 THREE WAY CATALYTIC CONVERTER Background

Catcon

Kinetics/Catalysis

Modeling

Rao et al.

Reactor Design

Kinetics

Modeling/Results

BACKGROUND - KINETICS

Surface Reactions

Consider reactions in which at least one of the steps of the reaction mechanism is the adsorption of one or more reactants onto a surface. The simplest surface reaction is a simple decomposition: A is here the reactant and S is an adsorption site on the surface, and the reaction has rate constants for the adsorption, desorption and reaction given as k1, k-1 and k2, respectively. Using what we already know about kinetics the global reaction rate would be: where CAS is the concentration of occupied sites, θ is the surface coverage and CS is the total number of sites (occupied or not). Assuming steady-state to AS, meaning that the change in CAS is zero: Rearranging for θ and using the global reaction rate above, CS is highly related to the total surface area of the adsorbent: the bigger 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.

Bimolecular Reactions

In a bimolecular reaction two molecules needs to undergo a reaction with the surface catalyst. Two mechanisms explain this in different ways.

Langmuir-Hinshelwood

Langmuir-Hinshelwood mechanism proposes that both molecules adsorb and the adsorbed molecules undergo a bimolecular reaction: The rate constants are now k1, k-1, k2, k-2 and k for adsorption/desorption of A, adsorption/desorption of B, and reaction. Using the same approach as in the simple decomposition, the global reaction rate is: and the surface coverage of A is: where θE is the fraction of empty sites, so θA + θB + θE = 1. The rate limiting step in this reaction is the reaction of the adsorbed molecules. This makes sense; the probability of two molecules colliding is relatively small. Then θA = K1CAθE, with Ki = ki/k-i, which is nothing but Langmuir isotherm for two adsorbed gases, with adsorption constants K1 and K2. Calculating θE from θA and θB we finally get the following: Depending on the relative adsorption of the different species (A and B), one can modify the final rate equation.

Eley-Rideal

Eley-Rideal mechanism proposes that only one of the molecules adsorbs and the other one reacts with it directly from the gas phase, without adsorbing: Constants are k1,k-1 and k and rate equation is r = kCSθACACB. Applying steady state approximation to AS and proceeding as before (considering the reaction the limiting step once more) we get By this equation one can see that different concentrations of A decides whether the reaction is in first order (low concentrations) or in the zeroth order. See here for more details about reaction order. The above figure shows the difference between a Langmuir-Hinshelwood (left) and an Eley-Riedeal (right) mechanism.

Catalysis

Catalysis is the process in which the rate of a chemical reaction is either increased or decreased by means of a chemical substance known as a catalyst. A catalyst is not consumed in the reaction, unlike the different reactants that participate in the chemical reaction. One can have catalysts that either speed up the reaction or ones that slows them down, the former called positive catalysts and the latter negative catalysts or inhibitors.

Catalysts generally react with one or more reactants to form intermediates that subsequently give the final reaction product, in the process regenerating the catalyst. The following is a typical reaction scheme, where C represents the catalyst, X and Y are reactants, and Z is the product of the reaction of X and Y: Although the catalyst is consumed by reaction 1, it is produced by reaction 4, giving the overall reaction Catalysts work by providing an (alternative) mechanism involving a different transition state and lower activation energy. In doing this, catalysts increases the number of molecule collisions that have enough energy for a reaction to occur. Hence, a catalyst can make a reaction which by itself may be blocked or extremely slow to occur. The catalyst may increase reaction rate or selectivity, or enable the reaction at lower temperatures. It does not, however, change the extent of the reaction: they have no effect on the chemical equilibrium of a reaction because the rate of both the forward and the reverse reaction are both affected. The figure above is a generic potential energy diagram showing the effect of a catalyst in a hypothetical exothermic chemical reaction X + Y to give Z. The presence of the catalyst opens a different reaction pathway (shown in red) with a lower activation energy. The final result and the overall thermodynamics are the same.

Heterogeneous Catalysis

Catalysts can be either heterogeneous or homogeneous depending on whether the catalyst exists in the same phase as the reactants. Heterogeneous catalysis is a chemistry term which describes catalysis where the catalyst is in a different phase (i.e. solid, liquid and gas, but also oil and water) to the reactants. Heterogeneous catalysts provide a surface on which the reaction may take place. In order for the reaction to occur, one or more of the reactants must diffuse to the catalyst surface and adsorb onto it (a in figure above). After reaction (b in figure), the products must desorb from the surface and diffuse away from the solid surface (c in figure). The transport of the reactants and the products between phases are considered playing a dominant role in the rate limiting step.

Homogeneous Catalysis

Homogeneous catalysis is a sequence of reactions that involve a catalyst in the same phase as the reactants. Most commonly, a homogeneous catalyst is co-dissolved in a solvent with the reactants. The proton is one of the most pervasive homogeneous catalysts. Illustrative of acid catalysis is the hydrolysis of esters: 