Osmosis and Osmotic Pressure

Osmosis is the spontaneous net flow of solvent molecules through a semipermeable membrane (SPM) from the region of lower solute concentration to the region of higher solute concentration.

A semipermeable membrane allows solvent molecules to pass through but blocks solute molecules/ions. Examples: cellophane, pig bladder, biological cell membranes.

Osmotic pressure ($\pi$) is the external pressure that must be applied to the solution side to just stop net osmotic flow.

For dilute solutions:
$\pi = MRT$

where:

• $\pi$ = osmotic pressure (in Pa or bar)
• $M$ = molarity of the solution (mol/L) — note: osmotic pressure uses molarity, not molality
• $R$ = gas constant = 0.0831 L·bar/(mol·K)
• $T$ = temperature in Kelvin

This equation is analogous to the ideal gas law ($pV = nRT$), with $M = n/V$.

Concentration types relative to the cell:

• Isotonic ($\pi_{\text{solution}} = \pi_{\text{cell}}$) → no net osmotic flow → cells maintain shape
• Hypotonic ($\pi_{\text{solution}} < \pi_{\text{cell}}$) → water enters cell → cell swells/bursts
• Hypertonic ($\pi_{\text{solution}} > \pi_{\text{cell}}$) → water leaves cell → cell shrinks (crenation)