Problem
A simcell with a water permeable membrane separates two compartments:
- Inside (simcell): 0.30 M sucrose
- Outside solution: 0.10 M sucrose
The membrane is permeable to water but not to sucrose. Determine (1) the direction of net water movement and (2) which side is hypertonic relative to the other.
Key biological idea
With a semipermeable (water-permeable) membrane, net osmosis moves water from the side with lower effective solute concentration (lower osmolarity; hypotonic) toward the side with higher effective solute concentration (higher osmolarity; hypertonic), until the driving force is balanced.
Step-by-step solution
Step 1: Identify what can cross the membrane
Water can cross the membrane; sucrose cannot. Therefore, sucrose stays on its original side, and water is the component that redistributes.
Step 2: Convert molarity to osmolarity (effective solute concentration)
For a non-electrolyte like sucrose, the van’t Hoff factor is \(i \approx 1\), so:
Inside: \(i \cdot M = 1 \cdot 0.30 = 0.30\ \text{Osm}\)
Outside: \(i \cdot M = 1 \cdot 0.10 = 0.10\ \text{Osm}\)
Step 3: Assign tonicity (relative comparison)
The inside has the higher osmolarity (0.30 Osm). Therefore:
- Inside is hypertonic relative to outside.
- Outside is hypotonic relative to inside.
Step 4: Predict the direction of net water movement
Water moves from the hypotonic side (lower osmolarity) to the hypertonic side (higher osmolarity). Hence, net water movement is from outside to inside. In a physical simcell (for example, a dialysis tubing “cell”), the inside compartment typically gains water and increases in volume/mass.
Summary table
| Compartment | Solute | Molarity (M) | van’t Hoff factor \(i\) | Osmolarity \(i \cdot M\) (Osm) | Tonicity (relative) |
|---|---|---|---|---|---|
| Inside (simcell) | Sucrose | 0.30 | 1 | 0.30 | Hypertonic (relative to outside) |
| Outside solution | Sucrose | 0.10 | 1 | 0.10 | Hypotonic (relative to inside) |
Visualization
Direct answers
- Direction of net water movement: from the 0.10 M sucrose side (outside) to the 0.30 M sucrose side (inside).
- Hypertonic side: the inside (0.30 M sucrose) is hypertonic relative to the outside.
Common checkpoints
- Tonicity is relative: “hypertonic” must be stated relative to the other compartment.
- Only nonpenetrating solutes matter: if sucrose could cross, tonicity would need to be re-evaluated; here sucrose is nonpenetrating by assumption.
- Equilibrium idea: even when net flow becomes zero, water molecules still move both directions; the rates balance.