Osmosis and Osmotic Pressure

Osmosis is a spontaneous process central to many biological systems: solvent molecules pass through a semipermeable membrane, moving from a solution of lower solute concentration into a solution of higher solute concentration. The name comes from the Greek word osmos, meaning "to push." A semipermeable membrane selectively allows only certain molecules to pass through it while blocking others.

The classic apparatus (Figure 9.13). A semipermeable membrane divides a chamber into two compartments. Pure water is placed in one compartment and aqueous NaCl solution in the other, with both liquid levels initially equal. Because the two sides differ in concentration, water molecules move from the pure-water side into the NaCl-solution side through the membrane (the membrane passes water in either direction but blocks NaCl entirely). This net inward flow of water into the salt-solution side increases its volume, which dilutes it (lowering its concentration) and simultaneously builds up a pressure difference between the two compartments. That growing pressure difference eventually pushes some water molecules back toward the pure-solvent side, until the rates of movement in both directions become exactly equal -- an equilibrium. The pressure difference at this equilibrium is called the osmotic pressure ($\pi$), which can equivalently be defined as: "the pressure that must be applied to the solution side to just stop the net inward flow of solvent (to stop osmosis) through the semipermeable membrane."

The van't Hoff equation. Van't Hoff found that, for dilute solutions, osmotic pressure is directly proportional to both the solute's molar concentration and the absolute temperature:

where $c$ is the concentration in molarity, $T$ is the absolute temperature, and $R$ is the gas constant. This has exactly the same mathematical form as the ideal gas equation, and is called the van't Hoff equation for dilute solutions.

Determining molar mass from osmotic pressure. Since $c=n/V$, equation 9.31 can be rewritten $\pi=\dfrac{nRT}{V}$, i.e.

For $w_B$ g of nonvolatile solute (molar mass $M_B$) dissolved to give a solution of volume $V$, $n=w_B/M_B$; substituting into 9.32 and rearranging,

so the molar mass can be found once the osmotic pressure of a solution of known mass and volume has been measured.

Worked example (Example Problem 6). At 400 K, 1.5 g of an unknown substance is dissolved and the solution made up to 1.5 L; its osmotic pressure is 0.3 bar. Using $R=8.314\times10^{-2}$ L bar mol$^{-1}$ K$^{-1}$:

Why osmotic pressure is favoured over the other three colligative properties. Its magnitude is comparatively large, even for very dilute solutions -- compare this against boiling-point elevation and freezing-point depression, where even a full 1-molal aqueous solution only elevates the boiling point by 0.512$^\circ$C and depresses the freezing point by 1.86$^\circ$C. Because osmotic pressure can be measured conveniently at room temperature, it is especially valuable for determining the molar mass of biomolecules that would denature or degrade at the higher temperatures a boiling-point measurement would need. …