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'Why are atoms so small?' asks 'naive physicist' in Erwin Schrodinger's book 'What is Life? The Physical Aspect of the Living Cell'. 'The question is wrong' answers the author, 'the actual problem is why we are built of such an enormous number of these particles'. The idea that everything is built of atoms is quite an old one. It seems that l Democritus himself borrowed it from some obscure Phoenician source . The arguments for the existence of small indivisible units of matter were quite simple. 2 According to Lucretius observable matter would disappear by 'wear and tear' (the world exists for a sufficiently long, if not infinitely long time) unless there are some units which cannot be further split into parts. th However, in the middle of the 19 century any reference to the atomic structure of matter was considered among European physicists as a sign of extremely bad taste and provinciality. The hypothesis of the ancient Greeks (for Lucretius had translated Epicurean philosophy into Latin hexameters) was at that time seen as bringing nothing positive to exact science. The properties of gaseous, liquid and solid bodies, as well as the behaviour of heat and energy, were successfully described by the rapidly developing science of thermodynamics.

Inhaltsverzeichnis

Frontmatter

1. Maxwell — Boltzmann Statistics

Abstract
The original explanation of the action of a thermal engine was a very mechanistic one: heat or phlogistic fluid falls from a higher to a lower temperature. This model was developed by the French scientist Sadi Carnot who actually himself found it to be not completely correct: it leads to the principle of conservation of heat (which in fact does not hold). The correct answer was given later by Clausius: the temperature is not the coordinate playing the role of potential (the vertical coordinate in the case of falling material bodies) but rather an analogue of a force. Notwithstanding its incorrectness, the idea that the passing of heat from high temperature bodies to low temperature bodies must be connected with a kind of ‘work’ was very fruitful. Thermodynamics as a branch of physics explaining specific laws of the ‘movement’ and transformation of heat is based on this idea.
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

2. Ensembles, Partition Functions, and Thermodynamic Functions

Abstract
Maxwell — Boltzmann statistics, with corrections for the quantum character of energy changes and the indistinguishable nature of molecules, works perfectly well when we consider systems of non-interacting molecules. If particles are interacting with each other, then the description of such systems by Maxwell — Boltzmann statistics becomes extremely difficult if not impossible. For example, consider a system of positive and negative ions interacting in pairs. The potential energy of such a system is:
$$ U = \sum\limits_i {\sum\limits_j {\frac{{e_i e_j }} {{2r_{ij} }}} } $$
(2.1)
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

3. The Law of Mass Action for Ideal Systems

Abstract
One of the peculiarities of the development of science was that the law of mass action was at first established as the kinetic law of mass action. In fact, chemists were anxious to find some parameter that would characterise the ability of compounds to react and form the required products. The reaction rates seemed to provide such a parameter but it was not that simple. The history of chemical discoveries that led to the formulation of the law of mass action is very important for an understanding of the contemporary interpretation of this rule. Glasstone [1], after mentioning the names of Albertus Magnus, Boyle, Newton and other precursors, described it as follows (italics are ours).
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

4. Reactions in Imperfect Condensed Systems. Free Volume

Abstract
One of the earliest theories of the liquid state developed by Jäger [1] described an’ ideal liquid’ as a collection of hard spheres of finite diameters comparable to the distances between their centres and held together by cohesive internal pressure. As has been mentioned in Chapter 3, the admission of finite diameters of molecules introduces repulsive interactions and the system of such particles cannot be considered as ideal. In fact, the ideal liquid of Jäger is a slightly imperfect liquid in which repulsive interactions are accounted for in the semi-empirical form of the finite volumes of molecules. Attractive interactions in the form of cohesive internal pressure are introduced irrespective of any molecular model.
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

5. Molecular Interactions

Abstract
In the preceding Chapter we introduced the effects of molecular interactions into the law of mass action assuming a formal dependence of free volume on the composition of reaction mixtures. In dilute solutions these effects reveal themselves by dependence of the equilibrium constant on molecular volume and vaporisation energy of the solvent, whereas in concentrated solutions deflections of van’t Hoff plots from linearity may be observed. A theoretical description of these phenomena requires a knowledge of the actual equation of state and/or the shape of the intermolecular potential. A very rough model has been used in order to obtain the relationship between free volume, volume and internal pressure. Nevertheless, the formalism derived explained a number of deviations of the law of mass action from ideality and predicted some critical phenomena.
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

6. Imperfect Gases

Abstract
In this Chapter we will investigate the effects of molecular interactions on the form of the law of mass action for equilibria in the gas phase. The volume of a gaseous system is directly connected with the number of molecules, and therefore a knowledge of the actual equation of state is important for the study of reactions in gases. In an ideal gas the volume of a system at constant pressure is linearly dependent on the number of molecules. A large number of empirical equations of state have been suggested for the description of real gases, among which the van der Waals equation is the most famous.
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

7. Reactions in Imperfect Condensed Systems. Lattice Energy

Abstract
In Chapter 4 we considered reactions in imperfect liquids on the basis of a semi-empirical and generally phenomenological model based on the assumption of the additivity of volume and energy of molecular interactions. This assumption implies the independence of molecular volumes and lattice energies of composition. It can also be said that under these conditions the energy of a molecule is independent of the nature of its surroundings. The non-ideality then reveals itself in the dependence of the free volume on composition. The lattice energy, when additive, contributes towards the standard internal energy of reaction and does not introduce any additional non-ideality terms into the equation of the law of mass action.
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

8. Chemical Correlations

Abstract
The law of mass action establishes a measure of chemical affinity in the form of equilibrium or rate constants or their equivalent, the standard free energies of reaction or activation. This is the first step in the formulation of the rules connecting chemical structure and reactivity. Statistical mechanics explains the origin of the relationship between molecular parameters and standard free energy of reaction or activation and enables corresponding formulae to be derived. However, quantitative calculations are (or rather were) only possible for a small number of simple reactions. Therefore, for the majority of practically important cases, a number of empirical correlations has been developed, effectively substituting variations of chemical reactivity and modification of the reaction mixture for theoretical relationships.
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

9. Concluding Remarks

Abstract
In the preceding Chapters several approaches to the problem of the derivation of the law of mass action for ideal and non-ideal systems based on molecular theory of solutions have been described. The main conclusions following from this material are systematised below in the most general form. Relationships presented admit an easy reduction to practically applicable equations by employing methods described in the corresponding Chapters and illustrated by numerous examples.
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

10. Appendices

Abstract
The laws of mechanics formulated by Newton only implicitly contain the concept of energy, a concept by far more general than the velocity, momentum and coordinates of a moving body. The law of conservation energy is one of the most general laws, revealing itself not only in the dynamics of moving bodies but also in electrical and chemical processes and in the processes of transformation of heat. It must also be mentioned that mathematical equations employing the concept of energy were introduced by Lagrange (1788) and Hamilton (1834) long before the energy ceased to be called ‘life force’ and the law of conservation of energy was formulated quantitatively. One of the most general principles of classical mechanics is the principle of least action formulated by Hamilton. According to this principle, the trajectory of a moving body corresponds to the least value of the integral W called the action or function of action:
$$ W = \int\limits_{t_0 }^{t_1 } {Ldt} $$
(10.1)
Andrei Koudriavtsev, Reginald F. Jameson, Wolfgang Linert

Backmatter

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