Homogeneous kinetics constant volume system

The solution procedure to this equation is the same as described for the temporal isothermal species equations described above. In addition, the associated temperature sensitivity equation can be simply obtained by taking the derivative of Eq. (2.87) with respect to each of the input parameters to the model. The governing equations for similar types of homogeneous reaction systems can be developed for constant volume systems, and stirred and plug flow reactors as described in Chapters 3 and 4 and elsewhere [31-37], The solution to homogeneous systems described by Eq. (2.81) and Eq. (2.87) are often used to study reaction mechanisms in the absence of mass diffusion. These equations (or very similar ones) can approximate the chemical kinetics in flow reactor and shock tube experiments, which are frequently used for developing hydrocarbon combustion reaction mechanisms. 

Another useful technique in kinetic studies is the measurement of the total pressure in an isothermal constant volume system. This method is employed to follow the course of homogeneous gas phase reactions that involve a change in the total number of gaseous molecules present in the reaction system. An example is the hydrogenation of an alkene over a catalyst (e.g., platinum, palladium, or nickel catalyst) to yield an alkane ... 

The production of species i (number of moles per unit volume and time) is the velocity of reaction,. In the same sense, one understands the molar flux, jh of particles / per unit cross section and unit time. In a linear theory, the rate and the deviation from equilibrium are proportional to each other. The factors of proportionality are called reaction rate constants and transport coefficients respectively. They are state properties and thus depend only on the (local) thermodynamic state variables and not on their derivatives. They can be rationalized by crystal dynamics and atomic kinetics with the help of statistical theories. Irreversible thermodynamics is the theory of the rates of chemical processes in both spatially homogeneous systems (homogeneous reactions) and inhomogeneous systems (transport processes). If transport processes occur in multiphase systems, one is dealing with heterogeneous reactions. Heterogeneous systems stop reacting once one or more of the reactants are consumed and the systems became nonvariant. 

Supercritical solvents can be used to adjust reaction rate constants (k) by as much as two orders of magnitude by small changes in the system pressure. Activation volumes (slopes of In k vs P) as low as —6000 cm3/mol were observed for a homogeneous reaction (97). Pressure effects can also be pronounced on reversible reactions (17). In one example the equilibrium constant was increased from two- to sixfold by increasing the solvent pressure. The choice of supercritical solvent can also dramatically affect an equilibrium constant. An obvious advantage of using supercritical fluid solvents as a media for chemical reactions is the adjustability of the reaction kinetics and equilibria owing to solvent effects. 

The analytical problems associated with differential reactors can be overcome by the use of the recirculation reactor. A simplified form, called a Schwab reactor, is described by Weisz and Prater . Boreskov.and other Russian workers have described a number of other modifications " . The recirculation reactor is equivalent kinetically to the well-stirred continuous reactor or backmix reactor , which is widely used for homogeneous liquid phase reactions. Fig. 28 illustrates the principle of this system. The reactor consists of a loop containing a volume of catalyst V and a circulating pump which can recycle gas at a much higher rate, G, than the constant feed and, withdrawal rates F. 

Volume II Properties of Matter in its Aggregated States. Part 1 Mechanical-Thermal Properties of States (1971), Part 2 Equilibria except Fusion Equilibria, Part 2a Equilibria Vapor-Condensate and Osmotic Phenomena (1960), Part 2b Solution Equilibria 1 (1962), Part 2c Solution Equilibria 11 (1964), Part 3 Fusion Equilibria and Interfacial Phenomena (1956), Part 4 Caloric Quantities of State (1961), Part 5a Transport Phenomena I (Viscosity and Diffusion) (1969), Part 5b Transport Phenomena 11 (Kinetics. Homogenous Gas Equilibria), (1968), Part 6 Electrical Properties 1 (1959), Part 7 Electrical Properties 11 (Electrochemical Systems) (1960), Part 8 Optical Constants (1962), Part 9 Magnetic Properties I (1962), Part 10 Magnetic Properties II (1967). 

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