correction is effected by making use of the fact that each molecule is composed of atoms; its weight must consequently be equal to the sum of the weight of the atoms contained in it.

The density of hydrochloric acid gas is found by experiment to be 1.247. Analysis proves that this gas contains 35-37 parts by weight of chlorine to 1 part by weight of hydrogen; therefore the molecular weight of this compound must either be m=1+35·37=36.37, or a simple multiple of this number, as less than a whole atom of hydrogen (-1) cannot be present in the compound, The product of the density by 28.87 is d× 28.87=1·247 × 28.87=36·0, which agrees with the value calculated from the atomic weights; the difference is due to errors of experiment, and 36-37 must be held to be the correct molecular weight.

Marsh gas contains 2.9925 parts by weight of carbon to 1 part by weight of hydrogen. The molecular weight must be represented as

m=n (1+2·9925)=n × 3·9925,

in which n stands for a whole number (possibly n=1). The density compared with air = 0.555, and the molecular weight will be approximately

m'=28.87 × 0·555=16·02.

This is roughly four times the smallest value possible; consequently the true value is

m=4 x 3.992515.97 (4+11.97).

=

The molecular weight consists of 4 parts by weight of hydrogen and 11.97 parts by weight of carbon. In this way the molecular weights of numerous substances which can be volatilised without decomposition have been determined.

§ 25. Determination of Atomic Weights from Molecular Weights.--As the atoms are indivisible particles (aтoμo) a molecule cannot contain less than a whole atom. Hence the molecular weights of compounds offer special facilities for the determination of the atomic weights of the elements.

The smallest quantity of an element which is found to

exist in the molecular weight of any of its compounds is the maximum value of the atomic weight. This smallest quantity must contain at least one atom; it may contain two, three, or more atoms. We are justified in regarding this smallest quantity as the atomic weight, if no good reasons exist for believing that this smallest quantity consists of more than one atom. We shall presently see that methods are not wanting which prevent the possibility of errors of this kind.

The table on the opposite page comprises a list of those substances which contain the smallest quantity of the given elements in the molecular weights of their compounds. The first column contains the names of the compounds; the second, under d, the density compared with air; the third, the corrected molecular weights calculated from the densities; the fourth, the amount of the element contained in the molecular weight; the fifth, the chemical equivalent; and finally, the sixth contains the thermic equivalent of the element, if the element be known in the solid state.

It is only in the case of a small number of elements that the chemical equivalent is identical with the atomic weight deduced from the molecular weight; as a rule, the chemical equivalent is a sub-multiple of the atomic weight, and is therefore entirely unsuited for the determination of atomic weights. The atomic weights coincide with the thermic equivalents and the latter agree with the crystallographic equivalents.

The smallest quantity of the element contained in the molecular weight of the compound is double the thermic equivalent only in the case of cuprous chloride. But even this case does not form an exception, if we assume that the molecule contains two atoms of copper. This shows that Cannizzaro was justified in the statement made in 1857 that the molecular weights can be determined by means of the vapour density and the atomic weights by the specific heat.

26. Possible Errors. It is obvious that the calculation of molecular weight from the density can only be made in the case of homogeneous gases. If it be attempted to apply this method to gaseous mixtures, the result obtained is only the mean value of all the molecular weights contained in the

The molecular weight calculated from the observed density of the vapour of ammonium chloride is

m' d x 28.87 0.89 x 28.87=25.69,

=

=

which becomes after correction by the known combining weights of hydrogen, chlorine, and nitrogen:

m=2+17.685+7·005=26.69.

The quantities of chlorine and nitrogen (17·685 and 7·005 parts by weight respectively) are only half as large as the amounts found in the molecular weights of other compounds. If these quantities really do occur in the molecular weight of this compound, they must be regarded as the atomic weights of these elements, and we must assume that at least two atoms of these elements are contained in all their other compounds. But Pebal has shown that ammonium chloride splits up into equal volumes of ammonia and hydrochloric acid when it is converted into vapour. Its density is therefore the arithmetical mean of the densities of these two gases, and only one-half of the molecules present in the vapours contain chlorine; the other half contain nitrogen.' The densities of the constituents are

Other ammonium salts, certain compounds of phosphorus, and other substances also exhibit abnormal vapour densities. These compounds cannot be used for molecular or atomic weight determinations.

On the other hand, if the vapour density is determined at

1 Translators' Note.—Perfectly dry ammonium chloride does not dissociate. At the temperature of boiling mercury the vapour density is 26-8. H=1. (H. B. Baker, Chem. Soc. Jour. 1894, 615; 1898, 425.)

too low a temperature the resulting molecular weight may be too high. Many substances when volatilised at the lowest possible temperature give a vapour the density of which, compared with air or other gases, is high, but at higher temperatures yield a relatively light vapour. If the vapour density is determined for a series of temperatures, it is found to decrease as the temperature rises until a point is reached above which it remains nearly constant. The chlorides of aluminium, gallium, and iron behave in this way. To explain this behaviour it is assumed that when these compounds are first converted into vapour they do not at once separate into isolated particles, but into aggregations of molecules, generally consisting of two molecules. These aggregations gradually break up as the temperature rises. Their dissolution may also be aided by reduction of pressure or by admixture with an indifferent gas.

§ 27. Molecular Weights of the Elements. The molecular weights of the elements can be determined in the same way as the molecular weights of compounds. Some are identical with the thermic atomic weights, but as a rule they are larger than the latter. The following table gives a list of all the molecular weights of the elements known at the present time. The first column contains the names, the second the density in the state of gas or vapour at the temperature mentioned in the third column, the fourth the molecular weight calculated from the density and corrected by the results of analysis, and the fifth the atomic weight determined by Avogadro's (Av) or by Dulong and Petit's (DP) method.

Most of the elements contained in this table are either non-metals or semi-metals. Only a few of the metals are embraced in it, since, as a rule, they are difficult to volatilise; on the other hand, only a small number of non-metals are absent. There is a wonderful difference between the two groups; the semi-metals and non-metallic elements contain two or more atoms in the molecule; the molecules of the true metals only contain one atom.

It is probable that the ductility and other properties of the metals are in some way determined by this peculiarity.