#### Langmuir-Hinshelwood Kinetics: Screencasts

Derives the kinetic rate expression for the catalytic reaction A + B → products, where surface reaction is assumed to be the rate-determining step. Langmuir isotherms are used to model adsorption of A and B, and the products are assumed to be weakly adsorbed.

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Explains how the apparent activation energy for a catalytic reaction depends on the surface reaction activation energy and the heats of adsorption of reactants.

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##### Important Equations:

\[\vartheta _A = \frac{K_AC_A}{1+K_AC_A+K_BC_B}\]

where \(\vartheta _A\) = fractional coverage of component A,

\(K_A\) = adsorption equilibrium constant for component A (L/mol),

\(K_B\) = adsorption equilibrium constant for component B (L/mol),

\(C_A\) = gas phase concentration of component A (mol/L), and

\(C_B\) = gas phase concentration of component B (mol/L),

\[K_A = K_{A0}exp(\frac{\lambda _A}{RT})\]

where \(K_{A0}\) = preexponential factor, and

\(\lambda _A\) = heat of adsorption \((-\Delta H_{ads})\) of component A

\[K_B = K_{A0}exp(\frac{\lambda _B}{RT})\]

where \(K_{A0}\) = preexponential factor, and

\(\lambda _B\) = heat of adsorption \((-\Delta H_{ads})\) of component B

*Langmuir-Hinshelwood rate expression when surface reaction is rate limiting, the reaction is irreversible both reactants adsorb on the same sites, and products are weakly adsorbed.*

\[r=\frac{kK_AK_BC_AC_B}{(1+K_AC_A+K_BC_B)^2}\]

where \(r\)= rate of reaction (mol/(L s)) or can be in units of mol/(g cat s), and

\(k\) =rate constant (mol/(L s)) or can be in units of mol/(g cat s).

*Langmuir-Hinshelwood rate expression when surface reaction is rate limiting, one reactant dissociatively adsorbs and products are weakly adsorbed.*

\[r=\frac{kK_AK_B^{0.5}C_AC_B^{0.5}}{(1+K_AC_A+K_B^{0.5}C_B^{0.5})^2}\]

where reactant B dissociatively adsorbs (e.g. \(H_2 +2S \leftrightarrow 2HS\) where S is a surface site, and HS is an atom adsorbed on a surface site).

*Langmuir-Hinshelwood rate expression when surface reaction is rate limiting, the reaction is irreversible and reactants (A,B) are products (C,D) adsorb on the same sites.*

\[r=\frac{k_fK_AK_BC_AC_B}{(1+K_AC_A+K_BC_B+K_CC_C+K_DC_D)^2}-\frac{k_rK_AK_BC_AC_B}{(1+K_AC_A+K_BC_B+K_CC_C+K_DC_D)^2}\]

where \(k_f\) = rate constant (mol/(L s) of forward reaction (can be in units of mol/(g cat s)), and

\(k_r\) = rate constant (mol/(L s)) of reverse reaction (can be in units of mol/(g cat s)).

*Langmuir-Hinshelwood rate expression in terms of partial pressure. This assumes the surface reaction is rate limiting, the reaction is irreversible, both reactants adsorb on the same sites, and products are weakly adsorbed.*

\[r=\frac{kK_AK_BP_AP_B}{(1+K_AP_A+K_BP_B)^2}\]

where \(K_A\) = adsorption equilibrium constant for component A (bar^{-1}),

\(K_B\) = adsorption equilibrium constant for component B (bar^{-1}),

\(k\) = rate constant (mol/( L s)) or can be in units of mol/(g cat s).

\(P_A\) = partial pressure of component A (bar), and

\(P_B\) = partial pressure of component B (bar),