is called the osmotic pressure.
The movement of a solute molecule within a solvent is over damped by the solvent molecules
that surround it. In fact, the solute movement is wholly determined by fluctuations of thermal
collisions with nearby solvent molecules. However, the average thermal velocity of the molecule
is the same had it been free in a gas phase
Whenever a solute movement is blocked by a wall it will transfer momentum to it and, therefore,
generate pressure on it. Since the velocity is the same as that of a free molecule, the pressure
will be the same as the pressure of an ideal gas of the same molecular concentration. Hence, the
osmotic pressure ?, is given by formula
? = cRT
where c is the molar solute concentration, R is the gas constant, and T is the absolute
temperature. This formula is the same as the pressure formula of an ideal gas.
Figure-1 shows connected vessels separated by a semi permeable membrane. If there is only
water in the device, the level will be the same at both sides. When solute molecules are added
to one side, water will start to flow into it, so that its level will go up at this side, and down at the
other side. The system will stabilize when the osmotic pressure is balanced by the hydrostatic
pressure generated by the difference in the water levels.
cRT = ?h
where ? is the water specific gravity.
The conservation laws of energy and momentum require that whenever particles collide with a
moving wall, they will change direction and increase or decrease their speed. Thus, they transfer
both momentum and energy to the wall. Therefore, the process of elastic collisions with a
moving wall is the mechanism by which the microscopic kinetic energy of the particles is
transformed into macroscopic mechanical work
The solute molecules generate osmotic pressure on all the solution boundaries, including the
membrane. But when water flows between the two sides it is the pressure on the moving free
surface of the solution which is pushing it upward, and thus is responsible for water pumping
from the other side.
This discussion of the flow mechanism usually does not appear in textbooks that deal with
osmosis. The effect of the osmotic pressure on the free surface of the solution was first
suggested by Hulett in 1902 but received little attention. It seems to have only few proponents
since then.
Osmosis is a reversible thermodynamic process. That is, the direction of water flow through the
membrane can be reversed at any moment by proper control of the external pressure on the
solution. Contrary to that, mixing a teaspoon full of sugar in a cup of tea is an irreversible
thermodynamic process. There is no way to reverse the process at any given moment and un-
mix the sugar back to the spoon.
Reversibility is a most important idea of thermodynamics. Osmosis is reversible, while disolving
sugar in water, essentially diffusion, is irreversible.
References:
F.W. Sears and G.L. Salinger, "Thermodynamics, Kinetic Theory and statistical
Thermodynamics", 3rd Ed., 16th printing, Addison Wesley, Reading Massachusetts
(1986) pp. 250-266
A. Einstein, "Investigations on the Theory of the Brownian Movement", Dover Publications,
Inc., New York (1956) pp. 1-18
E. Fermi, "Thermodynamics", Dover Publications, Inc., New York (1937) pp. 118-123
J.H. van't Hoff, "The Role of Osmotic Pressure in the Analogy between Solutions and Gases",
Zeitschrift fur physikalische Chemie, vol 1, pp. 481-508 (1887)