It may be supposed, but neither definitely affirmed nor experimentally confirmed, that nitrogen and oxygen first give nitric oxide, NO, and only subsequently the brown vapours N 2 O 3 and NO 2 . Such a sequence in the combination of nitrogen with oxygen can only be supposed on the basis of the fact that NO forms N 2 O 3 and NO 2 directly with oxygen. If it be admitted that NO (and not N 2 O or NO 2 ) be first formed, then this instance would also confirm the law of Avogadro-Gerhardt, because nitric oxide contains equal volumes of nitrogen and oxygen. So, also, it may be admitted that, in the combination of hydrogen with oxygen, hydrogen peroxide is first formed (equal volumes of hydrogen and oxygen), which is decomposed by the heat evolved into water and oxygen. This explains the presence of traces of hydrogen peroxide (Chapter IV.) in almost all cases of the combustion or oxidation of hydrogenous substances; for it cannot be supposed that water is first formed and then the peroxide of hydrogen, because up to now such a reaction has not been observed, whilst the formation of H 2 O from H 2 O 2 is very easily reproduced.
Thus a whole series of phenomena show that the chemical reaction of substances actually takes place, as a rule, between equal volumes, but this does not preclude the possibility of the frequent reaction of unequal volumes, although, in this case, it is often possible to discover a preceding reaction between equal volumes.11
The law of Avogadro-Gerhardt may also be easily expressed in an algebraical form. If the weight of a molecule, or of that quantity of a substance which enters into chemical reaction and occupies in a state of vapour, according to the law, a volume equal to that occupied by the molecules of other bodies, be indicated by the letters M1, M2 ... or, in general, M, and if the letters D1, D2, ... or, in general, D, stand for the density or weight of a given volume of the gases or vapours of the corresponding substances under certain definite conditions of temperature and pressure, then the law requires that
M1 / D1 =
M2 / D2 ⋯ =
M / D = C where C is a certain constant. This expression shows directly that the volumes corresponding with the weights M1, M2 ... M, are equal to a certain constant, because the volume is proportional to the weight and inversely proportional to the density. The magnitude of C is naturally conditioned by and dependent on the units taken for the expression of the weights of the molecules and the densities. The weight of a molecule (equal to the sum of the atomic weights of the elements forming it) is usually expressed by taking the weight of an atom of hydrogen as unity, and hydrogen is now also chosen as the unit for the expression of the densities of gases and vapours; it is therefore only necessary to find the magnitude of the constant for any one compound, as it will be the same for all others. Let us take water. Its reacting mass is expressed (conditionally and relatively) by the formula or molecule H2O, for which M = 18, if H = 1, as we already know from the composition of water. Its vapour density, or D, compared to hydrogen = 9, and consequently for water C = 2, and therefore and in general for the molecules of all substances
M / D = 2.
Consequently the weight of a molecule is equal to twice its vapour density expressed in relation to hydrogen, and conversely the density of a gas is equal to half the molecular weight referred to hydrogen.