The authors have defined 15 reactions to occur:
Langmuir-Hinshelwood form of kinetics is used for most of the heterogeneous reactions while Arrhenius-type kinetics (with the assumption of reactions being elementary) is used for the oxygen storage reactions (reactions 10 – 15).
Let’s look at reaction 5; CO + NO goes to CO2 + 0.5N2. Here, CO and NO are adsorbing to the catalyst, then undergoing a reaction and finally released from the catalyst. This is the mechanism behind Langmuir-Hinshelwood kinetics. The intermediate reactions are:
where S is the catalyst substrate and the subscript ADS indicates that the molecule is adsorbed at the surface. As the theory states, the rate limiting step is the reaction of the adsorbed molecules (low the probability of two molecules colliding), and this should give the rate equation:
where K, K1 and K2 are rate constants (not important to quantify, the authors start with constants given in the literature).
The authors end up with this rate equation:
So, what are the differences, and why?
As one can see, the Cs disappears and an exponential term is introduced in the numerator, while the denominator has gained two extra factors.
The disappearance of the Cs can be explained by that the R5 is different from the RLH derived earlier by a factor of Cs-1, i.e. R5 is the reaction rate per catalytic site. This conversion is often used in both catalysis as well as in enzymology.
The exponential factor exp(-E5/(RgTs) includes the temperature dependence of the reaction. As the temperature changes within the catalyst, this contributes to different values of the rate at different points in the catalyst.
The two extra factors in the denominator are due to the complexity of the total reaction. The ideal RLH doesn’t take into account the other reactions occurring at the same time in the catalyst. The factors are due to the inhibition of the CO, C3H6 and the NO; the more molecules occupying the catalyst sites the less room the reaction can take place on, thus lowering the rate of the reaction.
A full listing of the reaction rate equations in this paper can be seen below.