Osmotic pressure

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.

[1] It is also defined as the measure of the tendency of a solution to take in its pure solvent by osmosis.

Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were separated from its pure solvent by a semipermeable membrane.

The transfer of solvent molecules will continue until equilibrium is attained.

[1][2] Jacobus van 't Hoff found a quantitative relationship between osmotic pressure and solute concentration, expressed in the following equation: where

is osmotic pressure, i is the dimensionless van 't Hoff index, c is the molar concentration of solute, R is the ideal gas constant, and T is the absolute temperature (usually in kelvins).

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

Harmon Northrop Morse and Frazer showed that the equation applied to more concentrated solutions if the unit of concentration was molal rather than molar;[3] so when the molality is used this equation has been called the Morse equation.

For more concentrated solutions the van 't Hoff equation can be extended as a power series in solute concentration, c. To a first approximation, where

The Pfeffer cell was developed for the measurement of osmotic pressure.

Osmotic pressure measurement may be used for the determination of molecular weights.

Osmotic pressure is an important factor affecting biological cells.

[4] Osmoregulation is the homeostasis mechanism of an organism to reach balance in osmotic pressure.

Turgor pressure allows herbaceous plants to stand upright.

It is also the determining factor for how plants regulate the aperture of their stomata.

Osmotic pressure is the basis of filtering ("reverse osmosis"), a process commonly used in water purification.

The water to be purified is placed in a chamber and put under an amount of pressure greater than the osmotic pressure exerted by the water and the solutes dissolved in it.

Part of the chamber opens to a differentially permeable membrane that lets water molecules through, but not the solute particles.

The osmotic pressure of ocean water is approximately 27 atm.

Reverse osmosis desalinates fresh water from ocean salt water and is applied globally on a very large scale.

The condition for this is that the chemical potential of the solvent (since only it is free to flow toward equilibrium) on both sides of the membrane is equal.

The compartment containing the pure solvent has a chemical potential of

, the balance of the chemical potential is therefore: Here, the difference in pressure of the two compartments

is defined as the osmotic pressure exerted by the solutes.

Holding the pressure, the addition of solute decreases the chemical potential (an entropic effect).

Thus, the pressure of the solution has to be increased in an effort to compensate the loss of the chemical potential.

Inserting the expression presented above into the chemical potential equation for the entire system and rearranging will arrive at: If the liquid is incompressible the molar volume is constant,

Thus, we get The activity coefficient is a function of concentration and temperature, but in the case of dilute mixtures, it is often very close to 1.0, so The mole fraction of solute,

For aqueous solutions of salts, ionisation must be taken into account.