Reconsider the surface-catalyzed bimolecular reaction in...

Reconsider the surface-catalyzed bimolecular reaction in Problem $29-55 .$ If $\mathrm{A}(\mathrm{g}$ ) and $\mathrm{B}(\mathrm{g})$ do not compete for surface sites, but instead each molecule uniquely binds to a different type of surface site, show that the rate law is given by $$ v=\frac{k_{3} K_{\mathrm{A}} K_{\mathrm{B}}[\mathrm{A}][\mathrm{B}]}{\left(1+K_{\mathrm{A}}[\mathrm{A}]\right)\left(1+K_{\mathrm{B}}[\mathrm{B}]\right)} $$

Reconsider the surface-catalyzed bimolecular reaction in Problem $29-55 .$ If $\mathrm{A}(\mathrm{g}$ ) and $\mathrm{B}(\mathrm{g})$ do not compete for surface sites, but instead each molecule uniquely binds to a different type of surface site, show that the rate law is given by
$$
v=\frac{k_{3} K_{\mathrm{A}} K_{\mathrm{B}}[\mathrm{A}][\mathrm{B}]}{\left(1+K_{\mathrm{A}}[\mathrm{A}]\right)\left(1+K_{\mathrm{B}}[\mathrm{B}]\right)}
$$

Key Concepts

Non-Competitive Adsorption

Non-competitive adsorption refers to the scenario where different reactant molecules bind to separate, distinct types of sites on the catalyst surface rather than competing for the same sites. This independence allows for the derivation of a rate law that is the product of the individual adsorption isotherms, with each reactant contributing its own equilibrium constant to the overall reaction rate expression.

Surface Catalysis and Bimolecular Reactions

Surface catalysis involves reactions that occur when reactant molecules are adsorbed on a catalyst’s surface. In bimolecular surface reactions, two distinct reactants migrate on the surface and react to form products. The reaction rate depends on the surface coverages of both reactants, and this leads to kinetic expressions where the probability of a reaction is proportional to the product of the individual adsorbate concentrations.

Adsorption Equilibrium

Adsorption equilibrium involves the reversible attachment of molecules from the gas phase onto a solid surface, leading to a dynamic balance between adsorption and desorption processes. In kinetic modeling, adsorption equilibrium is characterized by equilibrium constants that link the concentration of the free molecules in the bulk phase to the fraction of occupied surface sites.

Langmuir Adsorption Isotherm

The Langmuir adsorption isotherm describes how molecules adsorb onto a surface with a finite number of identical sites, leading to a saturation behavior as the pressure or concentration increases. In contexts where each molecule binds to a unique site, the isotherm provides an independent description for each species’ surface coverage, which is key to deriving rate laws in surface-catalyzed reactions.

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