In this problem we derive Equation 29.45, the rate law for...

In this problem we derive Equation $29.45$, the rate law for the oxidation reaction $2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})$ assuming that the reaction occurs by the Langmuir-Hinshelwood mechanism. The overall rate law for this mechanism is $$ v=k_{3} \theta_{\mathrm{Co}} \theta_{\mathrm{o}_{2}} $$

In this problem we derive Equation $29.45$, the rate law for the oxidation reaction $2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})$ assuming that the reaction occurs by the Langmuir-Hinshelwood mechanism. The overall rate law for this mechanism is
$$
v=k_{3} \theta_{\mathrm{Co}} \theta_{\mathrm{o}_{2}}
$$

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Key Concepts

Rate Law Derivation in Heterogeneous Catalysis

The derivation of a rate law in heterogeneous catalysis involves identifying the elementary steps of the reaction mechanism, particularly the adsorption, surface reaction, and desorption steps. By quantifying the surface coverages and identifying the rate-determining step, one can express the overall reaction rate in terms of these surface concentrations, thereby connecting the molecular-level details of the mechanism to the observable kinetics.

Surface Adsorption and Coverage

Surface adsorption refers to the binding process of molecules to the active sites on a catalyst. The fraction of these sites occupied by a given species, usually represented by theta (?), is critical in determining the reaction rate in catalytic processes. The coverage provides a measure of how likely the reactive species are to be present on the surface, facilitating the reaction.

Langmuir-Hinshelwood Mechanism

This mechanism is used in heterogeneous catalysis to describe reactions where reactant molecules first adsorb on a catalyst's surface, then react with one another while being adsorbed, and finally desorb as product molecules. The rate of the reaction depends on the surface coverages of the reactants, linking molecular events on the catalyst surface with the overall reaction kinetics.

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