Surface reactions are often described using global reactions rather than as a series of elementary reactions. Some of the most common global rate expressions used for surface reactions are the Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) rate expressions. The former applies to the case where adsorption and desorption are assumed to be in equilibrium, and a reaction on the surface between adsorbed species is rate determining. The latter applies to the case of a reaction between a gas-phase species and an adsorbed species being rate-limiting. Although originally developed for specific cases, these names are now used to refer to a variety of rate expressions with similar forms. If a LH reaction is used, a single global reaction might constitute the entire surface chemistry mechanism. The "Langmuir" part of the name for the LH rate expression originates from the inclusion of the Langmuir adsorption isotherm, which assumes that the adsorption sites on the surface are independent from each other (single site adsorption), the sites are equivalent, and the surface coverage decreases the number of sites available for adsorption only, but does not alter the energetics of adsorption/desorption.

The following example of a LH reaction illustrates its features. Species A and B coadsorb onto the surface, react to products C and D, which can then desorb. The reaction between adsorbed A and adsorbed B is assumed to be rate-limiting and irreversible, while the adsorption/desorption processes are assumed to be in equilibrium. In the LH formulation, the elementary chemical reactions shown in Equation 4–16 would be replaced by the single overall reaction shown in Equation 4–17 , which does not explicitly include any surface species.

(4–16)

(4–17)

The effects of surface-sites being blocked by various species are included via the adsorption/desorption equilibria. This "lumping" of a number of elementary steps together results in a rate expression that differs substantially from a simple mass-action rate expression. The rate of progress variable is given by:

(4–18)

where the s are the equilibrium constants for the adsorption/desorption steps and s are the concentrations of the species. As product species, C and D do not appear in the numerator, but as adsorbed species they can block surface sites, so they do appear in the denominator. The is expressed in terms of Arrhenius parameters, as are the s. The equilibrium constant is defined as , in parallel with the standard expression for rate constants. Often, the equilibrium constants in the numerator are lumped into a representative rate constant, giving:

(4–19)

The generalized form of the above expression is:

(4–20)

where represents gas-phase species in the reaction, and the exponent of 2 in the denominator comes from the fact that the reaction rate is determined by the reaction between two adsorbed species. In practice, this rate form is often used for empirical parameter fitting, so we further generalize it to:

(4–21)

where:

For example, hydrogen (H2) and toluene (T) can react over a catalyst to produce methane (M) and benzene (B):

The rate law for hydrodemethylation of toluene at 600 C is given by the Langmuir-Hinshelwood form as [28]:

(4–22)

where P_i is partial pressure in atm.

Because reaction rates in Surface Kinetics are area-based, the catalyst-mass-based rate given in Equation 4–22 has to be converted accordingly. By assuming each gram of catalyst provides 0.5 cm² of active surface area, the area-based rate law is found to be:

(4–23)

By comparing Equation (2) to the generalized LH rate expression given by Equation 4–21 , the reaction for hydrodemethylation of toluene can be presented in Surface Kinetics format as:

C6H5CH3 + H2 => C6H6 + CH4 2.8E-8 0.0 0.0 LANG /C6H6 1.26 0.0 0.0 1.0/ LANG /C6H5CH3 1.01 0.0 0.0 1.0/ LHDE /1/ LHPR /atm/

Auxiliary keywords for the Langmuir-Hinshelwood reaction are described in Table 4.6: Alphabetical Listing of Surface Reaction Auxiliary Keywords of the Chemkin Input Manual Input Manual.

Eley-Rideal (also called Rideal-Eley) reactions are less common than LH reactions. The following example illustrates its features. Species A adsorbs onto the surface, then reacts with gas-phase species B to produce C, which can then desorb. The reaction between adsorbed A and gas-phase B is assumed to be rate-limiting and irreversible, while the adsorption/desorption processes are assumed to be in equilibrium. In the ER formulation, the elementary chemical reactions shown in Equation 4–24 would be replaced by the single overall reaction shown in Equation 4–25 , which does not explicitly include any surface species.

(4–24)

(4–25)

In this case, the rate of progress variable is given by:

(4–26)

or

(4–27)

The generalized form of this is:

(4–28)

which is the same as the Equation 4–20 above for LH kinetics, except that the denominator has an overall exponent () of one rather than two. ER reactions are thus treated as a special case of the LH rate law.

Using the LH option requires paying careful attention to the units of the reaction rates. The discussion above assumes that the rate expressions are given in terms of gas concentrations, which is the standard for Gas-phase Kinetics. However, literature values for LH rate parameters, especially equilibrium constants, are often provided in pressure units. To reduce the number of units conversions required of the user, equilibrium constants may be input in either pressure units or concentration units. This option is currently limited to the LH rate expression and only for the equilibrium constants. Rate parameters still must be input in concentration units. In Surface Kinetics, the default units, unless altered on the REACTIONS line, for the rate of a reaction are moles cm^-2 sec^-1. Rate parameters given in pressure units, for example in atm sec^-1, do not have the same dimensions as moles cm^-2 sec^-1. Such a rate would need to be divided both by and the surface-area to volume ratio (), before use. Rates given in terms of weight of catalyst need to be converted to a rate expressed in terms of the effective surface area of the catalyst via the surface area per unit weight of catalyst and the dispersion. Rates given on a per site basis should also be converted to a per area basis.