[25] For rapid and accurate determinations of this kind, advantage is taken of those methods of chemical analysis which are known as ‘titrations’ (volumetric analysis), and consist in measuring the volume of solutions of known strength required for the complete conversion of a given substance. Details respecting the theory and practice of titration, in which potassium permanganate is very frequently employed, must be looked for in works on analytical chemistry.
[26] The measurements of velocity and acceleration serve for determining the measure of forces in mechanics, but in that case the velocities are magnitudes of length or paths passed over in a unit of time. The velocity of chemical change embodies a conception of quite another kind. In the first place, the velocities of reactions are magnitudes of the masses which have entered into chemical transformations; in the second place, these velocities can only be relative quantities. Hence the conception of ‘velocity’ has quite a different meaning in chemistry from what it has in mechanics. Their only common factor is time. If dt be the increment of time and dx the quantity of a substance changed in this space of time, then the fraction (or quotient) dx/dt will express the rate of the reaction. The natural conclusion, come to both by Harcourt and Esson, and previously to them (1850) by Wilhelmj (who investigated the rate of conversion, or inversion, of sugar in its passage into glucose), consists in establishing that this velocity is proportional to the quantity of substances still unchanged—i.e. that dx/dt = C(A - x), where C is a constant coefficient of proportionality, and where A is the quantity of a substance taken for reaction at the moment when t = 0 and x = 0—that is, at the beginning of the experiment, from which the time t and quantity x of substance changed is counted. On integrating the preceding equation we obtain log(A/(A - x)) = kt, where k is a new constant, if we take ordinary (and not natural) logarithms. Hence, knowing A, x, and t, for each reaction, we find k, and it proves to be a constant quantity. Thus from the figures cited in the text for the reaction 2KMnO4 + 108C2H2O4 + 14MnSO4, it may be calculated that k = 0·0114; for example, t = 44, x = 68·4 (A = 100), whence kt = 0·5004 and k = 0·0114, (see also Chapter XIV., Note [3], and Chapter XVII., Note [25 bis]).
[27] The researches made by Hood, Van't Hoff, Ostwald, Warder, Menschutkin, Konovaloff, and others have a particular significance in this direction. Owing to the comparative novelty of this subject, and the absence of applicable as well as indubitable deductions, I consider it impossible to enter into this province of theoretical chemistry, although I am quite confident that its development should lead to very important results, especially in respect to chemical equilibria, for Van't Hoff has already shown that the limit of reaction in reversible reactions is determined by the attainment of equal velocities for the opposite reactions.
CHAPTER XXII
IRON, COBALT, AND NICKEL
Judging from the atomic weights, and the forms of the higher oxides of the elements already considered, it is easy to form an idea of the seven groups of the periodic system. Such are, for instance, the typical series Li, Be, B, C, N, O, F, or the third series, Na, Mg, Al, Si, P, S, Cl. The seven usual types of oxides from R2O to R2O7 correspond with them (Chapter [XV.]) The position of the eighth group is quite separate, and is determined by the fact that, as we have already seen, in each group of metals having a greater atomic weight than potassium a distinction ought to be made between the elements of the even and uneven series. The series of even elements, commencing with a strikingly alkaline element (potassium, rubidium, cæsium), together with the uneven series following it, and concluding with a haloid (chlorine, bromine, iodine), forms a large period, the properties of whose members repeat themselves in other similar periods. The elements of the eighth group are situated between the elements of the even series and the elements of the uneven series following them. And for this reason elements of the eighth group are found in the middle of each large period. The properties of the elements belonging to it, in many respects independent and striking, are shown with typical clearness in the case of iron, the well-known representative of this group.
Iron is one of those elements which are not only widely diffused in the crust of the earth, but also throughout the entire universe. Its oxides and their various compounds are found in the most diverse portions of the earth's crust; but here iron is always found combined with some other element. Iron is not found on the earth's surface in a free state, because it easily oxidises under the action of air. It is occasionally found in the native state in meteorites, or aerolites, which fall upon the earth.
Meteoric iron is formed outside the earth.[1] Meteorites are fragments which are carried round the sun in orbits, and fall upon the earth when coming into proximity with it during their motion in space. The meteoric dust, on passing through the upper parts of the atmosphere, and becoming incandescent from friction with the gases, produces that phenomenon which is familiar under the name of falling stars.[2] Such is the doctrine concerning meteorites, and therefore the fact of their containing rocky (siliceous) matter and metallic iron shows that outside the earth the elements and their aggregation are in some degree the same as upon the earth itself.
The most widely diffused terrestrial compound of iron is iron bisulphide, FeS2, or iron pyrites. It occurs in formations of both aqueous and igneous origin, and sometimes in enormous masses. It is a substance having a greyish-yellow colour, with a metallic lustre, and a specific gravity of 5·0; it crystallises in the regular system.[2 bis]