Catalyst Fundamentals

W. Addy Majewski

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Abstract: A catalyst is a substance which can increase the rate of a chemical reaction. Heterogeneous catalysts supported on high surface area porous oxides are used in emission control applications. The overall catalytic conversion in a heterogeneous catalyst is composed of several sub-processes which involve chemical reaction, bulk mass transfer and pore diffusion. Catalytic processes controlled by reaction kinetics can be modeled using the Arrhenius equation. Catalytic conversions in the mass transfer controlled region can be estimated using mass transfer correlations developed for monolithic catalyst supports. Even though catalysts are not used in the reaction, they undergo gradual deterioration due to thermal deactivation and poisoning.

Chemical Reaction Kinetics

A chemical reaction that results from the simultaneous combination of a molecules of A, b molecules of B, and c molecules of C … can be represented by the following equation:

aA + bB + cC … ↔ rR + sS + …(1)

The reaction rate for the forward reaction may be written as

r = k·CAa·CBb·CCc…(2)

where:
r - rate of reaction, kmole/(m3·s)
k - reaction rate constant, 1/s
Ci - concentration of reactant i, kmole/m3.

Equation (2) defines the reaction rate constant (k) which, under ideal conditions, depends only on temperature and the nature of the reaction. Another important term is the order of the reaction, defined as the sum of the exponents a, b, c … of Equation (1). This sum equals to 1 for a first-order reaction, 2 for a second-order reaction, etc.

Some chemical reactions may not proceed completely to the end, i.e., to the right side of Equation (1). Rather, a thermodynamic equilibrium may be established where certain concentrations of reactants A, B, C, … will co-exist in the system with certain concentrations of products R, S, …. From the chemical kinetics point of view, this is represented as a dynamic balance, where the original reactants A, B, C, … are being re-created in a reverse reaction between R, S, …. This bi-directional character of the process is indicated by the double-head arrow in the reaction equation. The rate of the reverse reaction can be written as

r' = k'·CRr·CSs…(3)

The net rate of the reaction is then equal to

r0 = r - r' = k·CAa·CBb·CCc… - k'·CRr·CSs…(4)

The net reaction rate equals zero at equilibrium, r0 = 0, thus

(CRr·CSs…)/(CAa·CBb·CCc…) = k/k' = K(5)

K is the reaction equilibrium constant, which depends on temperature. It can be calculated from thermodynamic functions of the system. Once known, the equilibrium constant allows for calculation of the concentrations of reaction products at equilibrium.

Reaction progress can be limited by reaction kinetics or by thermodynamic equilibrium. If the reaction rate constant (k) is low, the reaction, even if thermodynamically allowed, may take a long time to complete. Some reactions are so slow that their rates practically equal zero, and the processes could take years to complete. Fortunately, reaction rates may be increased by the use of catalysts.

On the other hand, if the reaction reaches its equilibrium, any further reaction progress is thermodynamically impossible. It is important to realize that catalysts have no effect on the reaction equilibrium. From the kinetics point of view, if a catalyst increases the forward reaction rate, Equation (2), it also increases, to the same degree, the reaction rate of the reverse reaction, Equation (3).

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