Osmotic Pressure
Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane separating the solution from the solvent. It arises because solvent molecules move spontaneously from a region of lower solute concentration (higher solvent chemical potential) to higher concentration by osmosis. Osmotic pressure is critical in biological systems — it maintains cell turgor, governs kidney function, and is the basis of reverse osmosis water purification.
Key Formula
π = i × M × R × T
LaTeX: \pi = i M R T
| Symbol | Meaning | Unit |
|---|---|---|
| π | Osmotic pressure | atm or Pa |
| i | van't Hoff factor | dimensionless |
| M | Molar concentration of solute | mol/L |
| R | Ideal gas constant (0.08206 L·atm/mol·K) | L·atm/mol·K |
| T | Absolute temperature | K |
Worked Example
Problem
A solution contains 5.85 g of NaCl (M = 58.5 g/mol) in 1.00 L at 25 °C. Calculate its osmotic pressure. (NaCl fully dissociates, i = 2; R = 0.08206 L·atm/mol·K)
Solution
Step 1 – Moles of NaCl = 5.85 ÷ 58.5 = 0.100 mol. Step 2 – Molarity M = 0.100 mol ÷ 1.00 L = 0.100 mol/L. Step 3 – T = 25 + 273.15 = 298.15 K. Step 4 – π = 2 × 0.100 × 0.08206 × 298.15 = 4.89 atm.
Answer
Osmotic pressure = 4.89 atm
Osmotic Pressure of Biological and Common Solutions at 37 °C
| Solution | Concentration (mol/L) | i | Osmotic Pressure (atm) |
|---|---|---|---|
| Blood plasma | 0.308 (isotonic) | 1 | ~7.7 |
| 0.9% NaCl (saline) | 0.154 | 2 | ~7.7 |
| Seawater | ~0.5 | 2 | ~27 |
| 1 M glucose | 1.0 | 1 | ~25.4 |
| 0.1 M sucrose | 0.1 | 1 | ~2.54 |
Interactive Tools
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Related Terms
Colligative Properties
Colligative properties are physical properties of solutions that depend only on the number of solute particles dissolved, not on the chemical identity of those particles. These properties include boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. They are widely used in industries such as food preservation, antifreeze formulation, and clinical medicine to control solution behaviour.
Raoult's Law
Raoult's Law states that the partial vapour pressure of each volatile component in an ideal solution is equal to the vapour pressure of the pure component multiplied by its mole fraction in the solution. This law quantifies vapour pressure lowering as a colligative property and is the foundation for understanding distillation and solution thermodynamics. Solutions that obey Raoult's Law perfectly (ideal solutions) have similar intermolecular forces between all components; deviations occur in real solutions due to unlike-molecule interactions.
Freezing Point Depression
Freezing point depression is the decrease in the freezing (solidification) point of a solvent caused by dissolving a solute, because the solute particles disrupt the formation of the ordered solid lattice. The magnitude of depression depends on the number of solute particles per unit mass of solvent, not their chemical nature. Practical applications include road de-icing with salt, antifreeze in vehicle radiators, and the preservation of biological samples in cryoprotective solutions.
From Greek "osmos" (a push or impulse), derived from "othein" (to push). The term was introduced by the Dutch botanist Hugo de Vries in the 1870s; van't Hoff provided the mathematical equation in 1886.