Introduction

The study of the energetics of chemical reactions introduces the topics of thermodynamics and thermochemistry. Thermodynamics is a study of matter in bulk that is concerned with energy changes in systems, chemical or mechanical, whereas thermochemistry is the study of heat changes in chemical reactions and is, thus, a branch of thermodynamics. Thermodynamics allows us to predict whether or not a reaction, say A→B, will occur spontaneously, that is, with a decrease in the energy of the system. It does not indicate the speed of the reaction, or even whether it will take place at all without the assistance of heat, irradiation or a catalyst; for this information we shall study reaction kinetics in a later chapter.

General laws of thermodynamics

Thermodynamics rests upon three fundamental principles, the laws of thermodynamics. The laws apply, in the most general sense, to the universe as a whole, and may be given in the following form.

The energy of the universe is constant, whatever processes take place in it.

The entropy of the universe increases, whatever processes take place in it, and must, therefore, tend towards a maximum value.

The absolute scale of temperature has a minimum value, absolute zero, and the entropy of any perfect, crystalline substance is zero at that temperature.

The development of the subject is based on these laws and we shall investigate how they are used in understanding reactions in chemistry.

Introduction

The determination of the structures of chemical species is an important and absorbing aspect of physical chemistry. Many methods have been devised as the subject of structure determination has developed, but among the most rewarding techniques currently in practice are those based either on spectroscopic or on diffraction methods. The extent of each of these fields is considerable, and here we shall introduce only parts of them. It is important in structure determination to acquire a knowledge of symmetry, and the application of symmetry principles in chemistry is far reaching. We give first a brief introduction to the symmetry of three-dimensional, finite bodies and its application in chemistry.

Symmetry concepts

We can see evidence of symmetry all around us; it is not just a feature of molecules and crystals. The emblems associated with the National Westminster Bank plc, the Isle of Man and Mercedes-Benz cars all reveal threefold symmetry; the latter shows other symmetry as well. The splendid Dobermann in Figure 3.1 illustrates reflection symmetry about a vertical, medial plane through her.

A symmetry operation applied to a molecule, or other body, moves it into a state that is indistinguishable from its initial state, thereby revealing the symmetry inherent in the body. We may link a symmetry operation with a symmetry element, which is a conceptual geometrical entity (point, line or plane) with respect to which a symmetry operation may be said to be performed.

Introduction

Matter exists in three states, gaseous, liquid and solid. It is convenient to discuss the properties of matter under these main headings, although certains types of substances, such as vitreous materials and liquid crystals, do not fall clearly into one or other of them.

The gaseous state is the most straightforward to study. The simplicity arises from the fact that the molecules of a gas are, normally, independent of one another, with negligible forces of interaction. Consequently, many of their properties are independent of their chemical nature and may be described by general gas laws; we have made use of this fact in the previous chapter and here we describe these laws in more detail.

Gases are characterized by large volume changes with change of temperature or pressure and by their ability to flow into and fill the space available to them; they are miscible with one another in all proportions. A liquid, like a gas, has no form, but it has a definite volume and takes up the shape of its containing vessel. It has a boundary surface that restricts its extent and which is responsible for many of its properties. The cohesive forces between molecules in a liquid are stronger than those between molecules in a gas, but weaker than those characteristic of solids. Under normal conditions, gases behave as an assemblage of freely moving molecules or atoms, whereas solids form rigid structures.

Introduction

A solid has a definite volume and shape, neither of which changes appreciably with changes in temperature or pressure. A study of the solid state is principally a study of crystalline materials, since almost all solids form crystals. Certain solids are described as amorphous: in some cases they are microcrystalline, but other examples, such as glass or many polymers, do not have the regularity in structure that is associated with true crystals. The term amorphous is best restricted to those solids in which order extends over only a few atomic dimensions. In crystals, the atoms or molecules are arranged on, or in a fixed relation to, the points of a Bravais lattice, where they vibrate about their mean positions. The mean positions are, normally, invariant with time, and the vibrational energy is a major contributory factor to the heat capacity of the solid.

The atomic vibrations are anharmonic (see also Section 3.6.5.1), so that an increase in temperature causes an increase in the distance between the mean positions of the atoms and the material expands. Even if the vibrations were harmonic, the increase in free energy with temperature would lead to an increase in volume, although the expansion from this source is, normally, a second-order effect.

The time-invariance of mean atomic positions may be invalidated by disorder. In some solids, atoms may exhibit free rotation (dynamic disorder) in the solid state, or they may show static disorder.

The representation of molecular and crystal structures by stereoscopic pairs of drawings has become commonplace in recent years. Computer programs are available that prepare stereoviews from structural data. Two diagrams of a given object are necessary and they must correspond to the views seen by the eyes in normal vision. Correct stereoscopic viewing requires that each eye sees only the appropriate drawing, and there are several ways in which it may be accomplished.

1. A stereoviewer may be purchased for a modest sum. The stereoscopic drawing may be viewed directly, and the three-dimensional image appears centrally between the images of the two given drawings. Two suppliers of stereoviewers are:

2. (a) Casella & Co Ltd, Regent House, Britannia Walk, London N1 7ND;

3. (b) Taylor-Merchant, 212 West 35th Street, New York, NY10001.

4. The unaided eyes can be trained to defocus, so that each eye sees only the appropriate diagram. The eyes must be relaxed and look straight ahead. This process may be aided by placing a white card edgeways between the two drawings. It may be helpful to close the eyes for a moment, open them wide without attempting to focus on the diagram, and then allow them to relax. Again, the stereoview appears centrally with respect to the left and right pair of images.