Thermodynamics of Transformation Reactions

Since most of the reactions discussed in the following chapters take place in aqueous media, we confine our thermodynamic considerations to reactions occurring in dilute aqueous solutions. For the gas-phase reactions of organic compounds with highly reactive oxidants (i.e., reactions in the atmosphere Chapter 16), we will assume that these reactions are always energetically favorable and, thus, proceed spontaneously. 

In Chapter 8, where we treated acid-base equilibria, we have seen that when dealing with reactions in dilute aqueous solutions, the appropriate choice of reference state for solutes is the infinite dilution state in water. The chemical potential of a compound i can then be expressed as  

The quantity dG/dnT, which is a measure of the free energy change in the system as the reaction progresses, is referred to as the free energy of reaction, which we denote as ArG. We use the subscript r to distinguish the free energy of reaction from the free energy of transfer that we used in Part II. Hence, 

Inserting Eq. 8-3 for each species taking part in the reaction into Eq. 12-3, and assessing a standard concentration [/]0 = 1 M for all species considered [note that, of course, 1 M is a hypothetical concentration for most of the organic compounds of interest, because their water solubilities are usually much lower (see Chapter 5)], we then obtain after some rearrangements  

The algebraic sum of the standard chemical potentials of the products and reactants is called the standard free energy of reaction, and is denoted as ArG°  

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Reversible reactions are those in which appreciable quantities of all reactant and product species coexist at equilibrium. For these reactions the rate that is observed in the laboratory is a reflection of the interaction between the rate at which reactant species are transformed into product molecules and the rate of the reverse transformation. The ultimate composition of the systems in which such reactions occur is dictated not by exhaustion of the limiting reagent, but by the constraints imposed by the thermodynamics of the reaction. 

In Chapter 8, we addressed proton transfer reactions, which we have assumed to occur at much higher rates as compared to all other processes. So in this case we always considered equilibrium to be established instantaneously. For the reactions discussed in the following chapters, however, this assumption does not generally hold, since we are dealing with reactions that occur at much slower rates. Hence, our major focus will not be on thermodynamic, but rather on kinetic aspects of transformation reactions of organic chemicals. In Section 12.3 we will therefore discuss the mathematical framework that we need to describe zero-, first- and second-order reactions. We will also show how to solve somewhat more complicated problems such as enzyme kinetics. 

The sequence of their occurrence is determined by the rates of chemical transformations at the interfaces. It cannot yet be theoretically predicted with full confidence for any particular reaction couple A-B. Having sufficient information on the equilibrium phase diagram, thermodynamics of chemical reactions, and the structure and physical-chemical properties of the compounds, it is possible to indicate those of them, which are most likely to occur and grow first at the A-B interface. 

The calculation of Af G° and Af H° of species from experimental data on apparent equilibrium constants and transformed enthalpies of reaction is described in R. A. Alberty, Thermodynamics of Biochemical Reactions, Wiley, Hoboken, NJ (2003) and a number of places in the literature. That is not discussed here because this package is oriented toward the derivation of mathematical functions to calculate thermodynamic properties at specified T, pH, and ionic strength. There are two types of biochemical reactants in the database ... 

Quoted in the fignre are the key quantities that determine E( ) with the reaction energy (AE°) giving the thermodynamic of the reaction and the activation energy (AE ) accounting for the kinetic information, both are crucial properties of the reaction that help characterize the chemical transformation. Also characterized on the figure are the respective activation and relaxation processes. Many chemical reactions require more than one elementary step to reach the products of the reaction in such cases, the whole chemical process may be defined through a sequence of such elementary steps. The reaction force F( ) is defined... 

Depending on the nature of the class, the instructor may wish to spend more time with the basics, such as the mass balance concept, chemical equilibria, and simple transport scenarios more advanced material, such as transient well dynamics, superposition, temperature dependencies, activity coefficients, the thermodynamics of redox reactions, and Monod kinetics, may be omitted. Similarly, by excluding Chapter 4, an instructor can use the text for a course focused only on the water environment. In the case of a more advanced class, the instructor is encomaged to expand on the material suggested additions include more rigorous derivation of the transport equations, discussions of chemical reaction mechanisms, introduction of quantitative models for atmospheric chemical transformations, use of computer software for more complex chemical equilibrium problems and groundwater transport simulations, and inclusion of case studies. References are provided with each chapter to assist the more advanced student in seeking additional material. 

Reactant and product structures. Because the transition state stmcture is normally different from but intermediate to those of the initial and final states, it is evident that the stmctures of the reactants and products should be known. One should, however, be aware of a possible source of misinterpretation. Suppose the products generated in the reaction of kinetic interest undergo conversion, on a time scale fast relative to the experimental manipulations, to thermodynamically more stable substances then the observed products will not be the actual products of the reaction. In this case the products are said to be under thermodynamic control rather than kinetic control. A possible example has been given in the earlier description of the reaction of hydroxide ion with ester, when it seems likely that the products are the carboxylic acid and the alkoxide ion, which, however, are transformed in accordance with the relative acidities of carboxylic acids and alcohols into the isolated products of carboxylate salt and alcohol. 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

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