Langmuir-Hinshelwood types of rate equations

For a Langmuir-Hinshelwood type of rate equation, such as Eq. (9-32), Eq. (10-26) is not valid because the adsorption-equilibrium-constant terms in the denominator of the rate expression are also temperature dependent. 

For the above three reactions, the following Langmuir—Hinshelwood types of rate equations developed by Sheppard, Maier, and Caram (1986) are used ... 

The structure of each of these factors or groups depends in a systematic way on the number of reactants and products considered and on which step in the reaction mechanism is considered as the RDS. As a result, Langmuir-Hinshelwood type of rate equations do not necessarily need to be derived mathematically, but can be constructed from tables that represent the various effects of the model assumptions on the structure of each of these factors or groups (28). 

This hyperbolic form of rate equation is known as a Langmuir-Hinshelwood type of rate equation in the field of heterogeneous catalysis, and as a Michaelis-Menten type of rate equation in biochemistry. 

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