Page - 4 - in Advanced Chemical Kinetics

Themathematical kinetics deals with the analysis of differentmathematical models used in directandinversechemicalkinetics.Thesemodelsrepresentasetofordinary/partialdifferential equationsandasetofalgebraicequations.Further,directkineticproblemsdealwiththeanalysis ofsteadystateornonsteadystatekineticmodelsconsistingofknownkineticparameters.Onthe other hand, an inverse kinetic problem reconstructs kinetic dependencies and estimates their parametersbasedonexperimentalkineticdata,eithersteadyornonsteadystate. Theconstructionof themathematicalmodel is thekeypartof chemicalkinetics,whichgivesa completedescriptionof reactionmechanismand its rates. It provides aworking tool tobetter understandanddesign chemicalprocesses, i.e., fooddecompositionand the complex chemis- try of biological systems, etc. These models are also used in designing the fast and slow trajectories of complex chemical reactions andmodification of chemical reactors to optimize product yield,more efficiently separateproducts, andeliminate environmentallyharmful by- products. In detailed kinetics, we study the reconstruction of detailed mechanism of reaction either based on kinetic or nonkinetic data. Thesemechanisms consist of a set of elementary steps having forward and reverse reactions alongwith the governing equation ofmass-action law for the kinetic dependencies. In catalyst reactions, it covers the reactant, products, intermedi- ate, surfaceproperties, reactionsteps, reactionroutes, adsorptionproperties, etc. Thegoalofappliedkinetics is tostudythekineticdependenceof therateofchemicalreactions on their involved or related conditions, i.e., temperature, pressure, concentration, and so on. This dependence can be related to a single or a series ofmathematicalmodels usually called kineticmodels.Thesekineticmodelsarenecessarytorepresent thehierarchyofmodelsateach stage, i.e., initial, intermediate, and final levels aswell as to develop an easyway formathe- matical simulationsofachemicalprocess. The reactions inwhich a singlemolecule rearranges itself tomake one ormore products are calledunimolecular reactions or a first-order reaction (A!B), like radioactivedecay inwhich particles are emitted from a single atom. The reactions inwhich twomolecules take part to form a product are called bimolecular reactions or second order (2A!B orA + B!C), like cycloadditionreaction.Thereactions inwhichthreeparticlescollideat thesameplaceandtime to formaproduct are called termolecular reactions or third order (3A!BorA + 2B!C). The third-order reactions are not very common as all the three reactants must have to collide simultaneously to formaproduct. The chemical reactions inwhich the reactants are in the samephases are calledhomogeneous reactions, i.e., the reaction between two gases, two solids, or two liquids. Let us consider a reversible chemical reactionrepresentedas X i αρiAi���! ���kþi k�i X i βρiBi, (1) here Ai and Bi are the reactants and products, ki is the rate constants for forward k þ i and backwarddirections k�i (thatdoesnotdependon the initial concentrationof the reactants and Advanced Chemical Kinetics4