An artificial membrane separates two sides of a beaker
An artificial membrane that separates two sides of a beaker models selective permeability: some particles cross the barrier readily, while others do not. When the membrane is permeable to water but impermeable to a dissolved solute such as sucrose, the dominant transport process becomes osmosis, and solution tonicity predicts the direction of net water movement.
Net osmosis reflects a competition between chemical potential (concentration) and pressure. Water moves toward the side with higher effective solute concentration until pressure differences counterbalance the osmotic tendency.
Assumed membrane properties and solutions
A clear quantitative prediction requires explicit permeability assumptions. The standard laboratory model (dialysis tubing) is represented by a membrane that is permeable to water but effectively impermeable to sucrose over the observation time.
- Water (solvent) permeability: present
- Sucrose (solute) permeability: absent
- Side A: 0.30 mol/L sucrose
- Side B: 0.10 mol/L sucrose
- Temperature: 25 °C (298 K)
Tonicity language for the two sides
With sucrose treated as a non-electrolyte (no dissociation), osmolarity is numerically equal to molarity. Side A therefore has higher osmolarity than Side B.
| Side | Solute | Molarity (mol/L) | Approx. osmolarity (Osm/L) | Relative tonicity (water-permeable membrane) |
|---|---|---|---|---|
| Side A | Sucrose | 0.30 | 0.30 | Hypertonic relative to Side B |
| Side B | Sucrose | 0.10 | 0.10 | Hypotonic relative to Side A |
Net water movement proceeds from the hypotonic side to the hypertonic side. Under the stated conditions, water moves from Side B → Side A, and Side A’s liquid level tends to rise relative to Side B.
Quantitative osmotic pressure estimate
The initial osmotic pressure of a dilute solution is commonly estimated by the van’t Hoff relation:
For sucrose, \(i \approx 1\). Using \(R = 0.082057\ \text{L·atm·mol}^{-1}\text{·K}^{-1}\) and \(T = 298\ \text{K}\):
The value above represents the initial pressure difference that would counterbalance osmosis at equilibrium in an idealized setup. Real systems show deviations from ideality and may include additional solutes that contribute to osmolarity.
Pressure balance and the stopping condition
As water enters Side A, hydrostatic pressure on that side increases (often visible as a height difference, \(\Delta h\)). Net osmosis approaches zero when the pressure difference across the membrane balances the osmotic pressure difference:
In a gravitational field, a height difference in connected columns is associated with \(\Delta P = \rho g \Delta h\). The observed \(\Delta h\) therefore serves as an experimental readout of the osmotic tendency, provided density \(\rho\) and geometry are controlled.
Selective-permeability scenarios
The phrase “an artificial membrane separates two sides of a beaker” can describe different experiments depending on which molecules cross the barrier.
- Water-permeable, sucrose-impermeable membranes: sustained osmosis and a pressure/height difference; sucrose remains largely confined to its starting side.
- Water- and sucrose-permeable membranes: diffusion of sucrose reduces the concentration gradient; net water movement diminishes as the two sides approach equal composition.
- Size-selective membranes (small solutes cross): tonicity depends on the “nonpenetrating” solute fraction; permeant solutes contribute less to sustained osmotic gradients.
Common pitfalls
- Molarity vs osmolarity: electrolytes require a dissociation factor \(i\); non-electrolytes such as sucrose typically use \(i \approx 1\) in introductory estimates.
- Tonicity vs concentration: tonicity depends on membrane permeability; the “effective” osmotic gradient is set by solutes that do not cross the membrane on the experimental time scale.
- Equilibrium interpretation: equal water levels are not required for osmotic equilibrium; a pressure difference can hold a concentration difference in balance.