If a vessel so prepared be filled with a solution of sugar, and be then placed in water, the water is found to pass through the membrane, but the membrane is impermeable to the sugar. In consequence pressure, termed _osmotic pressure_, is found to occur within the pot, and may be measured by suitable means. These osmotic pressures may at times be very large: thus a 1 per cent. solution of sugar may exert a pressure of half an atmosphere, and in the case of a solution of potassium nitrate of the same concentration it may amount to a couple of atmospheres.
Pfeffer determined the relation of the osmotic pressures to the concentration of solutions of these substances, measuring the pressures in centimetres of mercury by a manometer attached to the closed porous vessel. His results in the case of sugar were as follows:
_Percentage _Pressure in cm. strength (C)._ of mercury (P)._ _P/C._
1 53.5 53.5 2 101.6 50.8 4 208.2 52.1 6 307.5 51.3
It will be seen from these numbers that the ratio P/C is practically constant—that is, _the osmotic pressure varies directly as the concentration_. It was further found that the osmotic pressure exerted by a solution of uniform strength increases with the temperature.
The importance, of these observations in relation to the general theory of solution was first recognised by Van ’t Hoff. Osmotic pressure was regarded by him as analogous to gaseous pressure. Since P/C is constant for any one substance, and since for a definite weight of the solute the concentration is inversely as the volume of the solution, we obtain an equation analogous to the statement of Boyle’s law, PV = constant. Van ’t Hoff also found that the _osmotic pressure is proportional to the absolute temperature_, like the gaseous pressure. From these results, in conjunction with Avogadro’s hypothesis, it follows that _the osmotic pressure exerted by any substance in solution is the same as it would exert if present as gas in the same volume as that occupied by the solution, provided that the solution is so dilute that the volume occupied by the solute is negligible in comparison with that occupied by the solvent_. Another important consequence is that _solutes, when present in the ratio of their molecular weights in equal volumes of the same solvent, exert the same osmotic pressure_. Such solutions are said to be _isomotic_ or _isotonic_. It can be proved by thermodynamical reasoning that depression of the vapour pressure and freezing-point of a solution is proportional to its osmotic pressure. The significance of this relation in connection with the determination of the molecular weight of a soluble substance has already been referred to.[6]
