Reactions on surfaces are reactions in which at least one of the steps of the reaction mechanism is the adsorption of one or more reactants. The mechanisms for these reactions, and the rate equations are of extreme importance for heterogeneous catalysis. Via scanning tunneling microscopy, it is possible to observe reactions at the solid gas interface in real space, if the time scale of the reaction is in the correct range. Reactions at the solid–gas interface are in some cases related to catalysis.
Simple decomposition If a reaction occurs through these steps:
A + S ⇌ AS → Products where A is the reactant and S is an adsorption site on the surface and the respective rate constants for the adsorption, desorption and reaction are k1, k−1 and k2, then the global reaction rate is:
r = k 2 C A S = k 2 θ C S {\displaystyle r=k_{2}C_{\mathrm {AS} }=k_{2}\theta C_{\mathrm {S} }}
where:
r is the rate, mol·m−2·s−1
C A {\displaystyle C_{A}} is the concentration of adsorbate, mol·m−3
C A S {\displaystyle C_{\mathrm {AS} }} is the surface concentration of occupied sites, mol·m−2
C S {\displaystyle C_{\mathrm {S} }} is the concentration of all sites (occupied or not), mol·m−2
θ {\displaystyle \theta } is the surface coverage, (i.e. C A S / C S {\displaystyle C_{AS}/C_{S}} ) defined as the fraction of sites which are occupied, which is dimensionless
t {\displaystyle t} is time, s
k 2 {\displaystyle k_{2}} is the rate constant for the surface reaction, s−1.
k 1 {\displaystyle k_{1}} is the rate constant for surface adsorption, m3·mol−1·s−1
k − 1 {\displaystyle k_{-1}} is the rate constant for surface desorption, s−1
C S {\displaystyle C_{\mathrm {S} }} is highly related to the total surface area of the adsorbent: the greater the surface area, the more sites and the faster the reaction. This is the reason why heterogeneous catalysts are usually chosen to have great surface areas (in the order of a hundred m2/gram) If we apply the steady state approximation to AS, then:
d C A S d t = 0 = k 1 C A C S ( 1 − θ ) − k 2 θ C S − k − 1 θ C S {\displaystyle {\frac {dC_{\mathrm {AS} }}{dt}}=0=k_{1}C_{\mathrm {A} }C_{\mathrm {S} }(1-\theta )-k_{2}\theta C_{\mathrm {S} }-k_{-1}\theta C_{\mathrm {S} }} so θ = k 1 C A k 1 C A + k − 1 + k 2 {\displaystyle \theta ={\frac {k_{1}C_{\mathrm {A} }}{k_{1}C_{\mathrm {A} }+k_{-1}+k_{2}}}}
and
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