Osmotic Pressure (Van't Hoff Equation)
The Van't Hoff equation calculates osmotic pressure from solute concentration and temperature.
Key to biology and chemistry.
The Formula
The Van't Hoff equation calculates the osmotic pressure of a solution. It has a form similar to the ideal gas law (PV = nRT), reflecting the behavior of dissolved particles.
Variables
| Symbol | Meaning |
|---|---|
| π | Osmotic pressure (measured in atmospheres, atm, or Pascals, Pa) |
| i | Van't Hoff factor — number of particles the solute dissociates into (dimensionless) |
| M | Molar concentration of the solute (measured in mol/L) |
| R | Universal gas constant (0.08206 L·atm/mol·K) |
| T | Absolute temperature (measured in Kelvin, K) |
Van't Hoff Factor (i)
| Solute Type | i value | Example |
|---|---|---|
| Non-electrolyte | 1 | Glucose (C₆H₁₂O₆), sucrose, urea |
| Strong electrolyte (1:1) | 2 | NaCl, KBr, HCl |
| Strong electrolyte (1:2 or 2:1) | 3 | CaCl₂, Na₂SO₄ |
| Strong electrolyte (1:3) | 4 | AlCl₃, FeCl₃ |
Example 1
Calculate the osmotic pressure of a 0.30 M glucose solution at 25°C (298 K). Glucose is a non-electrolyte (i = 1).
Apply the formula: π = iMRT = 1 × 0.30 × 0.08206 × 298
π = 7.34 atm
Example 2
What is the osmotic pressure of a 0.10 M NaCl solution at 37°C (310 K)? NaCl dissociates into Na⁺ and Cl⁻ (i = 2).
Apply the formula: π = iMRT = 2 × 0.10 × 0.08206 × 310
π = 5.09 atm
Biological Significance
Osmotic pressure is critical in biology and medicine.
- Isotonic solutions have the same osmotic pressure as blood (~7.7 atm at 37°C). IV fluids must be isotonic to avoid cell damage.
- Hypertonic solutions (higher pressure) cause cells to shrink (crenation) as water flows out.
- Hypotonic solutions (lower pressure) cause cells to swell and potentially burst (lysis) as water flows in.
When to Use It
Use the Van't Hoff equation for osmotic pressure calculations in chemistry and biology.
- Calculating osmotic pressure of solutions for IV fluids and dialysis
- Determining molar mass of proteins and polymers from osmotic pressure measurements
- Understanding water movement across cell membranes
- Reverse osmosis water purification — the applied pressure must exceed the osmotic pressure
- Food preservation — high salt or sugar concentrations create osmotic stress on microorganisms