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Answer :
Final Answer
At equilibrium, there will be no net movement of water or ions across the membrane, resulting in equal concentrations of water and sodium chloride on both sides of the membrane.
Explanation
When water is added to one side of the membrane (side A) and a 5% solution of sodium chloride (NaCl) is added to the other side (side B), water molecules will diffuse through the membrane due to its full permeability to water and small ions.
As water molecules move from side A to side B, they will dilute the concentration of the sodium chloride solution on side B. Similarly, some sodium and chloride ions will move from the solution on side B to the water on side A due to the tendency to equalize concentrations.
As this process continues, the concentration of water molecules on side B will increase while the concentration of sodium chloride on side B will decrease. Simultaneously, the concentration of water molecules on side A will decrease while the concentration of sodium chloride will increase due to the movement of ions.
This will continue until the concentration gradient of water and ions reaches a point where the movement of water molecules and ions becomes equal and opposite, resulting in no net change in concentrations on either side of the membrane.
In mathematical terms, the equilibrium is reached when the chemical potential (μ) of water and ions on both sides of the membrane is the same.
The equation for chemical potential is μ = RTln(C), where R is the gas constant, T is the temperature, and C is the concentration. At equilibrium, μ_water(A) = μ_water(B) and μ_NaCl(A) = μ_NaCl(B), resulting in equal concentrations of water and sodium chloride on both sides.
In conclusion, the equilibrium state will involve equal concentrations of water and sodium chloride on both sides of the membrane due to the continuous movement of water molecules and ions until their chemical potentials are balanced.
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