POSITION OF ATOMS IN MOLECULES

73

exhibit certain points of difference, and the nature of this difference depends on the composition of the molecules and the nature of the atoms, it seems probable that these points of difference must already exist in the atoms and molecules themselves. The attractive force of affinity is active at these points. It endeavours to attract the other atoms and keep them in positions, which lie in these lines of force at a definite distance from the centre of gravity of the first atom. The distances between the centres of gravity may vary considerably for different atoms. There will be only one such position in the vicinity of a monovalent atom, in which a second atom can be fixed; but there will be two such points for a divalent and three for a trivalent atom, &c.

We may also venture to determine the position of these points in space. In the case of a compound consisting of two monovalent atoms only the distance between the atoms is fixed; the system will be in a state of equilibrium in any position. This may be the reason why compounds formed of two monovalent atoms generally crystallise in the regular system. A polyvalent atom requires a number of points corresponding to its chemical valency; these positions must be symmetrically arranged, at equal distances from the centre of gravity of the polyvalent atom. If this is not the case an exchange in the position of the atoms will produce 'isomeric' compounds-that is, compounds possessing the same composition, but exhibiting dissimilar properties. For example, there would be two potassium hydroxides, K-0---H, and H-O--- K, and two

H

K, and

H

K

N

H.

amides of potassium, H - N Apparent examples of this kind of isomerism have from time to time been discovered, but on closer investigation they have invariably been proved to be spurious. It is, therefore, exceedingly probable that the points are symmetrically arranged at equal distances round the surface of a sphere. In a divalent atom the points will be diametrically opposite each other; in a trivalent atom the points will be arranged in a circle, at angles of 120°; in a tetravalent atom the points will be arranged in space like the angles of a regular tetrahedron; in a hexavalent atom the points will occupy the solid angles of an octahedron,

or the centres of the faces of a cube; in an octovalent atom the points are arranged like the corners of a regular cube, or the centres of the faces of an octahedron. A perfectly symmetrical arrangement of five or seven points on the surface of a sphere is not possible, but it is probable that in this case the arrangement will be as symmetrical as possible.

Starting from these assumptions, it is easy to represent the configuration of the molecules, which are composed of monovalent atoms and only one polyvalent atom. A compound consisting of two monovalent atoms, or two monovalent and one polyvalent atom, is represented by a formula lying in a straight line:

One trivalent and three monovalent atoms lie in a plane :

H H

NH

One tetravalent and four monovalent atoms are arranged round the centre of a tetrahedron, at the solid angles. In fact, physical investigations of such compounds have made it exceedingly probable that their molecules really possess this form.1

It is difficult to follow this hypothesis when the monovalent atoms are wholly or partly replaced by polyvalent atoms, for one atom cannot occupy several positions at the same time. Attempts to overcome this difficulty are made by assuming that the atom alternately occupies the different positions moving between them like a pendulum, or rotating about them. This view receives support from the observation that compounds containing polyvalent atoms attached to each other by multiple linkings occupy a larger space than those compounds do in which the polyvalent atoms are united together by a single linking. Again, it is observed that those carbon compounds which contain doubly or trebly linked carbon atoms easily split

1 Conclusions drawn from the friction of gases, with reference to the size of the section of molecules, appear to confirm these views.

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75

up at the points where the double or treble linking exists. Great importance must not be attached to speculations of this nature at present, as they are much too hypothetical; but they serve a useful purpose by enabling us to survey a variety of observations from a common standpoint.

§ 44. Investigation of the Constitution of Chemical Compounds. The chemical valency of the elements and the composition of their compounds are intimately related. Not only the number of the atoms, but their arrangement in the molecule, depends on the valency of the elements. The possibility of investigating and ascertaining the manner in which the atoms are arranged, was for a long time a disputed question. Although some chemists attempted to investigate the arrangement of the atoms, others looked upon such investigations as absolutely valueless. But even the followers of the latter school could not avoid holding certain views regarding the manner in which the atoms combine together to form compounds, for they rejected as unwarranted the doubts which existed as to the correctness and permissibility of their views. This dispute lasted more than twenty years, and, strange to say, it ended in the overthrow of these old dogmas by new hypotheses, by means of which we have acquired an unexpected insight into the nature of chemical compounds. At the present day the investigation of the 'constitution' or 'structure' of the chemical compounds is one of the chief problems of the science; more particularly is this the case in organic chemistry, which treats of the compounds of carbon. In the course of the last fifty years these investigations have been brought to such a state of perfection, that it is now usual to dogmatically insert the results of such investigations in text-books as the fixed truth, without giving any exact account of the methods which have led to the attainment of such intimate knowledge.

It is desirable to know the exact grounds on which our knowledge rests, not only in the interests of those who specially devote themselves to such subjects, but also in the interests of the general history of civilisation and the history of science in particular. These investigations form one of the most striking examples of the power of the human mind to penetrate into things which are as a sealed book to our senses alone. The

path which the science of chemistry pursued, to attain its present position, was long, and not entirely free from error. But in looking back we can separate the essential from the non-essential and gain without difficulty a clear idea of the chief features of this development.

The chief difference between our present views and the older conceptions consists in this: formerly it was more or less explicitly assumed that a chemical compound was held together by the total attractive force of the affinities of all the atoms contained in it, but as our knowledge increased it was gradually recognised that the connection is between atom and atom and that the atoms are attached to each other like the links in a chain, the continuity ceasing if even a single link of the chain is removed. This kind of combination is termed 'atomic linking'; the idea involved was not suddenly realised, but was the gradual outcome of previous conceptions.

The necessity of studying the atoms themselves was clearly stated by A. Kekulé in 1857, and by A. S. Couper in 1858. The doctrine of atomic linking is the outcome of the investigation of organic compounds, and at the present day it is chiefly applied to organic bodies; but numerous conclusions with regard to the constitution of inorganic compounds have been deduced by its aid.

The theory of atomic linking first gave a satisfactory explanation of the common observation that two or more chemical compounds having the same composition may exhibit widely different properties. This remarkable phenomenon has long been known as 'isomerism,' from loos, same, and μépos, the part. Isomeric bodies are those which contain the same constituents, loa μépn. We distinguish between 'metamerism' and 'polymerism'; metamerism embraces those cases in which the constituents are present in exactly the same number and quantity, but are differently arranged: the grouping of the constituents, has been altered by a change of position, 'metastasis.' 'Polymerism,' or, better, ' pleomerism,' applies to those compounds in which the relative proportion between the constituents is the same, but the absolute number of atoms contained in the molecular weight of one compound is double or treble the number contained in the other.

There are several methods of investigating atomic linking which mutually support and supplement each other. In the first place, in many simple cases the atomic linking can be deduced on purely theoretical grounds from the composition and molecular weight of the compound and the chemical valency of its constituents. But this can be done only when a single form of combination is possible, and the composition only permits of one interpretation. When the conditions are not so simple we make use of analysis and synthesis, assuming that those constituents which remain combined together when a compound is decomposed were previously united, and inversely in building up a compound, the parts which were united before remain united after the combination has taken place. Finally, we have a very important aid to such investigations, in the connection which has been established by innumerable comparisons between the chemical and physical properties of a body and its atomic linking.

§ 45. Theoretical Determination of the Possible Forms of Combination. After the composition of the molecular weight of a compound has been empirically determined, the next question is to ascertain the manner in which the atoms are linked together. This is a purely mathematical problem and the answer can, when necessary, be calculated by permutations. It is obvious that any indefinite number of atoms cannot unite together to form distinct compounds: for instance, the number of monovalent atoms is limited, as each monovalent atom can only unite with one other atom, and cannot lengthen the chain to any greater extent. Compounds composed entirely of monovalent atoms can only exist in the form represented by type I. (§ 40). Compounds composed of one polyvalent atom and several monovalent atoms exhibit forms exemplified by types II. to VIII. The number of monovalent atoms which can enter into combination corresponds to the valency of the polyvalent atom. If a second or third polyvalent atom is added, then two valencies are required for the linking of each additional polyvalent atom, and are, therefore, not available for union with monovalent atoms. The number of monovalent atoms is increased by a number equal to two less than the valency of the new polyvalent atom. If N1, N2, N3, N49