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In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter method based on a result developed by the authors is given to derive the solution of a fractional diffusion equation. Fox functions and Mittag-Leffler functions are used for closed-form representations of the solutions of the respective differential equations.

We show that a DNA-based chemical system can be constructed such that it closely approximates the dynamic behavior of an arbitrary system of coupled chemical reactions. Using strand displacement reactions as a primitive we explicitly construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows for individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, correctly reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into chemistry. We illustrate our method on a chaotic Rossler attractor; simulations of the attractor and of our proposed DNA-based implementation show good agreement.

To outline corrosion reaction chemistry we turn in the first place to acid corrosion, considering iron in dilute hydrochloric acid solution as a typical example. The reaction equation is $$ (\text{Fe})_m + 2(\text{HCl})_l \to (\text{FeCl})_l + (\text{H}_\text{2} )_g , $$ (2.1) where the subscripts m, l, and g indicate the phases solid metal, liquid aqueous solution, and gas, containing the species solid pure iron, dissolved hydrochloric acid, dissolved ferrous chloride, and gaseous hydrogen, respectively. When components of different phases participate in a reaction, this indexing is useful, but we shall drop it nevertheless whenever possible without danger of confusion, in order to simplify notation. The arrow ‘→’ indicates that the reaction spontaneously proceeds as written from left to right: metallic iron and dissolved hydrochloric acid are the reactants, dissolved ferrous chloride and gaseous hydrogen the products of the overall reaction.

A chemical reaction between the reactant species A a , A b , etc., that forms the product species A c , A d , etc., is often written as $${v_a}{A_a} + {v_b}{A_b} + \ldots \to {v_c}{A_c} + {v_d}{A_d} + \ldots $$ (6.1) where the v i are termed the stoichiometric coefficients of the reaction. Since every chemical reaction can generally proceed in both directions, the arrow in Eq. 6.1 may be replaced by an equal sign. The general form of the reaction equation now becomes $$ \sum\limits_i {{v_i}{A_i}} = 0 $$ (6.2) where, by convention, the stoichiometric coefficients v i are positive for the product species and negative for the reactant species.

This chapter reviews the most common methods by which coordination compounds are prepared. However, current research is almost invariably aimed at producing the unusual and exotic, not the common. So, a contemporary research journal would describe methods rather less simple than most of those covered here. A flavour of the current has therefore been included, although the reader is unlikely to meet some of the compounds outside the research laboratory. In the reactions described in this chapter, there are two important variables—coordination number and oxidation number (the latter is often called the valence state). In principle, either may increase, decrease or remain unchanged in a reaction, and the reader may find it helpful to classify the preparative methods described according to changes in these two numbers. In practice it is not always possible to be certain of either without more information than that contained within a chemical equation or chemical formula. A ligand which is potentially tridentate may, for example, act as a bidentate ligand and so the coordination number differs from that expected. Similarly, is the complex ion [Co(NH3)5NO]2+ a complex of cobalt(II) or one of cobalt(III)? It depends on whether you believe that the NO is better represented as NO˙ (where, in the complex, the odd electron is paired with a cobalt electron) or as NO-. This problem of formal valence states will reappear later in this chapter and again in Chapter 6.

Under ideal conditions the combustion of hydrocarbons leads to mainly carbon dioxide and water. Ideal conditions may be specified by stoichiometric composition of the combustible mixture, i.e. the oxygen content of the mixture everywhere is sufficient to convert the fuel completely according to the formal chemical equation $${C_x}{H_y} + \left( {x + y/4} \right){O_2} \to xC{O_2} + y/2{H_2}O$$ . Under these conditions a maximum of heat is released and a maximum of chemical energy is available for mechanical work.

CKB’s computer chemistry project CARSA (Computer-Assisted Research in Synthesis and Application) is a modular structured system, which at present consists of the following parts: WIFODATA (substance — and finding — documentation; database) QSAR (programs for quantitative structure-activity-relationships) RDSS (Reaction Design by Synthon Substitution; program package for synthesis planning) The system is devised as a tool for synthesis chemistry and of special importance in industrial research.

The question of how movement is brought about has been one of the most interesting unsolved problems in biology. Muscle contraction, active transport, and the synthesis of ATP by proton transport are coupled vectorial processes that interconvert the chemical energy of ATP and mechanical or osmotic work, often in reversible reactions. This is described by Eq. (1). The problem is to understand the meaning of the $${\text{ATP}}\rightleftharpoons{\text{ADP}} + {\text{Pi}} +{\text{work}}$$ (1) coupling in these systems, as described by this equation. It is not obvious how to think about a chemical equation of this kind; it is not useful to compare it with a steam engine or approach it with Carnot cycles or irreversible thermodynamics. We would like to define the questions that must be answered in order that we can say that we understand the mechanism of a coupled vectorial process.

As an introduction to the panel discussion I shall present a short review on chemical mechanisms for ATP synthesis by electron transport phosphorylation, which have been proposed in chemical equations or are on the tip of the tongue, but not expressed precisely in chemical terms. The different mechanistic proposals will be compared, if possible, with the related experience of inorganic and organic chemistry to give a chemical basis for the discussion of the enzymatic process.