Thermodynamics chemical reaction systems, fundamental equations

In order to make design or operation decisions a process engineer uses a process model. A process model is a set of mathematical equations that allows one to predict the behavior of a chemical process system. Mathematical models can be fundamental, empirical, or (more often) a combination of the two. Fundamental models are based on known physical-chemical relationships, such as the conservation of mass and energy, as well as thermodynamic (phase equilibria, etc.) and transport phenomena and reaction kinetics. An empirical model is often a simple regression of dependent variables as a function of independent variables. In this section, we focus on the development of process models, while Section III focuses on their numerical solution. 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

In this chapter, we summarize the fundamental thermodynamic relationships relevant to chemical equilibria. Particular attention will be given to the thermodynamics of adsorption and the derivation of adsorption isotherms. Equations relating the effect of temperature on chemical equilibria are derived. The solution methods of chemical equilibria for complex reaction systems are presented. 

Solution of the model for a particular problem requires specification of the chemical species considered, their respective possible reactions, supporting thermodynamic data, grid geometry, and kinetics at the metal/solution interface. The simulation domain is then broken into a set of calculation nodes that may be spaced more closely where gradients are highest (Fig. 6.22). Fundamental equations describing the many aspects of chemical interactions and species movement are finally made discrete in readily computable forms. The model was tested by comparing its output with the results of several experiments with three systems ... 

A mechanical system, typified by a pendulum, can oscillate around a position of final equilibrium. Chemical systems cannot do so, because of the fundamental law of thermodynamics that at all times AG > 0 when the system is not at equilibrium. There is nonetheless the occasional chemical system in which intermediates oscillate in concentration during the course of the reaction. Products, too, are formed at oscillating rates. This striking phenomenon of oscillatory behavior can be shown to occur when there are dual sets of solutions to the steady-state equations. The full mathematical treatment of this phenomenon and of instability will not be given, but a simplified version will be presented. With two sets of steady-state concentrations for the intermediates, no sooner is one set established than the consequent other changes cause the system to pass quickly to the other set, and vice versa. In effect, this establishes a chemical feedback loop. 

Thermodynamics is essential to understand the physicochemical properties of the individual reactants, solvents, and products involved (Chapter 2). Also, it provides information on the interaction between the various components present in the reaction mixture, from which phenomena such as phase behavior and partitioning can be derived. This information is usually accessible by using the appropriate equation of state for a given system studied. A close collaboration between chemical physicists, chemists, and chemical engineers is required to take full advantage of this fundamental knowledge. 

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