At the same temperature, but under another pressure P′ the gas will have a different volume V′. Since, according to Boyle's law, PV is constant (P′V′ = PoVo), it will still equal PoVoT / 273. Therefore PoVo / 273 is also constant. This quantity is called "the gaseous constant," and if we represent it by the symbol R, we obtain the general formula PV = RT for all gases, or PV / T = R.
Suppose, for instance, we have a gramme-molecule of a gas at 0° C. in a space of 1 litre. It has a pressure of 22.35 atmospheres at 0° C., or 273° absolute temperature. Since PV = RT, R = PV / T = 1 × 22.35 / 273 = .0819. This number .0819 is the numerical value of the constant R for all gases, volume being measured in litres and pressure in atmospheres.
Substances in solution behave exactly like gases, they follow the same laws and have the same constants. All the conceptions which have been acquired by the study of gases are applicable to solutions, and therefore to the phenomena of life. The osmotic pressure of a solution is the force with which the molecules of the solute, like gaseous molecules, strive to diffuse into space, and press on the limits which confine them, the containing vessel being represented by the surfaces of the solution. Osmotic pressure is measured in exactly the same way as gaseous pressure. To measure steam pressure we insert a manometer in the walls of the boiler. In the same way we may use a manometer to measure osmotic pressure. We attach the tube to the walls of the porous vessel, allow the solvent to increase in volume under the pressure of the solute, and measure the rise of the liquid in the manometer tube.
Pfeffer's Apparatus.—Pfeffer has designed an apparatus for the measurement of osmotic pressure. It consists of a vessel of porous porcelain, the pores of which are filled with a colloidal solution of ferrocyanide of copper. This forms a semi-permeable membrane which permits the passage of water into the vessel, but prevents the passage of sugar or of any
colloid. The stopper which hermetically closes the vessel is pierced for the reception of a mercury manometer. The vessel is filled with a solution of sugar and plunged in a bath of water. The volume of the solution in the interior of the vessel can vary, since water passes easily in either direction through the pores of the vessel. The boundary of the solvent has become extensible, and its volume can increase or diminish in accordance with the osmotic pressure of the solute. Under the pressure of the sugar water is sucked into the vessel like air into a bellows, the solution passes into the tube of the manometer, and raises the column of mercury until its pressure balances the osmotic pressure of the sugar molecules.
Osmotic Pressure follows the Laws of Gaseous Pressure.—This osmotic pressure is in fact gaseous pressure, and may be measured in millimetres of mercury in just the same way. We may thus show that osmotic pressure follows the laws of gaseous pressure as defined by Boyle, Dalton, and Gay-Lussac. The coefficient of pressure variation for change of temperature is the same for a solute as for a gas. The formula PV = RT is applicable to both. The numerical value of the constant R is also the same for a solute as for a gas. being .0819 for one gramme-molecule of either, when the volume is expressed in litres and the pressure in atmospheres. The formula PV = RT shows that for a given mass, with the same volume, the pressure increases in proportion to the absolute temperature.
Osmotic Pressure of Sugar.—A normal solution of sugar, containing 342 grammes of sugar per litre, has a pressure of 22.35 atmospheres, and it may well be asked why such an enormous pressure is not more evident. The reason will be found in the immense frictional resistance to diffusion. Frictional resistance is proportional to the area of the surfaces in contact, and this area increases rapidly with each division of the substance. When a solute is resolved into its component molecules, its surface is enormously increased, and therefore the friction between the molecules of the solute and those of the solvent.
Isotonic Solutions.—Two solutions which have the same
osmotic pressure are said to be iso-osmotic or isotonic. When comparing two solutions of different concentration, the solution with the higher osmotic pressure is said to be hypertonic, and that with the lower osmotic pressure hypotonic.