seen that Pfeffer found the osmotic Hence pressure of a 1 per cent. V=34.2, T=279.8. R=840. P=0.664 × 10333, At first I thought this was a pure accident, and was disinclined, at least in the case of sugar, to attach any physical meaning to this result. Equality of both values of R, i. e. for gas and solution, has only one meaning however, viz. that the sugar exerts an osmotic pressure equal to the pressure which gaseous sugar of the same concentration and at the same temperature would exert. In other words, this is the application of Avogadro's law to sugar-solutions, the only difference being in the substitution of osmotic pressure for ordinary gas-pressure. II. The Theory of Dilute Solutions. Although the above remarkable equality of osmotic and gas-pressure at equal molecular concentration and temperature appeared at first to be a mere chance, yet it occurred again and again, and was connected with so many known and afterwards with newly discovered regularities, that at last there seemed to be no room left for doubt. De Vries was the first to determine successfully the molecular weights of substances in solution by an application of the extended Avogadro's law. According to Loiseau-Scheibler the molecule of raffinose contained 18 atoms of carbon, C18, whilst Berthelot gave it a formula with C. In order to settle the question, a comparison was made with sugar, and from each substance a few isotonic solutions were prepared, i. e. solutions having equal osmotic pressures. This was accomplished in an extraordinary manner with the help of plant-cells containing protoplasm. The membrane of the protoplasm is semi-permeable, and when the cells are placed in solutions having greater osmotic pressures, the protoplasm contracts and separates from the cell-wall, or what is termed plasmolysis takes place. If the solution has a lower osmotic pressure than the contents of the cell, the protoplasm continues to fill the cell completely. The point at which the protoplasm just begins to recede from the cell-wall when it is placed in solutions of sugar and raffinose is sought out, and the solutions thus proved to be isotonic. It is then only necessary, as in the case of gases, to determine the ratio of the amounts of sugar and raffinose contained in equal volumes of the solutions in order to calculate the molecular weight. In this way it was found that the formula of raffinose contained CThis conclusion has since been confirmed by the splitting up of raffinose into equal quantities of the three sugars-glucose, levulose, and galactose, each containing six atoms of carbon. We will now consider the laws associated with osmotic pressure. Fig. 3. The Lowering of the Vapour-Pressure. If we suppose, with Arrhenius, that we have osmotic equilibrium with a 1 per cent. p-4p sugar-solution, as in fig. 3, where H is the rise due to osmotic pressure, then the column of solution H represents the osmotic pressure and the column of vapour H the lowering of the vapour-pressure. Hence, for any solvent whatever, we obtain, as before, Lowering of vapour-pressure H where s represents the specific gravity of the solvent and M its molecular weight in the gaseous state. Should the osmotic pressure be equal to the gas-pressure, then, by comparison with hydrogen, it will be for a 1 per cent. solution of a substance having the molecular weight m. Hence This is the well-known law of Raoult, which states that the molecular relative lowering of vapour-pressure is equal to 100 of the molecular weight of the solvent. It is to be noted that here, as in all laws relating to dilute solutions, we have only a limiting law which strictly applies to infinitely dilute solutions, where the accurate expression of the above law becomes dp The following table contains the results obtained with fairly dilute solutions. The Raising of the Boiling-Point.-Fig. 4 contains portions of the vapour-pressure curves for solvent and solution. The P Fig. 4. Solvent T horizontal line ab corresponds to the atmospheric pressure, a is the boiling-point of the solvent, b that of the solution, ab the rise of boiling-point (dT), and ac the lowering of vapour-pressure (dp). If, in the well-known equation dlp dr = dT 2T?' where q represents the latent heat of evaporation per kilo9 gramme-molecule, the above expression of Raoult's law, is introduced, we obtain m = 0.01 M, Ap Ρ MAT= which is the well-known van't Hoff-Beckmann-Arrhenius expression for the molecular rise of boiling-point, the experimental confirmation of which is contained in the following table (W=the latent heat of evaporation per kilogramme). 0-02T W The Lowering of the Freezing-Point.—Similarly, represents the molecular lowering of the freezing-point, and reference may be made to a memoir read before the Swedish Academy, where I first described Avogadro's law for solutions as a "propriété curieuse de la matière diluée," along with a confirmation of Raoult's so-called Normal Numbers. Before publishing the above memoir I took the precaution to ask Prof. Petterson if he would determine the latent heat of fusion of ethylene bromide, which I had predicted, from the consideration of Raoult's data, would be 13. This prediction was found to be correct, and has since been confirmed in a great many cases, especially by Eykman. The following table contains the calculated and found values for the latent heat of fusion : Unfortunately I have no more time at my disposal to follow out all the other relationships which are founded on the assumption that R 846, so that the following tabular survey must suffice : = = |