5. The Lowering of the Freezing Point.
Cryoscopy.—The usual method employed for the determination of the molecular concentration and osmotic pressure of a solution is by cryoscopy—the measurement of its temperature of congelation. A very sensitive thermometer is used, the scale of which extends over only 5° and is divided into hundredths of a degree. The liquid under examination is placed in a test tube, in which the bulb of the thermometer is plunged, and this is supported in a second tube with an air space all round it. The whole is then suspended to the under side of the cover of the refrigerating vessel, which may be cooled either by filling it with a freezing mixture, or by the evaporation of ether. During the whole of the operation the liquid is agitated by a mechanical stirrer. The first step is to determine the freezing point of distilled water. As the water cools the mercury gradually descends in the stem of the thermometer till it reaches a point below the zero mark at 0° C. As soon as ice begins to form the mercury rises, at first rapidly and then more slowly, reaches a maximum, and finally descends again. This maximum reading is the true point of congelation. The inner tube is then emptied, care being taken to leave a few small ice crystals to serve as centres of congelation for the subsequent experiment, thus avoiding supercooling of the solution. The process is then repeated with the solution under examination. The difference between
the two freezing points is the required "lowering of the freezing point."
Cryoscopy is the method most used in biological research to determine molecular concentration. It has, however, some grave defects. It necessitates several cubic centimetres of the liquid under examination. It gives us the constants of the solution at the temperature of freezing, which is far below that of life. Organic liquids are easily altered and are extremely sensible to minute differences of temperature, cryoscopy therefore gives us no information as to the constitution of solutions under normal conditions. It is desirable to have some other method of determining molecular concentration and the other interdependent constants at the normal temperature of life. A much better method, were it possible, would be the direct determination of the vapour tension of the solutions under normal conditions of temperature and pressure.
Molecular Lowering of the Freezing Point.—For every substance whose solution is not ionized and therefore does not conduct electricity, the lowering of the freezing point is the same, viz. 1.85° C. for each gramme-molecule of the solute per litre of the solution.
Determination of the Molecular Concentration.—In order to obtain the molecular concentration of a non-ionizable substance, we have only to determine the lowering of the freezing point. Let A be the lowering of the freezing point of any solution. On dividing it by 1.85 (the lowering of the freezing point for a normal solution), we obtain the number of gramme-molecules in a litre of the solution. If n be the number of gramme-molecules per litre, then n = A / 1.85.
Determination of the Osmotic Pressure.—The osmotic pressure P of a solution may be obtained by multiplying its molecular concentration n by 22.35 atmospheres. P = n × 22.35 = A / 1.85 × 22.35.
Determination of Molecular Weight.—The lowering of the freezing point also enables us to calculate the molecular
weight of any non-ionizable solute. Thus Bouchard has been able to determine by means of cryoscopy the mean molecular weight of the substances eliminated by the urine. A weight x of the substance is dissolved in a litre of water, and the lowering of the freezing point is observed. The value thus found divided by 1.85 gives us n, the number of gramme-molecules per litre. The molecular weight M may be determined by dividing the original weight x by n.
The study of osmotic pressure was begun by the Abbé Nollet; and one of his disciples, Parrot, at an early date thus described its importance: "It is a force analogous in all respects to the mechanical forces, a force able to set matter in motion, or to act as a static force in producing pressure. It is this force which causes the circulation of heterogeneous matter in the liquids which serve as its vehicle. It is this force which produces those actions which escape our notice by their minuteness and bewilder us by their results. It is for the infinitely small particles of matter what gravitation is for heavy masses. It can displace matter in solution upwards against gravity as easily as downwards or in a horizontal direction."