Osmotic pressure

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in water by osmosis. Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were separated from distilled water by a selectively permeable membrane. The phenomenon of osmosis arises from the propensity of a pure solvent to move through a semi-permeable membrane and into a solution containing a solute to which the membrane is impermeable. This process is of vital importance in biology as the cell's membrane is semipermeable.

In order to visualize this effect, imagine a U-shaped tube with equal amounts of water on each side, separated by a water-permeable membrane made from dialysis tubing at its base that is impermeable to sugar molecules. Sugar has been added to the water on one side. The height of the liquid column on that side will then rise (and that on the other side will drop) proportional to the pressure of the two solutions due to movement of the pure water from the compartment without sugar into the compartment containing the sugar water. This process will stop once the pressures of the water and sugar water on both sides of the membrane become equal.

Jacobus van 't Hoff first proposed a "law" relating osmotic pressure to solute concentration

where ${\displaystyle \Pi }$ is osmotic pressure, [C_solutes] is the molar concentration, equal to the number of moles of solute in the solution divided by the solution volume, the total molar concentration of all solutes that cannot pass through a water-permeable membrane. T is the temperature in kelvins. This formula states that osmotic pressure is simply proportional to the solute concentration. It applies when the solute concentration is sufficiently low that the solution can be treated as an ideal solution. The proportionality to concentration means that osmotic pressure is a colligative property. Note the similarity of this formula to the ideal gas law in the form${\displaystyle P={n \over V}RT=[C_{\text{gas}}]RT}$ where n is the total number of moles of gas molecules in the volume V, and n/V is the molar concentration of gas molecules.

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