# Page - 169 - in Advanced Chemical Kinetics

## Image of the Page - 169 -

## Text of the Page - 169 -

dÎ·
dt Â¼K TÃ° ÃžÎ¦ Î· (5)
The temperature function K(T) is generally considered to be the rate constant, while the
conversion function Î¦(Î·) 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 TÃ° ÃžÂ¼Aexp ï¿½Ea=RTÃ° Ãž (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:
dÎ·
dt Â¼A ï¿½S ï¿½Î¦ Î· exp ï¿½Ea=RTÃ° Ãž (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

back to the
book Advanced Chemical Kinetics"

Advanced Chemical Kinetics

- Title
- Advanced Chemical Kinetics
- Author
- Muhammad Akhyar Farrukh
- Editor
- InTech
- Location
- Rijeka
- Date
- 2018
- Language
- English
- License
- CC BY 4.0
- ISBN
- 978-953-51-3816-7
- Size
- 18.0 x 26.0 cm
- Pages
- 226
- Keywords
- Engineering and Technology, Chemistry, Physical Chemistry, Chemical Kinetics
- Categories
- Naturwissenschaften Chemie