Surface Catalysis: Why Reaction Rate Peaks Instead of Climbing Forever

Two gases have to land on the same patch of metal

Heterogeneous catalysis — a gas-phase reaction sped up by a solid surface — is how industrial chemistry runs at scale: the Haber-Bosch synthesis of ammonia over iron, catalytic converters oxidising CO over platinum, hydrogenation over nickel. The Langmuir-Hinshelwood mechanism describes the most common case, where both reactants first adsorb onto the catalyst surface and then react only if they land on neighbouring sites. It is a three-step story: adsorption of A, adsorption of B, and a surface reaction between an adsorbed A and an adjacent adsorbed B — the gas phase itself never reacts directly.

The Langmuir isotherm: how full is the surface?

Before the rate can be written down, you need to know what fraction of surface sites is occupied by each species at a given gas pressure — the Langmuir adsorption isotherm. For a single species at equilibrium between adsorption and desorption:

theta = (K * P) / (1 + K * P)     // K: adsorption equilibrium constant, P: partial pressure

At low pressure theta grows roughly linearly with P; at high pressure the surface saturates and theta approaches 1 no matter how much more gas you add, because there are only so many sites. With two competing species A and B sharing the same sites, each one's coverage is suppressed by the other's presence:

theta_A = (K_A * P_A) / (1 + K_A * P_A + K_B * P_B)
theta_B = (K_B * P_B) / (1 + K_A * P_A + K_B * P_B)
rate    = k_surf * theta_A * theta_B         // both must be adsorbed AND adjacent

The volcano: too little coverage, too much coverage

The rate expression above contains the whole story of why Langmuir-Hinshelwood kinetics produce a peaked, volcano-shaped curve when you plot rate against the pressure ratio of A to B (or against binding strength in the Sabatier-principle sense). If A barely adsorbs, theta_A is near zero and the rate is starved no matter how much B is present. If A adsorbs too strongly, it saturates the surface and crowds out B — theta_A approaches 1 but theta_B is driven toward zero, and the rate collapses again from the other side. The maximum sits at an intermediate balance where both species have meaningful coverage. This is the microscopic version of the Sabatier principle: a good catalyst binds a reactant neither too weakly (nothing sticks long enough to react) nor too strongly (the product, or the reactant itself, never lets go, poisoning the surface).

Self-poisoning and rate-limiting coverage

A catalyst can be a victim of its own effectiveness. If one reactant (or an inert impurity, or the product itself) binds so strongly that it dominates the site count, the surface becomes self-poisoned — carpeted with a species that is not reacting, or has already reacted and will not leave. Classic examples are carbon monoxide poisoning platinum surfaces meant to oxidise other gases, and sulfur compounds poisoning catalytic converters. Because Langmuir-Hinshelwood rate is a product of two coverages that must share the same finite pool of sites, pushing one reactant's partial pressure up without limit is not a reliable way to speed up the reaction — past the volcano's peak it actively slows it down.

Langmuir-Hinshelwood vs Eley-Rideal

The competing mechanism, Eley-Rideal, has only one species adsorb; the other reacts directly from the gas phase by striking the adsorbed molecule. Eley-Rideal kinetics are first order in the gas-phase reactant's pressure and do not show the same competitive-suppression volcano, since there is no second species competing for sites. Distinguishing the two experimentally usually comes down to how the rate responds as one partial pressure is pushed to saturation: Langmuir-Hinshelwood rates fall off past the peak, Eley-Rideal rates keep climbing (or saturate smoothly) because the gas-phase reactant never needs a site of its own.

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