CHAPTER VII MOLECULES AND ATOMS. THE LAWS OF GAY-LUSSAC AND AVOGADRO-GERHARDT

the properties of the medium in which they are dissolved, almost in proportion to the molecular weight and almost independently of their composition. The greater the number of molecules disseminated—i.e. the stronger the solution—the more clearly defined will those properties become which depend upon the composition of the dissolved substance and its relation to the molecules of the solvent, for the distribution of one kind of molecules in the sphere of attraction of others cannot but be influenced by their mutual chemical reaction. These general considerations give a starting point for explaining why, since the appearance of Van't Hoff's memoir (1886), ‘The Laws of Chemical Equilibrium in a Diffused Gaseous or Liquid State’ (see Chapter I., Note ²⁰), it has been found more and more that dilute (weak) solutions exhibit such variations of properties as depend wholly upon the weight and number of the molecules and not upon their composition, and even give the means of determining the weight of molecules by studying the variations of the properties of a solvent on the introduction of a small quantity of a substance passing into solution. Although this subject has been already partially considered in the first chapter (in speaking of solutions), and properly belongs to a special (physical) branch of chemistry, we touch upon it here because the meaning and importance of molecular weights are seen in it in a new and peculiar light, and because it gives a method for determining them whenever it is possible to obtain dilute solutions. Among the numerous properties of dilute solutions which have been investigated (for instance, the osmotic pressure, vapour tension, boiling point, internal friction, capillarity, variation with change of temperature, specific heat, electroconductivity, index of refraction, &c.) we will select one—the ‘depression’ or fall of the temperature of freezing (Raoult's cryoscopic method), not only because this method has been the most studied, but also because it is the most easily carried out and most frequently applied for determining the weight of the molecules of substances in solution, although here, owing to the novelty of the subject there are also many experimental discrepancies which cannot as yet be explained by theory.²⁹

If 100 gram-molecules of water, i.e. 1,800 grms, be taken and n gram-molecules of sugar, C₁₂H₂₂O₁₁, i.e. n 342 grms., be dissolved in them, then the depression d, or fall (counting from 0°) of the temperature of the formation of ice will be (according to Pickering)

which shows that for high degrees of dilution (up to 0·25 n ) d approximately (estimating the possible errors of experiment at ±0°·005) = n 1·10, because then d = 0°, 0°·0110, 0°·0275, 0°·1100, 0°·2750, 1°·1000, and the difference between these figures and the results of experiment for very dilute solutions is less than the possible errors of experiment (for n = 1 the difference is already greater) and therefore for dilute solutions of sugar it may be said that n molecules of sugar in dissolving in 100 molecules of water give a depression of about 1°·1 n . Similar data for acetone (Chapter I., Note ) give a depression of 1°·006 n for n molecules of acetone per 100 molecules of water. And in general, for indifferent substances (the majority of organic bodies) the depression per 100H 2 O is nearly n 1°·1 to n 1°·0 (ether, for instance, gives the last number), and consequently in dissolving in 100 grms. of water it is about 18°·0 n to 19°·0 n , taking this rule to apply to the case of a small number of n (not over 0·2 n ). If instead of water, other liquid or fused solvents (for example, benzene, acetic acid, acetone, nitrobenzene or molten naphthaline, metals, &c.) be taken and in the proportion of 100 molecules of the solvent to n molecules of a dissolved indifferent (neither acid nor saline) substance, then the depression is found to be equal to from 0°·62 n to 0°·65 n and in general K n . If the molecular weight of the solvent = m , then 100 gram-molecules will weigh 100 m grms., and the depression will be approximately (taking 0·63 n ) equal to m 0·63 n degrees for n molecules of the substance dissolved in 100 grms. of the solvent,