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An experiment is conducted in which a selectively permeable membrane separates two sides of a U-tube.

- Side A contains pure water.
- Side B contains an aqueous solution of 0.2 mol of Na\(^+\) and 0.2 mol of Br\(^-\).

The membrane is permeable to water and Na\(^+\) but not to Br\(^-\).

When equilibrium is reached and there is no net movement of water across the selectively permeable membrane, which side will have a lower column of fluid?

Answer :

At equilibrium, Side B will have a lower column of fluid due to the net effect of both water and Na[tex]^+[/tex] movement.

In this experiment, we're dealing with a selectively permeable membrane that separates two sides of a U-tube: Side A containing pure water and Side B containing an aqueous solution with Na[tex]^+[/tex] and Br[tex]^-[/tex] ions.

  1. Membrane Permeability: The membrane allows water and Na[tex]^+[/tex] ions to pass through but not Br[tex]^-[/tex] ions.

  2. Concentration Gradient: Side B has a higher concentration of solute due to the presence of Na[tex]^+[/tex] and Br[tex]^-[/tex] ions compared to Side A, which is pure water.

  3. Movement of Water: Initially, water will tend to move from Side A (pure water) to Side B (higher solute concentration) to try to equalize the concentration on both sides due to osmosis.

  4. Equilibrium: However, because the membrane is permeable to water and Na[tex]^+[/tex], Na[tex]^+[/tex] ions will also move from Side B to Side A. The movement of Na[tex]^+[/tex] to Side A reduces the concentration of solute on Side B.

  5. Final Equilibrium: When equilibrium is reached, the net movement of water stops as the osmotic pressure balance is achieved.

  6. Fluid Level Outcome: Since the water moves initially towards Side B and Na[tex]^+[/tex] moves towards Side A to balance out concentration differences, the fluid column height will increase on Side A as water and Na[tex]^+[/tex] accumulate there.

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Rewritten by : Barada

Side B will have a lower column of fluid; when equilibrium is reached and there is no net movement of water across the selectively permeable membrane.

Initially, water molecules will move from Side A (pure water) to Side B (aqueous solution of Na+ and Br-) through the membrane by osmosis, diluting the solution on Side B.

However, since the membrane is permeable to Na+ ions, they will also move from Side B to Side A, down their concentration gradient.

At equilibrium:

The concentration of water is equal on both sides.

The concentration of Na+ is equal on both sides.

But Br- ions, being impermeable to the membrane, remain only on Side B.

The presence of Br- ions on Side B contributes to the total osmotic pressure, but they cannot cross the membrane to equalize their concentration.

Since Side B still has the impermeable Br- ions, its osmotic pressure remains higher than Side A.

To balance this, the column of fluid on Side B will be lower than Side A due to the difference in osmotic pressure.

This phenomenon is known as Donnan equilibrium or Gibbs-Donnan effect.