Osmotic pressure is the pressure applied by a solution to prevent the inward flow of water across a semipermeable membrane.
The phenomenon of osmotic pressure arises from the tendency 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 selective towards many of the solutes found in living organisms.
In order to visualize this effect, imagine a U shaped clear tube with equal amounts of water on each side, separated by a membrane at its base that is impermeable to the sugar molecules (made from dialysis tubing). Sugar has been added to the water on one side. The height of the water on each side will change proportional to the pressure of the solutions.
Osmotic pressure causes the height of the water in the compartment containing the sugar to rise, due to movement of the pure water from its compartment into the compartment containing the sugar water. This process will stop once the pressures of the water and sugar water toward both sides of the membrane are equated. (See Osmosis).
Jacobus Henricus van 't Hoff first proposed a formula for calculating the osmotic pressure, but this was later improved upon by Harmon Northrop Morse.
Osmotic potential is the opposite of water potential, which is the degree to which a solvent tends to stay in a liquid.
Consider the system at the point it has reached equilibrium. The condition for this is that the chemical potential of the solvent (since only it is free to flow towards equilibrium) on both sides of the membrane is equal. The compartment containing the pure solvent has a chemical potential of μ0(l,p). On the other side, the compartment containing the solute has an additional contribution from the solute (factored as the mole fraction of the solute, χs < 1) but there also appears an addition in pressure. The balance is therefore:
where the presence of the solute decreases the potential due to χs being smaller than 1.
where p denotes the external pressure, l the solvent, χs the mole fraction of the solvent and Π the osmotic pressure exerted by the solutes. The addition of solute decreases the chemical potential (an entropic effect), while the pressure increases the chemical potential, and thus a balance is reached.
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