§ C-14 Osmotic Pressure (van ’t Hoff’s Law Π = iCRT) & Semipermeable Membrane (Grade 9–11 · Osmotic Pressure)
Selective solvent diffusion across a semipermeable membrane in a U-tube osmometer, van ’t Hoff factor i, and reverse osmosis desalination. The osmotic pressure of a dilute solution equals the pressure the solute would exert if it existed as an ideal gas in the same volume at the same temperature.
Theory Summary & Scientific Mechanism
Osmosis is the spontaneous net movement of solvent molecules (H₂O) across a semipermeable membrane from a region of lower solute concentration into a region of higher solute concentration. The membrane’s micropores pass small water molecules while blocking larger hydrated solute ions.
The hydrostatic pressure required to halt the net osmotic influx is the osmotic pressure Π, governed by van ’t Hoff’s law: Π = i C R T, where C is molarity and i = 1 + α(k - 1) is the van ’t Hoff factor accounting for electrolyte dissociation (i = 1 for glucose, i ≈ 2 for NaCl, i ≈ 3 for CaCl₂).
When an external pressure exceeding the osmotic pressure is applied to the solution side (Pₑxt > Π), water is forced backward out of the concentrated brine into the pure water chamber, the principle of reverse osmosis (RO) used worldwide for seawater desalination.
Everyday Analogy
Sprinkling salt on cucumbers draws water out across cell membranes toward higher ion concentration (osmosis). Pushing back on saltwater with pressure Pₑxt > Π forces pure water out, reverse osmosis filtration!
Interactive Question & Derivation
Why does a 0.1 mol/L NaCl solution exert nearly twice the osmotic pressure Π of a 0.1 mol/L glucose (C₆H₁₂O₆) solution at the same temperature T?
- A: Osmotic pressure is a colligative property (Π = iCRT): strong electrolyte NaCl dissociates into 2 ions (Na⁺ and Cl⁻, van ’t Hoff factor i ≈ 2), doubling total particle concentration
- B: Because the molar mass of NaCl is twice the molar mass of glucose
- C: Because Na⁺ and Cl⁻ pass freely through the semipermeable membrane while glucose is blocked
Study Hint: Osmotic pressure Π = iCRT scales with total particle concentration: NaCl dissociates into 2 ions (i ≈ 2), generating twice the osmotic pressure of non-electrolyte glucose (i = 1).
Proof & Explanation: Osmotic pressure depends on the total concentration of kinetically independent solute particles (colligative property). Non-electrolyte glucose does not dissociate (i = 1), whereas strong electrolyte NaCl dissociates into two ions (Na⁺ and Cl⁻, i ≈ 2), doubling its effective osmolarity iC and osmotic pressure Π = iCRT.
Key Equations & 3D Simulation Parameters
Π = i C R T, Δ h ∝ Π - Pₑxt
- Solute molar concentration C (right arm): 0.05 … 0.5 mol/L (default: 0.2 mol/L)
- van ’t Hoff factor i (1=glucose, 2=NaCl, 3=CaCl₂): 1 … 3 (default: 2)
- Absolute solution temperature T: 273 … 353 K (default: 298 K)
- External piston pressure Pₑxt (reverse osmosis if P > Π): 0 … 30 atm (default: 0 atm)