Usually, when the symbols of the elements are written or printed with a figure to the right, it is understood that this indicates a molecule of the element, the symbol alone representing an atom. Thus, the symbols H2 and P4 indicate that the molecules of hydrogen and phosphorus respectively contain 2 and 4 atoms. Since, according to the molecular theory, in all cases of chemical change the action is between molecules, such symbols as these ought always to be employed. Thus, the formation of hydrochloric acid from hydrogen and chlorine is correctly represented by the equation
H2 + Cl2 = 2HCl;
that is to say, a molecule of hydrogen and a molecule of chlorine give rise to two molecules of hydrochloric acid; whilst the following equation merely represents the relative weights of the elements which enter into reaction, and is not a complete expression of what is supposed to take place:—
H + Cl = HCl.
In all cases it is usual to represent substances by formulae which to the best of our knowledge express their molecular composition in the state of gas, and not merely the relative number of atoms which they contain; thus, acetic acid consists of carbon, hydrogen and oxygen in the proportion of one atom of carbon, two of hydrogen, and one of oxygen, but its molecular weight corresponds to the formula C2H4O2, which therefore is always employed to represent acetic acid. When chemical change is expressed with the aid of molecular formulae not only is the distribution of weight represented, but by the mere inspection of the symbols it is possible to deduce from the law of gaseous combination mentioned above, the relative volumes which the agents and resultants occupy in the state of gas if measured at the same temperature and under the same pressure. Thus, the equation
2H2 + O2= 2H2O
not only represents that certain definite weights of hydrogen and oxygen furnish a certain definite weight of the compound which we term water, but that if the water in the state of gas, the hydrogen and the oxygen are all measured at the same temperature and pressure, the volume occupied by the oxygen is only half that occupied by the hydrogen, whilst the resulting water-gas will only occupy the same volume as the hydrogen. In other words, 2 volumes of oxygen and 4 volumes of hydrogen furnish 4 volumes of water-gas. A simple equation like this, therefore, when properly interpreted, affords a large amount of information. One other instance may be given; the equation
2NH3 = N2 + 3H2
represents the decomposition of ammonia gas into nitrogen and hydrogen gases by the electric spark, and it not only conveys the information that a certain relative weight of ammonia, consisting of certain relative weights of hydrogen and nitrogen, is broken up into certain relative weights of hydrogen and nitrogen, but also that the nitrogen will be contained in half the space which contained the ammonia, and that the volume of the hydrogen will be one and a half times as great as that of the original ammonia, so that in the decomposition of ammonia the volume becomes doubled.
Formulae which merely express the relative number of atoms of the different elements present in a compound are termed empirical formulae, and the formulae of all compounds whose molecular weights are undetermined are necessarily empirical. The molecular formula of a compound, however, is always a simple multiple of the empirical formula, if not identical with it; thus, the empirical formula of acetic acid is CH2O, and its molecular formula is C2H4O2, or twice CH2O. In addition to empirical and molecular formulae, chemists are in the habit of employing various kinds of rational formulae, called structural, constitutional or graphic formulae, &c., which not only express the molecular composition of the compounds to which they apply, but also embody certain assumptions as to the manner in which the constituent atoms are arranged, and convey more or less information with regard to the nature of the compound itself, viz. the class to which it belongs, the manner in which it is formed, and the behaviour it will exhibit under various circumstances. Before explaining these formulae it will be necessary, however, to consider the differences in combining power exhibited by the various elements.
Valency.—It is found that the number of atoms of a given element, of chlorine, for example, which unite with an atom of each of the other elements is very variable. Thus, hydrogen unites with but a single atom of chlorine, zinc with two, boron with three, silicon with four, phosphorus with five and tungsten with six. Those elements which are equivalent in combining or displacing power to a single atom of hydrogen are said to be univalent or monad elements; whilst those which are equivalent to two atoms of hydrogen are termed bivalent or dyad elements; and those equivalent to three, four, five or six atoms of hydrogen triad, tetrad, pentad or hexad elements. But not only is the combining power or valency (atomicity) of the elements different, it is also observed that one element may combine with another in several proportions, or that its valency may vary; for example, phosphorus forms two chlorides represented by the formulae PCl3 and PCl5, nitrogen the series of oxides represented by the formulae N2O, NO, (N2O3), N2O4, N2O5, molybdenum forms the chlorides MoCl2, MoCl3, MoCl4, MoCl5, MoCl6(?), and tungsten the chlorides WCl2, WCl4, WCl5, WCl6.
In explanation of these facts it is supposed that each element has a certain number of “units of affinity,” which may be entirely, or only in part, engaged when it enters into combination with other elements; and in those cases in which the entire number of units of affinity are not engaged by other elements, it is supposed that those which are thus disengaged neutralize each other, as it were. For example, in phosphorus pentachloride the five units of affinity possessed by the phosphorus atom are satisfied by the five monad atoms of chlorine, but in the trichloride two are disengaged, and, it may be supposed, satisfy each other. Compounds in which all the units of affinity of the contained elements are engaged are said to be saturated, whilst those in which the affinities of the contained elements are not all engaged by other elements are said to be unsaturated. According to this view, it is necessary to assume that, in all unsaturated compounds, two, or some even number of affinities are disengaged; and also that all elements which combine with an even number of monad atoms cannot combine with an odd number, and vice versa,—in other words, that the number of units of affinity active in the case of any given element must be always either an even or an odd number, and that it cannot be at one time an even and at another an odd number. There are, however, a few remarkable exceptions to this “law.” Thus, it must be supposed that in nitric oxide, NO, an odd number of affinities are disengaged, since a single atom of dyad oxygen is united with a single atom of nitrogen, which in all its compounds with other elements acts either as a triad or pentad. When nitric peroxide, N2O4, is converted into gas, it decomposes, and at about 180° C. its vapour entirely consists of molecules of the composition NO2; while at temperatures between this and 0° C. it consists of a mixture in different proportions of the two kinds of molecules, N2O4 and NO2. The oxide NO2 must be regarded as another instance of a compound in which an odd number of affinities of one of the contained elements are disengaged, since it contains two atoms of dyad oxygen united with a single atom of triad or pentad nitrogen. Again, when tungsten hexachloride is converted into vapour it is decomposed into chlorine and a pentachloride, having a normal vapour density, but as in the majority of its compounds tungsten acts as a hexad, we apparently must regard its pentachloride as a compound in which an odd number of free affinities are disengaged. Hitherto no explanation has been given of these exceptions to what appears to be a law of almost universal application, viz. that the sum of the units of affinity of all the atoms in a compound is an even number.
The number of units of affinity active in the case of any particular element is largely dependent, however, upon the nature of the element or elements with which it is associated. Thus, an atom of iodine only combines with one of hydrogen,