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other chemists. These double atoms were supposed to enter into combination in pairs, and every pair represented precisely what others termed 'the proportion' or 'equivalent.' Water was therefore composed of a double atom of hydrogen united to one atom of oxygen, and this combination was represented by the symbol HO. Hydrochloric acid and ammonia were formed, the first of one double atom of hydrogen united to one double atom of chlorine, the second of one double of nitrogen united to three double atoms of hydrogen. The formulæ HO, HCl, H2N, were really equivalent to the formulæ H ̧O, H¿C11⁄2, HÅN1⁄2, but remind us of the notation HO, HCl, H2N, employed by Gmelin and others. It was, in fact, a step backwards. In admitting double atoms Berzelius unnecessarily doubled a number of formulæ ; and if it is true that H2O, H2Cl2, represent, from a certain point of view, equivalent quantities of water and hydrochloric acid, it is equally true that these formulæ do not represent true molecular magnitudes. Gerhardt subsequently showed that if a molecule of water, occupying two volumes of vapour, is represented by the formula HO, a molecule of hydrochloric acid occupying two volumes of vapour should be represented by the formula HCl, and a molecule of ammonia by H,N. It is true that the formula HCl, corresponds to the formula PbCl2, ZnCl2, CaCl2, and KCl2, by which Berzelius represented the chlorides of lead, zinc, calcium, and potassium. But we now know that the molecules. of all these chlorides are not, strictly speaking, equivalent, and that if the three first are true the fourth must be halved. The law of specific heats forces us, in fact,

F

2

to halve the atomic weight of potassium, and consequently to represent its chloride by the formula KCl, which answers to HCl. The latter formula represents two volumes of vapour, as do the formulæ of water, H2O, and of ammonia, H ̧N.

All these inaccuracies which we have pointed out in Berzelius's system of atomic weights and notations arose from an erroneous conception of the law of volumes. Instead of regarding as equidistant, and equally distributed in equal volumes of gases or vapours, the particles of the second order, or the molecules of simple and compound bodies, as Avogadro and Ampère had done, and later Gerhardt, Berzelius only considered the primordial atoms of certain simple gases, holding that they alone, and not the 'compound atoms,' are distributed in equal numbers in equal volumes. We know now that this is an erroneous idea, and that the hypothesis of Avogadro and Ampère, long forgotten, but restored to its due place of honour by Gerhardt, applies to the single molecules or particles of the second order, which, whether simple or compound, constitute the ponderable matter of gases and

vapours.

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CHAPTER IV.

SYSTEM OF CHEMICAL EQUIVALENTS-EQUIVALENT NOTATION.

I.

THE interpretation which Berzelius had given of the law of volumes formed, as we have seen in the preceding pages, one of the foundations of his system of atomic weights and of his notation. This foundation was destroyed by the researches of Dumas, and subsequently of Mitscherlich, upon vapour densities commenced in 1827. Dumas noticed that the vapour density of mercury is sensibly equal to 100, hydrogen being taken as unity. The vapour densities of mercury and of oxygen are as 100: 16 or as 50: 8. If the atomic weights were proportional to the densities, 8 of oxygen should combine with 50 of mercury to form mercuric oxide. This is not the case; mercuric oxide is composed of 8 of oxygen and 100 of mercury, and it is the latter number which Berzelius had adopted for the atomic weight of mercury. If equal volumes of oxygen and of mercury vapour contain the same number of atoms, their densities should be in the ratio of 8 to 100, or, in other words, the density of mercury vapour

is only half what it should be. We have here evidently a well-marked exception, or, better, a manifest contradiction between the facts and the principle admitted by Berzelius. Other exceptions may be mentioned. The vapour densities of sulphur and phosphorus determined by Dumas in 1832 were found to be, in the first case, three times as great, and in the second twice as great, as those indicated by theory. Chemical considerations have caused a composition, expressed by the formulæ HS and SO3, to be attributed to sulphuretted hydrogen and sulphuric anhydride. From these formulæ the ratio between the atomic weights of sulphur, oxygen, and hydrogen is expressed by the numbers 32:1:16, and the densities should be in the same ratio. Now, the vapour density of sulphur taken at about 560° is 96, hydrogen being taken as unity. From this density a quantity weighing 32 in the molecule of sulphuretted hydrogen would not represent an atom of sulphur, but of an atom, and the formula of sulphuretted hydrogen, expressed in conformity with the law of volumes, would be H2S, which is inadmissible.

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From the formulæ PH, and P2O5, adopted for phosphoretted hydrogen and phosphoric anhydride respectively, the relation between the atomic weights of phosphorus, hydrogen, and oxygen should be expressed by the numbers 31:1:16. Now, the vapour density of phosphorus is equal to 2 x 31-62. If, therefore, the density of sulphur vapour is three times greater than that indicated by theory, that of phosphorus is twice as great. The case is the same with that of arsenic, from

an experiment of Mitscherlich, who also confirmed, in 1833, the results obtained by Dumas upon the vapour of mercury, sulphur, and phosphorus.

We here, therefore, meet with a serious difficulty. For its solution two courses are open to us: we must either maintain the principle of the equality of the number of atoms in equal volumes of gases or vapours, and determine to assign to mercury, sulphur, phosphorus, and arsenic atomic weights which shall conform to the vapour densities, although they are less probable, and consequently to give their compounds the formulæ Hg,0, H2S, P1⁄2H ̧; or else it will become necessary to sacrifice the principle under discussion, in order to enable us to adopt the atomic weights, HgO, indicated by chemical analogies and the law of specific heats. The atomic weights of mercury, sulphur, phosphorus, and arsenic being, therefore, 200, 32, 31, 75, referred to hydrogen as unity, the preceding formulæ become HgO, H2S, PH„, and AsH ̧.

It is the latter course which chemists have adopted, since they were properly unwilling to neglect more evident analogies. But the adoption of these atomic weights involves the following consequences:

1. The vapour of mercury, the density of which is only half that required by the atomic weight assigned to mercury, evidently contains half the number of atoms contained in an equal volume of hydrogen.

2. The vapour of sulphur, which at 500° is three times as dense as it should be from the atomic weight assigned to sulphur, contains, at this temperature, three times the number of atoms contained in an equal volume of hydrogen.