolarity is the molar concentration of particles, not of the original solute:
osmolarity = i × M
A 0.15 M NaCl solution has 0.30 osmol/L (i = 2). A 0.30 M glucose solution also has 0.30 osmol/L (i = 1). For osmotic effects, they’re equivalent — same number of particles per liter.
This is why “0.9% saline” (0.154 M NaCl) and “5% dextrose” (0.278 M glucose) are both isotonic to blood despite very different molar concentrations.
Biological reference values
| Fluid | Osmolarity | Osmotic pressure (37°C) |
|---|---|---|
| Human blood plasma | 0.290 osmol/L | 7.4 atm |
| Cytoplasm (most cells) | 0.290 osmol/L | 7.4 atm (isotonic with plasma) |
| Tears | 0.290-0.310 osmol/L | 7.4-7.9 atm |
| Saliva | 0.050-0.100 osmol/L | 1.3-2.5 atm |
| Urine (normal) | 0.300-0.900 osmol/L | 7.6-22.8 atm |
| Maximum concentrated urine | 1.200 osmol/L | 30 atm |
| Seawater | 0.900-1.100 osmol/L | 22-28 atm |
| Sap in xylem | 0.020-0.100 osmol/L | 0.5-2.5 atm |
| Soil solution (typical) | 0.001-0.020 osmol/L | 0.025-0.5 atm |
| Saturated NaCl (~6 M) | 11.4 osmol/L | ~280 atm |
Isotonic, hypotonic, hypertonic — what cells experience
Cells without rigid walls (animal cells, protozoa) lyse or shrivel based on the surrounding solution:
| Surrounding solution | Effect on RBC |
|---|---|
| Hypotonic (< 0.29 osmol/L) | Water flows in; cell swells; lyses if extreme |
| Isotonic (0.29 osmol/L) | No net water movement; normal shape |
| Hypertonic (> 0.29 osmol/L) | Water flows out; cell shrinks (crenation) |
A red blood cell in pure water swells and bursts within seconds. A red blood cell in 1.0 M NaCl shrivels and dies. This is why IV fluids must be carefully formulated — never inject pure water or concentrated solutions into a vein.
Plant cells handle it differently
Plant cells have rigid cell walls that prevent bursting. In hypotonic solutions, water enters until the cell wall pushes back (turgor pressure), giving plants their stiff structure. In hypertonic solutions, the cell membrane pulls away from the wall (plasmolysis) — the wilting you see in a dry plant or one in salty soil.
This turgor mechanism is why a freshly cut flower revives in fresh water and wilts in seawater. The osmotic pressure literally drives the structural state of the plant.
Reverse osmosis — beating thermodynamics
To force water from saltwater into freshwater (against the concentration gradient), you must apply mechanical pressure exceeding the osmotic pressure:
- Seawater (≈0.9 osmol/L): osmotic π ≈ 25-28 atm at 25°C
- Brackish water (≈0.05-0.1 osmol/L): π ≈ 1.5-3 atm
- Real-world RO desalination pressure: 55-85 atm (high safety margin, plus membrane losses)
- Brackish RO: 6-15 atm
This is why desalination is energy-expensive: you’re physically pushing water uphill against a 25+ atm pressure gradient. The theoretical minimum energy to desalinate seawater is about 0.78 kWh/m³; real plants use 3-6 kWh/m³.
Worked example — IV fluid
Standard 0.9% saline (isotonic) at 37°C:
- 0.9% w/v NaCl = 9 g/L ÷ 58.44 g/mol = 0.154 M
- i ≈ 1.85 (slight ion pairing at this concentration)
- T = 310 K (37°C body temp)
- π = 1.85 × 0.154 × 0.08206 × 310 = 7.25 atm
Which matches plasma’s ~7.4 atm closely enough that red blood cells are safe in this solution. Saline is calibrated for exactly this reason.
The kidney’s countercurrent multiplier
Mammalian kidneys can concentrate urine 4x more than blood plasma (up to ~1,200 mOsm/L vs 290 mOsm/L). This requires an osmotic pressure of ~30 atm in the medulla — generated by a countercurrent multiplier in the loop of Henle. It’s one of the most osmotically extreme environments in physiology.
Bottom line
Osmotic pressure follows van ’t Hoff’s elegant equation π = iMRT. The van ’t Hoff factor i accounts for ionic dissociation — 1 for sugars, 2 for NaCl, etc. Biology lives in narrow osmotic ranges; deviations cause cells to swell or shrivel. The pressures involved are surprisingly large — 7 atm in blood, 25+ atm in seawater — which is why desalination is energy-intensive and why salt-tolerant plants need specialized adaptations.