Formulæ and equations are a kind of short hand for expressing briefly and in the language of the atomic theory the facts of chemical composition and reaction. The convenience of this method of expressing the facts justifies a short description of it here.
On comparing the percentage composition of a series of compounds the proportions in which the elements combine appears to be regulated by no simple law. For example:
| Realgar. | Orpiment. | Mispickel. | Pyrites. | |
| Arsenic | 71.4 | 60.9 | 46.0 | — |
| Sulphur | 28.6 | 39.1 | 19.6 | 53.3 |
| Iron | — | — | 34.4 | 46.7 |
| ——— | ——— | ——— | ——— | |
| 100.0 | 100.0 | 100.0 | 100.0 |
But if in these examples the composition is calculated, not on 100 parts, but on 107, 246, 163, and 120 parts respectively, evidence of a simple law becomes apparent.
| Realgar. | Orpiment. | Mispickel. | Pyrites. | |
| Arsenic | 75.0 | 150.0 | 75.0 | — |
| Sulphur | 32.0 | 96.0 | 32.0 | 64.0 |
| Iron | — | — | 56.0 | 56.0 |
| ——— | ——— | ——— | ——— | |
| 107.0 | 246.0 | 163.0 | 120.0 |
It will be seen that the proportion of arsenic is 75 or twice 75, that of iron is 56, and that of sulphur 32 or some simple multiple of 32. The series of examples might be extended indefinitely, and it would still be found that the "combining proportions" held good. The number 75 is spoken of as the "combining weight," or, more frequently, as the "atomic weight" of arsenic. Similarly 56 is the atomic weight of iron, and 32 the atomic weight of sulphur. The importance of this law of chemical combination is altogether independent of the atomic theory; but this theory furnishes the simplest explanation of the facts. According to it a chemical compound is made up of exactly similar groups of particles. The particles of each elementary substance are all alike, but differ from those of other elements in weight. Ultimate particles are called atoms, and the groups of atoms are called molecules. The atomic weight of any particular element is the weight of its atom compared with the weight of an atom of hydrogen. The atom of sulphur, for instance, is 32 times as heavy as the atom of hydrogen, and the atomic weight of sulphur is 32. The molecular weight is the sum of the atomic weights of the group. The molecule of pyrites contains two atoms of sulphur and one of iron: on referring to the table of atomic weights it will be seen that the atomic weights are—sulphur 32, and iron 56. The molecular weight, therefore, is 32 + 32 + 56—that is, 120. The meaning of this is, 120 parts by weight of iron pyrites contain 64 parts of sulphur and 56 parts of iron; and this is true whether the "parts by weight" be grains or tons.
The symbol or formula of an atom is generally the initial letter or letters of the Latin or English name of the substance. The atom of hydrogen is written H, that of oxygen O, of sulphur S, of iron (ferrum) Fe, and so on. A list of these symbols is given in the table of atomic weights.
The formula of a molecule is obtained by placing together the symbols of the contained atoms. Thus, Fe represents an atom of iron, S an atom of sulphur, while FeS represents the molecule of sulphide of iron as containing one atom of each element.
When more than one atom of an element is present this is shown by writing a figure under and after the symbol; thus, FeS2 represents a molecule with one atom of iron and two atoms of sulphur, Fe2S3 similarly shows one with two atoms of iron and three of sulphur. When a group of atoms is enclosed in brackets, a figure after and under the bracket multiplies all within it; for example, Pb(NO3)2 is another way of writing PbN2O6. Sometimes it is convenient to represent the atoms of a molecule as divided into two or more groups; this may be done by writing the formulæ of the groups, and separating each simple formula by a full stop. Slaked lime, for instance, has the formula CaH2O2; or, as already explained, we may write it Ca(HO)2; or, if for purposes of explanation we wished to look on it as lime (CaO) and water (H2O), we could write it CaO.H2O. A plus sign (+) has a different meaning; CaO + H2O indicates quantities of two substances, water and lime, which are separate from each other. The sign of equality (=) is generally used to separate a statement of the reagents used from another statement of the products of the reaction; it may be translated into the word "yields" or "becomes." The two statements form an equation.
Ignoring the quantitative relation, the meaning of the equation CaO + H2O = CaO.H2O is: "lime and water yield slaked lime." By referring to a table of atomic weights we can elicit the quantitative relations thus:—