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

ABNORMAL DENSITIES

41

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 mixture (vide § 23). Mistaking such a mixture for a homogeneous gas may lead to grave errors.

the

The molecular weight calculated from the observed density of 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 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 nonmetals or semi-metals. Only a few of the metals are embraced in it, as they are, as a rule, 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.

MOLECULAR WEIGHTS OF THE ELEMENTS

43

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

=

It has

already been mentioned in § 17 that the vapour density at 500° is greater than at higher temperatures. This density corresponds to a molecular weight S. 191.88, although it has not been decided with certainty whether the vapour of sulphur at a temperature a little above its boiling point (446° C.) is really composed entirely of hexatomic molecules. The density of the vapour changes as the temperature rises in a similar way to that exhibited by the compounds mentioned in § 26.

On the other hand the density of iodine (and in a lesser degree of bromine and of chlorine) is abnormally low at very high temperatures. This is explained by assuming that some of the molecules are split up by the action of heat into individual atoms, and that more molecules are split up as the temperature rises.

If the decomposition of the iodine molecules into atoms were complete, the original density would be halved. and chlorine exhibit similar peculiarities.

Bromine

28. Nascent State. The necessity of distinguishing between atoms and molecules of elements has been but slowly recognised; it has proved of great service in providing an explanation of certain apparently inexplicable phenomena. It has frequently been observed that many elements which, as a rule, do not readily enter into combination easily unite if brought together at the moment of their liberation from other compounds. In this specially active condition the elements are said to be in the nascent state.' The peculiar behaviour of elements in the nascent state is accounted for by assuming that they are then present as isolated atoms. Naturally these isolated atoins are more ready to enter into combination than they would be if they were already united to similar atoms in the form of molecules.

Hydrogen offers a striking example of the activity of elements in the nascent state. It is only at a high temperature that free hydrogen burns in oxygen, forming water, but both elements will unite at the ordinary temperature, or even at a lower temperature, at the moment of their liberation from other compounds. It is more difficult to combine free nitrogen with oxygen or hydrogen, but if the elements are in the nascent state combination readily takes place. It is easy to understand that isolated atoms at once unite when they meet each other, but when an atom is united to one or more atoms to form a molecule, it must first of all be detached from this molecule before it can form a new compound. In the case of nitrogen the tendency of the two atoms to combine and form the free molecule appears to be very strong.

§ 29. Determination of the Stœchiometric Values.—Having considered the grounds on which the determination of the atomic weights is based, we must now proceed to the description of the methods employed in the exact determination of these highly important values. The process is far from simple. In the first place it is necessary to know, with the utmost degree of accuracy, the proportions by weight with which the given element unites with other elements. This knowledge can only be acquired by careful analyses or syntheses of compounds. But all our methods of analysis and synthesis are vitiated by certain errors, which can never be entirely avoided, but must be