Page - 169 - in Advanced Chemical Kinetics

dη dt ¼K Tð ÞΦ η (5) The temperature function K(T) is generally considered to be the rate constant, while the conversion function Φ(η) is generally considered represent the process mechanism. It is assumed that the reaction mechanism is solely dependent on the conversion, and not the temperature. Eq. (3) resembles a single-step kinetic equation, even though it represents the kinetics of a complex condensed-phaseprocess. The single-stepkinetic approximation results in the substitution of a generally complex set of kinetic equations with the sole single-step kinetic equation. Eq. (5) represents a mathematical formulation of the single-step kinetic approximation.With fewexceptions, the temperature function is exclusivelyexpressedby the Arrheniusequation: K Tð Þ¼Aexp �Ea=RTð Þ (6) whereA and Ea are considered to be the pre-exponential factor and the activation energy, respectively,T is theabsolute temperature, andR is thegasconstant. Asourknowledgeabout theatomicandmolecularstructureofmatter increased,coupledwith the development of quantummechanics, newdirections in chemical kinetics have emerged. These directions are typically related to the interactions of individual atoms andmolecules, which are more fundamental studies. The set of elementary events is called the reaction mechanism.Fundamental studies on the reactionmechanismsallowus to formulatephysical explanations to thekineticparameters (A,Ea, etc.),whichwereoriginally introducedasempir- ical constants. For example, the activation energyEa is an energy barrier thatmust be over- come bymolecules in the reactionmixture to reach an interatomic distancewhere they can froma chemical bond. FromEq. (5), it is clear that, if the concentration of substances or the temperature inthegivensystemvariesfrompoint topoint.Thus, it is impossible tointroducea commonreaction rate for the entire system. Inorder toget closer to these ideal conditions, in classical kinetic experimentswemust continuouslymix the reagents andmaintain a constant temperaturebyuseofa thermostat. In the case of heterogeneous reactions involving a condensedphase,where the reactants are notmixedon themolecular level, there is anadditional parameter,which controls the rate of interaction, i.e., thecontactsurfacearea(S)betweenthereagents [2]. In thiscase, therateof the chemical reactionscanberepresentedas follows: dη dt ¼A �S �Φ η exp �Ea=RTð Þ (7) Thepresenceof condensedphases complicates the reaction; thisphase requires that transport playsarole in thereaction.Thus, ingeneral, thekineticsofsuchreactionsaredeterminedboth by the intrinsic rate of the chemical reaction and by mass transport (e.g., diffusion). The transport phenomena are essential for replenishing the reactants thatwere consumed in the reactionzone [4].Describing the reaction rate is further complicatedwhen the temperatureof the reactingenvironment is changingwith time. In this case, alongwith theprocessesofmass Kinetics of Heterogeneous Self-Propagating High-Temperature Reactions http://dx.doi.org/10.5772/intechopen.70560 169