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of the first class we have carbon as diamond or graphite; sulphur is an example of the second class.

The diamond and graphite can exist unaltered side by side, and it is only at a very high temperature that the diamond is converted into graphite. On the other hand the rhombic form of sulphur is only stable below, and the monoclinic form above, a temperature of 95°.6 C.; both modifications can exist unchanged for some time outside these limits But they are in a state of unstable equilibrium, which is easily upset by heating, or shaking, or more particularly by contact with a crystal of that modification which is stable at the prevailing temperature, and the whole mass is converted into this form.

Many dimorphous organic compounds behave like sulphur in this respect, and as a rule only one modification is stable, and the other unstable above and below a certain definite temperature.

This kind of physical isomerism is supposed to be due to a difference in the arrangement of the particles or molecules, which are in themselves identical. The accuracy of this hypothesis cannot be proved, as we do not possess any method by which the nature, or even the size, of the molecules of solid bodies can be ascertained. But when we see that under suitable conditions crystals of both modifications can be obtained from one and the same liquid, it seems probable that these modifications are composed of similar molecules, just as different kinds of buildings can be constructed from the same kinds of bricks. This class of isomerism may be termed 'isomerism of aggregation.'

§ 54. Physical Isomerism of the Molecules.-There are also cases of physical isomerism caused by a difference in the molecules. The examples of real polymerism belong to this class, e.g. when a body has different molecular weights in the gaseous and liquid states. In the case of sulphur the molecules at temperatures near the boiling point consist of six atoms, S., which are split up at higher temperatures into molecules consisting of two atoms, S. Many organic and inorganic compounds, such as certain aldehydes, acetic acid, nitrogen peroxide, &c., exhibit analogous behaviour.

The allotropic modifications of phosphorus are probably due to differences in the number of atoms composing the molecules.

H

་

If phosphorus be heated above 210° in a closed vessel too small to permit the element being completely converted into vapour, it passes from the gaseous state into a red solid modification, from which the colourless variety is regenerated, if sufficient space be offered for complete volatilisation. The red modification is produced from the compressed and the colourless from the expanded vapour at the same temperature (210-300°). It is therefore probable that both modifications already existed in the state of vapour as isolated molecules. A difference in the vapour can only be due to a difference in the molecules. It is not yet known whether this difference is to be ascribed to polymerism.

§ 55. Optical Isomerism. The most remarkable form of isomerism, is that in which the isomeric bodies crystallise in forms which are identical in all their individual parts, such as angles and faces, and are symmetrical but not superposable, and bear the same relation to each other that an object bears to its reflected image in a mirror, or that a right-hand glove bears to a glove for the left hand. This peculiar behaviour is generally associated with another remarkable property, viz. the bodies are optically active. One turns the plane of polarised light to the right, to the same extent that the other does to the left. The bodies thus acting on polarised light are divided into two classes. Some substances are optically active only when they are in a solid and crystalline state; others are optically active as liquids, either in solution or in a molten state; and a few gases or vapours are optically active. The members of the first class either crystallise in the regular form or are uniaxial and crystallise in the quadratic or hexagonal systems. If the two kinds of crystals are placed in parallel lines it is noticed that certain hemihedral faces which occur on the right side of the one set of crystals are found on the left side of the other crystals.

Cinnabar, quartz in the form of rock crystal, chlorates, bromates, periodates, thiosulphates, sodium sulphantimoniate, and some organic bodies belong to this class.

As the rotation of light by these substances depends on their crystalline form and ceases when the substances are brought into the liquid state by fusion or by solution, it is evident that the rotation is not due to the nature of the molecules, but is caused

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by a peculiarity in their arrangement. It is assumed that the molecules are arranged in a spiral form, and that in one form of crystal the spiral turns to the right and in the other to the left.

The second class of optically active compounds exhibits this property in the liquid state. In these cases the molecules are free to move about and do not take up fixed positions. Hence it appears that the rotation of light is not due to the relative position of the molecules, but to their peculiar nature.

Of course this does not exclude the possibility of these substances (if they are capable of crystallising) exhibiting a peculiar arrangement of the molecules. This is indeed the case with many compounds; e.g.tartaric acid (C,H,O) crystallises in two different forms, which are non-superposable and bear the same relation to each other that an object does to its reflected image. Only a few of these compounds crystallise in the regular system (amylamine alum) or are optically uniaxial (strychnine sulphate): these bodies rotate the plane of polarised light in the crystalline state.

Most of these substances belong to the rhombic, monoclinic, or triclinic systems, and form optically biaxial crystals, which do not exhibit the phenomenon of rotation.

§ 56. Asymmetrically linked Carbon Atoms.-In investigating the cause of the rotation of light due to the nature of the molecules, it is important to notice that this peculiar phenomenon is only observed in organic compounds, and only a comparatively small number of carbon compounds exhibit this property. This observation led to the hypothesis that the phenomenon is due to a peculiarity in the linking of the atoms. In fact, in 1874 two different investigators, Van t' Hoff and Le Bel, independently discovered the connection existing between the rotation of light and atomic linking and offered a perfectly satisfactory explanation of this optical isomerism.

As stated in § 43, the four affinities of a carbon atom are uniformly arranged in space, and consequently the four atoms united to the carbon atom are arranged round it like the four corners of a tetrahedron round its centre. If these four atoms all differ from each other either in their nature or in being combined with different atoms, then two forms of combination are possible. These are sketched in perspective and numbered I. and II.

The four atoms or radicals, a, b, c, d, are attached to the carbon

atom in such a way that the two figures are non-superposable, and one is the reflected image of the other. Imagine your eye is placed in the position of one of the atoms, say a, and directed towards the other three atoms; then it sees b c d in I. in the direction in which the hand of a clock moves, but in II. in the reverse direction.

A carbon atom in this condition is said to be an unsymmetrically linked carbon atom, or briefly an asymmetrical carbon atom. A careful examination of all those compounds which can in the liquid state rotate light shows that each of these bodies contains at least one asymmetrical carbon atom; several contain more than one. The property of rotation depends on the presence of an asymmetric carbon atom.

Let a=H, b=HO, c=COOH, d=CH2; these groups are contained in malic and tartaric acids: both of these acids exist in two symmetrical forms.

According to the formulæ generally in use, only one form of malic acid is possible, viz.

HO—COCH–CH,CO–OH

OH

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But if we take into consideration the fact that the carbon atom attached to the HO group is asymmetrical, then two formulæ are possible. Starting from the hydroxyl, the sequence of the other atoms or radicals is in the direction of the hands of a clock in one formula—

H,CO-OH,CH,-CO-OH

and in the reverse direction in the other—

H,CH2-CO-OH,CO—OH.

The two formulæ are non-superposable.1

$57. Active and Inactive Forms.-The rotatory power of a compound ceases when the asymmetrical carbon atom disappears; for example, malic acid is converted by reduction into succinic acid

HO–CO–CH,CH, CO–OH

which is inactive.

The rotatory power also ceases when equivalent quantities of both modifications unite and crystallise together. For example, the two optically active malic acids unite and form an inactive acid because the rotatory power of the one neutralises that of the other. In such cases the components may be separated by means of suitable agents; for example, one constituent may combine more readily with other dextrogyrate bodies; the other may unite more easily with other lævogyrate compounds. We are acquainted with two optically active malic acids which unite together, forming an inactive modification.

If a compound contains two asymmetrical carbon atoms which are united to similar atoms or radicals, then there can exist two optically active and two inactive forms. This is the case with regard to tartaric acid; we have dextro- and lævo-tartaric acid. One inactive acid (racemic) is a compound of the two active forms, but the second acid owes its inactivity to the

1 To make this point perfectly clear, divide the surface of two wooden balls of the same size into eight equal spherical triangles or quadrants by means of three circles cutting each other at right angles. Bore a hole down to the centre of the globe in the middle of each alternate quadrant. Insert four rods of equal length, one in each hole: these indicate the direction of the forces of affinity. Fix four balls of different colours to the free ends of the rods, and you have a representation of an asymmetrical carbon atom. According to the sequence of the coloured balls, the groups will be either identical or symmetrical, i.e. the reflected image of each other.