The extension of the gaseous laws into the domain of soiutions necessitates the hypothesis that in the case of some solutions the molecules of the dissolved substance unite to form more complicated molecular associations; while in other cases (including those substances which are electrolytes, such as the solutions of strong acids, bases, and salts) the molecules of the substances undergo dissociation into their ions. For, just as in the case of gases where departures from the strict gaseous laws are seen to take place, on account of the dissociation in some instances, and the association in others, of the various molecules; so it is believed that the deviations from the strict continuity of the ideal gaseous laws into the realm of solution are due to the operation of similar causes.

CRYSTALLINE FORMS.

When a saturated solution of a solid in a liquid is either cooled or allowed to evaporate, the dissolved solid begins to deposit, and it does so in most cases in definite geometric shapes, termed crystals. (Solids which exhibit no crystalline structure are said to be amorphous.)

The same arrangement of molecules into geometric forms often takes place when substances in a state of fusion (as distinguished from solution) pass into the solid condition, as, for example, when melted sulphur, or mercury, or water are cooled to their respective solidifying points; and it also frequently takes place when vapours condense to the solid state.

The more slowly the process of solidification takes place, the larger and more symmetrical are the crystals that are formed.

The variety of geometric forms that are met with in naturally occurring and artificially produced crystals is practically infinite. They are, however, susceptible of a classification, based upon their development with respect to certain imaginary planes, called the planes of symmetry. These are planes cut through the crystal in such a manner, that the divided portions are the mirrored reflections the one of the other, the mirror being the plane itself. All crystals may be referred to one or other of six great families, according to their symmetry, known as crystallographic systems. I. The Regular system. Crystals belonging to this system have nine planes of symmetry, namely, three principal planes at right angles to each other, and six others which

intersect one another at angles of 60°. Forms of this system (such, for example, as the cube) possess the highest possible order of symmetry.

II. The Hexagonal system. Crystals having seven planes of symmetry, namely, one principal plane, normal to a vertical axis in the crystal, and six other planes at right angles to the principal plane, and intersecting each other at angles of 30°.

III. The Quadratic system. Embracing crystals having five planes of symmetry, namely, one principal plane, normal to a vertical axis in the crystal, and four other planes at right angles to the principal plane, and intersecting each other at angles of 45°.

IV. The Rhombic system. Including crystals having three planes of symmetry at right angles to each other.

V. The Monosymmetric or Monoclinic system. Crystals with only one plane of symmetry.

VI. The Asymmetric or Triclinic system. Including crystals which have no plane of symmetry. The forms belonging

to this system having symmetry with respect to a point only.

This system of classification brings the various crystalline forms into direct relations with many of the physical properties possessed by crystals, such, for example, as their optical characters: thus, in the Regular system, the crystals in their normal condition are singly refracting crystals—they are said to be isotropic. In the Hexagonal and Quadratic systems they are optically uniaxial; while in the Rhombic, Monosymmetric, and Asymmetric systems they are all optically biaxial.

*

All crystals may be regarded as derivations from certain typical forms belonging to one of these six systems. One of the simplest forms of each system is the double pyramid, which in the hexagonal system takes the shape of a double six-sided pyramid, and in the remaining systems that of a double four-sided pyramid, or octahedron. Thus we have the regular octahedron, the quadratic octahedron, the rhombic octahedron, and so on.

By the development of certain related faces, the octahedron passes

* The study of the relations between the various derivatives and the simpler types forms a part of the science of crystallography, and falls outside the scope of a general chemical text-book.

L

into the prism, hence we get the quadratic prism, the rhombic prism, the hexagonal prism, &c. It will be obvious, therefore, that the description of a crystal as being prismatic, or octahedral, in form, is incomplete unless the particular system to which it is referred be also stated.

Crystals, whether naturally occurring or artificially obtained, very seldom exhibit the perfect symmetry of the ideal form. By great care, however, in regulating the formation of a crystal, by the maintenance of a constant temperature, and controlling the rate of evaporation of the solvent, it is possible to cause crystals to grow in such a way that they will approach very closely to the ideal geometric form. Fig. 149* represents crystals of alum, in the form of regular octahedra, or double four-sided pyramids, which were obtained by careful crystallisation from aqueous solution; and it will be seen how near to the ideal they approach. In Fig. 110,* also, are seen illustrations of crystals of sulphur, in the form of rhombic octahedra. These crystals were produced by the carefully controlled deposition of the sulphur, from a solution of the element in carbon disulphide, and they illustrate the kind of variations in the form that are introduced by the development of new faces. Fig. 150* shows a group of naturally occurring crystals, namely, quartz, in the form of hexagonal prisms, terminating in hexagonal pyramids.

In order to determine the system to which a given crystal belongs, it is necessary to make a number of accurate measurements of its angles, and since the inclinations of the faces to one another bear geometric relations to the planes of symmetry, and the inclinations of these planes towards each other, these latter may be calculated from the former values. The instruments by means of which such measures are made are termed goniometers.

Two or more substances which crystallise in the same form are said to be isomorphous (see page 51), and, on the other hand, a substance which is capable of crystallising in two forms which do not belong to the same system is termed a dimorphous substance. Thus sulphur is dimorphous, as it is capable of crystallising in the form of rhombic octahedra (Fig. 110), and in monosymmetric prisms (Fig. 111).

Occasionally a dimorphous substance is isomorphous with another dimorphous body, in both its forms. To this double isomorphism the term isodimorphism is applied.

* From a photograph of the actual crystals.

CHAPTER XV

THERMO-CHEMISTRY

WE have seen that by means of symbols and formulæ chemists express, in the form of equations, a certain amount of information respecting chemical changes: thus by the equation C+O, CO2 there are conveyed the facts, that carbon unites with oxygen to form carbon dioxide, that 12 grammes of carbon combine with 32 grammes of oxygen, yielding 44 grammes of carbon dioxide, and that the volume of the gaseous carbon dioxide obtained is the same as that of the oxygen taking part in its formation. All such equations bear upon the face of them the truth, that matter can neither be destroyed nor created. The total quantity of matter taking part in the action is unaltered by the process, although it appears in altered form in the products of the reaction.

In all chemical changes, besides matter, energy also takes a part; not only do the materials concerned undergo rearrangement or readjustment, but at the same time there is a rearrangement or readjustment of energy. This energy change is not expressed by the ordinary symbolic equation. Thus in the equation

SO2+ H2O = H2SO4

the fact is embodied that 80 grammes of sulphur trioxide combine with 18 grammes of water and form 98 grammes of sulphuric acid; but the equation takes no cognisance of the fact, that when these weights of these two substances unite to form 98 grammes of sulphuric acid an amount of energy, in the form of heat, is disengaged that would raise the temperature of 213 grammes of water from o° to the boiling-point.

Similarly, in the equation 2NCI ̧=N2+3C1, there is no recognition of the fact that during this change an enormous amount of energy leaves the system in the form of external work (overcoming the atmospheric pressure); in other words, that the conversion of nitrogen trichloride into its constituent elements is attended with the most violent explosion.

Energy, like matter, can neither be created nor destroyed, but as a result of chemical action it reappears as energy in another form. Thus it may appear as heat, as electrical energy, as kinetic energy, or as chemical energy; and just as the total amount of matter taking part in a chemical change reappears in altered form in the products of the change, so the disappearance of energy in any of its forms gives rise to the reappearance of a proportionate amount of energy in another form. This is the law of the conservation of energy, which may be thus stated: * "The total energy of any material system is a quantity which can neither be increased nor diminished by any action between the parts of the system, although it may be transformed into any of the forms of which energy is susceptible."

Chemical energy, or that form of energy that is set free during chemical processes, cannot be measured by any direct method. This energy, however, is generally transformed, during chemical change, into heat, and may therefore be measured by, and expressed in, heat units. Thermo-chemistry may therefore be defined as the science of the thermal changes which accompany chemical changes.

All matter is regarded as containing a certain amount of energy in some form, and the purpose of thermo-chemistry is, by measuring the thermal disturbance that is conditioned by a chemical change, to ascertain the difference between the amount of energy contained in a system before and after such a change.

If all the energy of a system in its original state (i.e. before the chemical change takes place) that undergoes transformation into other forms of energy passes into heat; if none of it leaves the system as energy in some other form, and thereby escapes measurement; then the difference between the amount of energy contained in the system in its original and its final state may be ascertained. It by no means follows, however, that this represents the chemical energy alone; it has already been explained that chemical changes are always attended by physical changes, such as change of volume, of physical state, and so on, and we have also learned that such physical changes are likewise accompanied by thermal changes; the problem, therefore, is often a complicated one, and it is not always possible to differentiate between the chemical and the physical causes that may be operating simultaneously, and to decide what share of the final result is due to the chemical phase

Clerk Maxwell, "Matter and Motion."