Osmotic Pressure Formula
Calculate the pressure exerted by dissolved solutes across a semipermeable membrane.
Key to biology and medicine.
The Formula
π = iMRT
Osmotic pressure drives water across a semipermeable membrane from low to high solute concentration. It is vital for understanding cell function, kidney filtration, and IV fluid preparation.
Variables
| Symbol | Meaning |
|---|---|
| π | Osmotic pressure (atm) |
| i | Van 't Hoff factor (number of particles per formula unit) |
| M | Molarity of the solution (mol/L) |
| R | Gas constant (0.0821 L⋅atm/mol⋅K) |
| T | Temperature (Kelvin) |
Example 1
Find the osmotic pressure of 0.1 M glucose (non-electrolyte) at 37°C
i = 1 (glucose does not dissociate), T = 310 K
π = 1 × 0.1 × 0.0821 × 310
π ≈ 2.55 atm
Example 2
Find the osmotic pressure of 0.15 M NaCl at 25°C
i = 2 (NaCl → Na⁺ + Cl⁻), T = 298 K
π = 2 × 0.15 × 0.0821 × 298
π ≈ 7.33 atm
When to Use It
Use the osmotic pressure formula when:
- Preparing IV solutions that are isotonic with blood
- Understanding water movement in plant and animal cells
- Designing reverse osmosis water purification systems
- Determining the molecular weight of unknown solutes