Osmosis

How the model works

Water molecules cross a semi-permeable membrane in both directions, but more cross from the side where water is more abundant, the dilute side. The net flow is towards the higher solute concentration.

In the U-tube, the water level rises on the concentrated side until the extra hydrostatic pressure balances the osmotic pressure difference. The van 't Hoff relation gives the osmotic pressure:

Π = i C R T

where i is the number of particles per formula unit (1 for sucrose, about 2 for NaCl), C the molar concentration and T the temperature in kelvin. The flow rate is proportional to the membrane permeability times the net pressure difference, Π_right − Π_left − ρ g Δh. As the solution on the rising side dilutes, the simulator updates concentrations to conserve solute.

Cells: in a hypotonic solution, a red blood cell swells; in a hypertonic one it shrinks (crenates); in an isotonic one (about 0.3 osmol/L) it keeps its shape.

Ideal dilute solutions, a perfectly semi-permeable membrane, and a narrow tube with a 1 cm² cross-section. Real tubes would need metres of height to balance even 0.1 M sucrose, so the display height is scaled.

Guided experiments

1. Water follows solute. Pure water on the left, 0.1 M sucrose on the right. Prediction: the right column rises. At equilibrium, Π = 0.1 × 8.314 × 298 ≈ 248 kPa (if fully balanced by height, about 25 m of water). Water vs sucrose
2. Salt counts double. 0.1 M NaCl instead of sucrose. Prediction: about twice the osmotic pressure (i ≈ 2), so roughly twice the rise. Water vs NaCl
3. Red blood cell. Put the cell in 0.05, 0.15 and 0.5 M NaCl. Prediction: swells and may burst in 0.05 M, stays normal in 0.15 M (0.3 osmol/L, isotonic), shrivels in 0.5 M. Cell in salt water

Challenge

Why do doctors use 0.9% saline (about 0.154 M NaCl) for intravenous drips, rather than pure water?

References

• OpenStax, Biology 2e, §5.2 “Passive Transport”.
• OpenStax, Chemistry 2e, §11.4 “Colligative Properties”.