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. Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it was not separated from its pure solvent by a semipermeable membrane. It is the difference between hydrostatic pressures of the solution and the pure solvent.

Osmosis occurs when two solutions containing different concentrations of solute are separated by a selectively permeable membrane. Solvent molecules pass preferentially through the membrane from the low-concentration solution to the solution with higher solute concentration. The transfer of solvent molecules continues until osmotic equilibrium is attained.

Theory and measurement

Jacobus van 't Hoff derived thermodynamically a quantitative relationship between osmotic pressure and solute concentration, expressed in the following equation, where

x

w

{\displaystyle x_{w}}

is the water activity:

Π

=

−

(

R

T

/

V

m

)

ln

⁡

(

x

w

)

.

{\displaystyle \Pi =-(RT/V_{m})\ln(x_{w}).}

For ideal solutions of low concentration, we can approximate this equation as

Π

=

i

c

R

T

{\displaystyle \Pi =icRT}

where

Π

{\displaystyle \Pi }

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). This formula 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.