instance, the 'normal' hydro-carbons, containing carbon atoms united in a single chain, must not be compared with their isomerides containing side-chains of carbon atoms; the former boil at considerably higher temperatures than the latter. Inasmuch as by the replacement of hydrogen by an elementary atom or radical the volatility is affected, and the extent and manner of this alteration is determined by the position of the hydrogen so replaced, those compounds can alone be regarded as homologous in which there is complete analogy in the position of the substituting elements or groups. It is, in fact, this far-reaching influence exerted by the mode of the atom linkage in the boiling point which has made the volatility of compounds of great service in the investigation of the linking of the atoms in different compounds; organic chemistry provides numerous illustrations of the application and value of this method of determining the constitution of compounds.

§ 84. Vapour Pressure of Mixed Liquids.—If several liquids are contained in the same vessel, each of these will give off vapour into the part not occupied by the liquid. Regnault has shown that in such cases the phenomena may be divided into three distinct classes.

When liquids do not mix with one another, then each constituent gives off as much vapour as if it existed alone, and the total pressure is equal to the sum of the partial pressures of the vapours of both. Therefore, a mixture of two such liquids will boil at a lower temperature than either of the constituents. For instance, if water be poured on to bromoform (CHBr1), which boils at 151° C., then ebullition commences at the surface separating the two at a temperature of 93° C., because at this temperature the sum of the vapour pressures of water and of bromoform is sufficient to overcome the pressure of the atmosphere. The boiling point remains constant so long as there is a sufficient quantity of each liquid present. Carbon bisulphide and water, ethyl iodide and water, and many other combinations behave in a similar manner. This property may lead to very considerable error in the determination of boiling points. Thus ethyl iodide in presence of a little water will boil 10° C. lower than the boiling point of the pure substance.

When liquids mix only to a limited extent with each other,

as for instance ether and water (vide § 75), then the vapour pressure of the mixture is less than the sum of the pressures of the single constituents, and in fact is only as great as that of the more volatile constituent; in the instance cited it would only be as great as that of ether. In such cases the boiling point of the more volatile liquid could be correctly determined in presence of the other. The more volatile component having distilled over with a portion of the less volatile liquid, the boiling then ceases, to commence again when the temperature at which the latter boils has been reached.

When liquids mix in all proportions, the vapour pressure of each reduces that of the other, so that the pressure of the mixture is considerably less than that of the more volatile constituent, and lies between their separate pressures. The pressure in such cases varies very considerably with the proportion of the constituents. If such a mixture is distilled, then the boiling point gradually rises in proportion as the more volatile constituent distils over. Separation by distillation in such cases is much. more difficult than in either of the above instances. Separation is then only possible when the distillation is frequently interrupted, as in fractional distillation, when the distillate, as well as the residue, are each separately redistilled.

§ 85. Relation of Density and Pressure of Vapours to Molecular Weights.-If a vapour be examined under a pressure much smaller than the maximum of its vapour pressure at the temperature of experiment, then it is found that Avogadro's law (§ 17) holds true for the vapour, i.e. equal volumes of different vapours contain the same number of molecules, and as many as are contained in the same volume of a gas, provided that gases and vapours alike are measured under the same conditions of temperature and pressure. Under these conditions the densities are proportional to the molecular weights, and may serve, therefore, for the determination of the latter, in the manner already described in §§ 19-21.

When gases and vapours or several vapours are contained within the same space, and provided these gases and vapours exert no chemical action upon one another, and do not when in the liquid state mix with one another or dissolve in one another, then the sum of all the molecules is the same as would be the

case were the space filled by a single gas or vapour under like conditions of temperature and pressure. In fact, the proportion of the pressure of each constituent to the total pressure is determined by the number of its molecules existing in the space. Methods for the determination of molecular weights have been based upon this property.

Thus, substances which cannot be heated without decomposing at the temperatures at which Avogadro's law can be applied may be mixed with indifferent gases, and the weight, pressure, and temperature of the mixture determined. Deducting from this the known or subsequently determined proportion of the admixed gas, the pressure and weight of the vapour are obtained, from which the density and molecular weight are calculated.

According to Alex. Naumann, the molecular weight of a volatile liquid can be determined by distilling it with another liquid with which it does not mix. For, in such cases, the pressure which each constituent of the mixture of vapour exerts is proportional to the number of its molecules in the vapour. The amount converted into vapour, and consequently that distilling over, is greater the larger the number and the greater the weight of the particles or the molecules. If P be the total pressure, and p and p1 the partial pressures, i.e. the vapour pressures of each of the separate vapours, then

P = p + P1•

Further, let m and m, be the molecular weights and g and 91 the weights of each substance distilling over, then

If m, is already known and the pressure p, be measured for the temperature at which the mixture distils, then we have

For instance, from a mixture of toluene and water, 86.6 grammes of toluene and 21.1 grammes of water distil over at 840-3 C. and 754.4 mm. At this temperature the pressure of aqueous vapour alone is 422.0 mm.; consequently we have

The molecular weight of toluene, according to the formula, C,H,, is 91-8. The agreement between these numbers is sufficiently satisfactory to leave no doubt as to the value of the molecular weight. This method can be used in many cases where others cannot be applied.

The vapour pressure may, according to Raoult, also be utilised to determine the molecular weights of substances in the liquid state. When a comparatively small amount of a solid or liquid is dissolved in a volatile liquid, such as ether, the vapour pressure of the solvent is thereby reduced and the reduction is almost proportional to the number of the molecular weights of the substance dissolved. For instance, the vapour pressure of ether is reduced almost by when 1 molecular weight of a substance is dissolved in 99 molecular weights of ether; with 2 molecular weights in 100, i.e. dissolved in 98 molecular weights of ether, the pressure is reduced by about 18, and so on; still, the proportion of the substance dissolved must not be too great, otherwise this rule ceases to be reliable.

If ƒ be the vapour pressure of pure ether, f' that of a solution containing g parts by weight of the dissolved substance in 100 parts of the solution, and consequently (100—g) per cent. of ether, m the molecular weight to be determined, m, the molecular weight of ether (C,H,,O= 73.84), and n the unknown number of molecules of the dissolved substance in 100 molecular weights of the solution, then the following proportion holds approximately :

and therefore

-

10

ff: 100

n: 100;

The molecular weights determined in this manner are only approximations and need correcting by the stachiometric formula, just as do the molecular weights deduced from the vapour density.

§ 86. Critical Temperature.-As the pressure of a vapour increases with the temperature, and, in fact, the increase is the more rapid the higher the temperature, consequently the higher the temperature the greater the pressure required for the condensation of a vapour. For every vapour there exists a temperature above which no pressure, however great, can effect the liquefaction of that vapour. Andrews, the discoverer of this property, has styled this temperature the 'critical temperature,' and the pressure required to effect the liquefaction at temperatures a little below this is spoken of as the critical pressure.' There is a critical temperature for every vapour, provided it is not decomposed by the heat necessary to raise it to this temperature.

This discovery of Andrews indicated the method to be employed in the liquefaction of the so-called permanent gases, such as hydrogen, oxygen, nitrogen, carbon monoxide, marsh gas, &c., which Natterer had attempted but without success, although he had employed a pressure of several thousand atmospheres. These gases were first successfully liquefied by Raoult Pictet, who not only compressed the gases, but also at the same time cooled them to temperatures much below their critical temperatures.

According to the recently published investigations of Cailletet and Collardeau, the conclusions of Andrews require certain limitations, insomuch that the possibility of a liquid existing as such does not suddenly cease at the critical temperature, but only the sharp definition of the liquid from the vapour disappears, to be replaced by a misty, ill-defined intermediate layer. At a little above the critical temperature the liquid still remains more dense, and is therefore heavier than the vapour, and also possesses other properties than those belonging to the vapour. This difference between the liquid and gas disappears more and more as the temperature rises.

Despite this limitation the critical temperature, which is also known as the absolute boiling point, still remains an important and characteristic constant.