CHAPTER VII.

ATOMIC AND MOLECULAR VOLUMES.

By the term atomic volumes of simple bodies is meant the volumes occupied by quantities of these bodies proportional to their atomic weights, and by the term molecular volumes of compound bodies, the volumes occupied by quantities of these bodies proportional to their molecular weights.

To determine the relative volumes occupied by atoms, we have only to divide the atomic weights by the weights of the unit of volume-that is to say, by the densities. The atomic volumes are the quotients of the atomic weights by the densities; the molecular volumes, the quotients of the molecular weights by the densities.

If matter were continuous, these quotients would give the true volumes occupied by atoms relatively to the volume of one of them taken as unity. But this is not the case.

The ultimate particles of bodies do not touch each other; they are separated by relatively large spaces. They move in ether, and in gaseous bodies their distance apart is immense in proportion to their size: it is very

considerable in solid and liquid bodies. The space occupied by the unit of volume of bodies is therefore far from being filled by the atomic substance itself; it comprises a portion of ether probably considerable. In other words, the conception of the density of bodies comprises two distinct but inseparable elementsnamely, the ultimate particles which we term atoms or molecules, and the interatomic or intermolecular spaces. This remark will show the exact meaning which must be attached to the expressions atomic volumes' and 'molecular volumes.'

If the molecules were situated at equal distances in the different bodies, it is clear that a given volume of the latter would contain the same number of molecules; the molecular weights would be proportional to the densities and the molecular volumes uniform. This is

the case with the gases. We admit that they do perceptibly contain, in a given volume, the same number of molecules; the relative weights of the latter are proportional to the densities. But it is different with solid and liquid bodies. Their molecules are situated at various distances, not only in different substances, but sometimes in the same body. Thus their coefficients of expansion are very different, and, moreover, vary for a given body, according to the temperature and physical condition of that body. This unequal distribution of molecules in solid and liquid bodies makes it impossible to discover a simple relation between the molecular weights and the density, like that which we have just mentioned in connection with gaseous bodies.

As regards liquid and solid elements, we know that

very wide limits must be assigned to the variations of their densities.

The lightest of metals, lithium, has a density of 0.59 and weighs 39 times less than the same volume of hammer-hardened platinum, the density of which is 23. These densities, moreover, vary according to the physical condition of the body, so that it is impossible to compare the densities of liquid and solid bodies, of amorphous and crystallised bodies, of bodies solidified after fusion. and bodies beaten and hammer-hardened after solidification. In order to draw any comparisons from the atomic volumes of simple bodies and the molecular volumes of compound bodies, we must, therefore, calculate the densities under similar conditions-namely, for liquid bodies, at equal distances from their points of ebullition, as Hermann Kopp recommends; and for solid bodies, as much as possible at equal distances from their points of fusion.

We will now proceed to give a brief account of the result of this work and of all the facts which have been collected with regard to the relative volumes occupied by atoms and molecules. We shall confine ourselves to general results, referring our readers to special works for numerical data and details.

The limits within which the atomic volumes of simple bodies vary are less considerable than in the case of densities, though still very wide. Mendelejeff has shown that these variations are a periodic function of their atomic weights; for if the elements are arranged in the order of the progression of their atomic weights, their atomic volumes increase and decrease periodically.

We have discussed this point at some length, and will not, therefore, return to it. We will only add that the numerical values of the atomic volumes of simple bodies will be found in the table given upon pp. 159, 160.

It appears from these facts that there must be a relation between atomic weights and atomic volumes. Of the precise nature of this relation we are, however, ignorant.

Dumas has remarked that certain simple bodies belonging to the same family have almost the same atomic volumes. This is the case with the following bodies:

We see that tellurium, antimony, and bismuth only partially conform to this rule; the following elements break through it entirely :

molecular volumes of compound bodies to the extensive researches of Hermann Kopp, who devoted his attention

principally to the molecular volumes of liquid bodies. The results of these researches may be summed up in the following propositions, which apply especially to organic liquids.

1. The molecular volume of compounds is expressed by the sum of the atomic volumes occupied by the elements.

2. In compounds possessing a similar atomic composition, the same element always possesses the same atomic volume. The latter being determined for every simple body, it follows that the molecular volume of a compound may be calculated if the atomic composition is known.

3. In compounds possessing different atomic structures the same element may occupy two different volumes. Thus, to borrow an expression from the theory of types, the atomic volume of oxygen differs with its position either as contained in a radical, or situated without that radical, in the state of typical oxygen. Nitrogen possesses a different atomic volume, according as it is contained in a compound derived from the ammonia type, combined with carbon as in cyanogen, or united to oxygen as in nitrous vapour.

Hermann Kopp succeeded in determining the atomic volumes of carbon, hydrogen, oxygen, nitrogen, &c., by means of ingenious considerations which we shall briefly describe as follows.

1. In comparing the molecular volumes of organic compounds, which differed from each other only by nCH,, he found that for each addition of CH2 the average increase of the volume of the molecule was 22.