Osmosis and Osmotic Pressure

A semipermeable membrane is a barrier — natural (a cell membrane, an animal bladder) or artificial (a parchment or cellophane film) — with pores fine enough to let small solvent molecules pass freely through, while completely blocking the passage of larger solute particles. When such a membrane separates a solution from its pure solvent, solvent molecules cross the membrane in both directions, but they cross from the pure-solvent side into the solution side at a higher rate than in the reverse direction — because on the solution side, part of the membrane's surface area adjacent to the solution is effectively "shielded" by solute particles that cannot themselves cross, so proportionally fewer solvent molecules strike the membrane from the solution side per unit time. This produces a net, spontaneous flow of solvent from the pure-solvent side into the solution side, called osmosis.

Osmosis continues, and the solution side visibly rises in level (see Figure 1), until the flow is stopped by applying just enough extra mechanical pressure to the solution side to exactly balance the tendency of solvent to flow in. This exact pressure — the minimum external pressure that must be applied to the solution to prevent any net inflow of solvent from the pure solvent across the membrane — is defined as the osmotic pressure, $\pi$, of the solution.

For a dilute solution, the osmotic pressure obeys an equation with exactly the same mathematical form as the ideal gas equation, discovered empirically by van't Hoff:

where $n_2$ is the number of moles of solute, $V$ is the volume of the solution in litres, $C = n_2/V$ is the molar concentration of the solute, $R$ is the gas constant ($0.0821\ \text{L atm mol}^{-1}\text{K}^{-1}$ when $\pi$ is in atm), and $T$ is the absolute temperature. Rearranged for the solute's molar mass, using $n_2 = w_2/M_2$, this gives the widely-used relation $M_2 = w_2 RT / (\pi V)$.

Two solutions with equal osmotic pressure at the same temperature are said to be isotonic; a solution of lower osmotic pressure than a reference solution is hypotonic, and one of higher osmotic pressure is hypertonic. This matters directly in physiology: red blood cells placed in a strongly hypotonic solution swell and can burst (haemolysis) as water flows in, while cells placed in a strongly hypertonic solution shrink (crenation) as water flows out — which is exactly why intravenous fluids must be formulated isotonic with blood plasma. Applying a pressure greater than the natural osmotic pressure to the solution side instead reverses the natural direction of solvent flow, forcing solvent from the solution back across the membrane into the "pure" side while the membrane continues to reject solute — this is reverse osmosis, the principle behind modern desalination plants and household water purifiers. …