Two independent models of the same Langmuir-Hinshelwood mechanism run side by side. The lattice (left) is a stochastic kinetic-Monte-Carlo simulation: CO sticks to one empty site, O₂ dissociates and needs two adjacent empty sites, and a CO*/O* pair adjacent on the grid reacts to CO₂ and desorbs. The volcano pane (bottom-right) is the classic analytic dissociative LH rate law for the same reaction, solved directly from the equilibrium adsorption constants — no particles, just algebra:
r = k_r · (K_A P_A) · √(K_B P_B)
/ (1 + K_A P_A + √(K_B P_B))²
Both K_A, K_B (adsorption equilibrium constants) and k_r (reaction rate constant) follow Arrhenius-like temperature dependence, so raising temperature shrinks K_A/K_B (weaker adsorption, more desorption) while growing k_r (faster reaction once adsorbed) — exactly the competition that produces the mean-field rate's bell-shaped "volcano" versus CO pressure and the lattice's saturation collapse when one reactant floods the surface.
- CO pressure / O₂ pressure — partial pressures feeding both the lattice's stochastic sticking and the mean-field K_A P_A, K_B P_B terms.
- Temperature — shifts both models' rate constants together; watch the volcano peak slide and the marker track it.
- Active site density — rebuilds the lattice at a different grid resolution; does not affect the mean-field curve (it is a per-site quantity).