## Abstract

Assume two compartments separated by a semipermeable membrane (see Fig. 26.1). One compartment contains pure solvent, which can freely cross the membrane, for example, water. The other compartment contains solvent plus a solute, which is too large to cross the membrane, say, a protein. If both compartments are open to the atmosphere – that is, exposed to the same pressure – then water will pass from the first compartment into the second in an attempt to equalise the chemical potentials on both sides. However, no matter how much water passes from compartment 1 to compartment 2, the protein concentration in the second compartment (and hence its chemical potential) will always be larger than that in the first. To establish an equilibrium, we have to apply an outside force that counteracts the force drawing water into compartment 2. This can be achieved by putting pressure onto compartment 2, which would press water from there into compartment 1. At a certain pressure, the pressure-driven flow of water from 2 → 1 will exactly balance the concentration driven flow from 1 → 2. We call this the osmotic pressure π of solution 2. This pressure is related to the solute concentration by where c is the concentration (in g∕ml), B

$$\Pi = \mathit{RT}\left ( \frac{1} {{M}_{\mathrm{r}}}c + {B}_{2}{c}^{2} + \ldots \,\right ),$$

(26.1)

_{2}the second virial coefficient(higher coefficients are not usually required), R is the universal gas constant, T the absolute temperature, and M_{r}the molecular mass. Thus, in principle, measuring the osmotic pressure of the solution of a macro-molecule with known mass concentration is a simple way to determine the molecular mass M_{r}.## Keywords

Molecular Mass Osmotic Pressure Mass Concentration High Coefficient Virial Coefficient## Copyright information

© Springer Science+Business Media, LLC 2011