Reactions on surfaces
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By reactions on surfaces it is understood 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
Simple decomposition
If a reaction occurs through these steps A + S ⇌ AS → ProductsWhere A is the reactant and S is an adsorption site on the surface. If the rate constants for the adsorption, desorption and reaction are k1, k-1 and k2 then, the global reaction rate is: [r=-\frac =k_2 C_=k_2 \theta C_S ]
where [C_] is the concentration of occupied sites, [\theta] is the surface coverage and [C_S] is the total number of sites (occupied or not). [C_S] is highly related to the total surface area of the adsorbent, the bigger surface area, the more sites and the faster the reaction, this is the reason why heterogeneous catalysts are usually sought to have great surface areas (in the order of hundred m2/gram)
If we apply the steady state approximation to AS then
[\frac }= 0 = k_1 C_A C_S (1-\theta)- k_2 \theta C_S -k_\theta C_S ] so [\theta =\frac +k_2}]
and therefore [r=-\frac = \frac +k_2}] which is completely equivalent to the Michaelis-Menten rate constant. The rate equation is complex, and the reaction order is not clear, in experimental work, usually two extreme cases are looked for, in order to prove the mechanism, in them, the rate-determining step is:
Limiting step: Adsorption/Desorption
[k_2 >> \ k_1C_A, k_], so [r \approx k_1 C_A C_S]. The order respect to A is 1. Examples of this mechanism are N2O on gold and HI on platinumLimiting Step: Reaction
[k_2 << \ k_1C_A, k_] so [\theta =\frac }] which is just Langmuir isotherm and [r= \frac ]. Depending on the concentration of the reactant the rate changes:- Low concentrations, then [r= K_1 k_2 C_A C_S], that is to say a first order reaction.
- High concentration, then [r= k_2 C_S]. It is a zeroth order reaction.
Bimolecular reaction
The mechanism is nowA + S ⇌ AS
B + S ⇌ BS
AS + BS → Products
The rate constants are now [k_1],[k_],[k_2],[k_] and [k] for adsorption of A, adsorption of B, and reaction. The rate law is: [r=k_2 \theta_A \theta_B C_S^2 ]
Proceeding as before we get [\theta_A=\frac+kC_S\theta_B}], where [\theta_E] is the fraction of empty sites, so [\theta_A+\theta_B+\theta_E=1]. Let us assume now that the rate limiting step is the reaction of the adsorbed molecules, which is easily understood: the probability of two adsorbed molecules colliding is low. Then [\theta_A=K_1C_A\theta_E], which is nothing but Langmuir isotherm for two adsorbed gases, with adsorption constants [K_1] and [K_2]. Calculating [\theta_E] from [\theta_A] and [\theta_B] we finally get [r=C_S^2 \frac].
The rate law is complex and there is no clear order respect to any of the reactants but we can consider different values of the constants, for which it is easy to measure integer orders:
Both reactants have low adsorption
[1 >> K_1C_A, K_2C_B], so [r=C_S^2 K_1K_2C_AC_B]. The order is one respect to both the reactantsOne of the reactants has low adsorption
[K_2C_B < K_1C_A, 1], so [r=C_S^2 \frac]. The reaction order is 1 respect to B. There are two possibilities now:- At low concentrations of A, [r=C_S^2 K_1K_2C_AC_B], and the order is one respect to A.
- At high concentrations, [r=C_S^2 \frac]. The order es minus one respect to A. The higher the concentration of A, the slower the reaction goes, in this case we say that A inhibits the reaction.
One of the reactants has very high adsorption
[K_1C_A >> 1, K_2C_B], so [r=C_S^2 \frac]. The reaction order is 1 respect to B and -1 respect to A. Reactant A inhibits the reaction at all concentrations. This is known as the Langmuir-Hinshelwood mechanism.One of the reactants does not adsorb at all
A + S ⇌ ASAS + B → Products
Constants are [k_1, k_] and [k] and rate equation is [r = k C_S \theta_A C_A C_B]. Applying steady state approximation to AS and proceeding as before (considering the reaction the limiting step once more) we get [r=C_S C_B\frac]. The order is one respect to B. There are two possibilities, depending on the concetration of reactant A:
- At low concentrations of A, [r=C_S K_1K_2C_AC_B], and the order is one with respect to A.
- At high concentrations of A, [r=C_S K_2C_B], and the order is zero with respect to A.
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