Table 2.

Rate equations in the 0th and first order

	Langmuir–Hinshelwood			First order
Step	Adsorption	Desorption	Reaction	Adsorption	Desorption	Reaction
Rate	$k_{ads}{\theta }_o$	$k_{des}{\theta }_a$	$k_r{\theta }_a^2$	$k_{ads}{\theta }_o$	$k_{des}{\theta }_a$	$k_r{\theta }_{aa}$
Ensemble-specific stoichiometric coefficients
$d{\theta }_a/dt$	1	−1	−4	1	−1	−4
$d{\theta }_o/dt$	−1	1	4	−1	1	4
$d{\theta }_{aa}/dt$	No explicit rate equations. ${\theta }_{ij}={\theta }_i{\theta }_j$			$2{\theta }_{ao}/{\theta }_o$	$-2{\theta }_{aa}/{\theta }_a$	$-\left(1+6{\theta }_{aa}/{\theta }_a\right)$
$d{\theta }_{ao}/dt$				$\left({\theta }_{oo}-{\theta }_{ao}\right)/{\theta }_o$	$\left({\theta }_{aa}-{\theta }_{ao}\right)/{\theta }_a$	$3\left({\theta }_{aa}-{\theta }_{ao}\right)/{\theta }_a$
$d{\theta }_{oo}/dt$				$-2{\theta }_{oo}/{\theta }_o$	$2{\theta }_{ao}/{\theta }_a$	$\left(1+6{\theta }_{ao}/{\theta }_a\right)$

Rate equations for each ensemble and each elementary step are constructed by product of the fundamental rate of the step (e.g., k_adsθ_o for A_(g) adsorption) and the corresponding ensemble-specific stoichiometric coefficient (e.g., 2θ_ao/θ_o for aa for A_(g) adsorption in the first order). The Langmuir–Hinshelwood model is unable to describe dynamics of multisite ensembles, and therefore entries for aa, ao, and oo are absent.