Heterogeneous Catalysis at Surfaces

Every heterogeneous catalytic reaction proceeds through a cycle rather than a single step. First, one or more reactant molecules from the gas or liquid phase adsorb onto specific locations on the solid surface called active sites — atoms or ensembles of atoms geometrically and electronically suited to weaken a particular bond. This step is governed by the same physisorption/chemisorption distinction and Langmuir isotherm machinery used to describe adsorption in isolation, but here adsorption is only the opening move. Once bound, the adsorbed species (an "adsorbate") may diffuse across the surface, react with a neighboring adsorbate, or react with an incoming gas-phase molecule. The product, once formed, must desorb to free the site for another cycle. If desorption is slow, the site is blocked and the observed rate falls — a phenomenon called product inhibition. Two limiting mechanisms describe how the surface reaction step occurs. In the Langmuir-Hinshelwood (LH) mechanism, both A and B adsorb, and the reaction occurs between two neighboring adsorbed species. This is the dominant pathway for CO oxidation on platinum, ammonia synthesis on iron, and most hydrogenations. In the Eley-Rideal (ER) mechanism, only one reactant adsorbs; the second reacts directly from the gas phase upon collision with the adsorbed species, without itself equilibrating on the surface. ER kinetics are rarer experimentally but well documented for reactions like H atom recombination on metal surfaces and some hydrogenation steps at high gas pressure. The catalyst's activity is controlled by the density of active sites, $N_s$, which is a property of the exposed surface, not the bulk. Surface area determination (BET analysis) gives total surface area; only a fraction of that area consists of catalytically active sites, often measured separately by selective chemisorption (e.g., CO or H₂ titration). The turnover frequency (TOF), the number of product molecules formed per active site per second, is the fundamental currency of catalytic activity — it lets a chemist compare a coarse powder and a single crystal on equal footing.

The second thing worth visualizing is how the rate itself behaves as a function of pressure — this is the experimental fingerprint that distinguishes surface-limited kinetics from ordinary homogeneous kinetics.

where: $\theta_A$ is fractional coverage of A, $K_A$, $K_B$ are Langmuir adsorption equilibrium constants, $p_A$, $p_B$ are partial pressures.

where: $k_s$ is the surface-reaction rate constant (units of rate per unit coverage-coverage product), $v_{LH}$ is the Langmuir-Hinshelwood rate.

where: $k_s'$ is the Eley-Rideal rate constant for direct gas-surface reaction, $\theta_A$ is the coverage of the surface-bound reactant.

where: $v$ is the measured reaction rate (molecules or moles per unit time), $N_s$ is the number of active sites (per unit mass, area, or total).

where: $r$ is the absolute rate (not per-site), useful when comparing catalysts of different loadings; $N_s$ enters explicitly rather than through TOF.

Example 1 — Foundational: extracting $k_s$, $K_A$, $K_B$ from initial rate data. CO oxidation, 2 CO + O₂ → 2 CO₂, is studied on a Pt catalyst at 480 K holding $p_{O_2}$ fixed at 20.0 kPa while varying $p_{CO}$. Suppose CO is the dominant adsorbate ($K_{CO}p_{CO} \gg K_{O_2}p_{O_2}$, a realistic regime for Pt at this temperature), so the LH expression simplifies to the CO-only self-poisoning limit:

Measured data: at $p_{CO} = 2.0$ kPa, $v = 4.8 \times 10^{-3}\ \text{mol m}^{-2}\text{s}^{-1}$; at $p_{CO} = 8.0$ kPa, $v = 1.2\times 10^{-3}\ \text{mol m}^{-2}\text{s}^{-1}$. Check the inverse proportionality: $v \cdot p_{CO}$ should be constant.

The product is constant, confirming $v = C/p_{CO}$ with

If independent chemisorption titration gives $K_{CO} = 0.85\ \text{kPa}^{-1}$ and $K_{O_2} = 0.010\ \text{kPa}^{-1}$ at 480 K, then since $C = k_s K_{O_2} p_{O_2}/K_{CO}$:

Sanity check: $k_s$ has units consistent with a surface-reaction rate constant for a bimolecular step written per unit coverage product, and its magnitude (order $10^{-2}$ mol m⁻² s⁻¹) is physically reasonable for a metal turnover at 480 K — comparable to literature values for Pt(111) CO oxidation extrapolated from single-crystal studies.

Example 2 — Applied, exam-level: computing turnover frequency and comparing ER vs. LH signatures. A hydrogenation catalyst (Pd on alumina, 2.0 g sample) is tested for the reaction H₂(g) + surface-bound alkene → alkane. CO chemisorption at 195 K gives an uptake of 0.45 cm³ (STP) of CO per gram of catalyst, with a 1:1 CO:Pd$_{surface}$ stoichiometry.

Step A — active site density. Moles of CO adsorbed per gram:

Number of surface Pd atoms (active sites) per gram, using $N_A = 6.022\times10^{23}\ \text{mol}^{-1}$:

For the whole 2.0 g sample:

Step B — measured rate. Under reaction conditions the alkane is produced at $v = 3.30\times10^{-7}\ \text{mol s}^{-1}$ for the whole sample. Convert to molecules per second:

Step C — turnover frequency.

This corresponds to one turnover roughly every 122 seconds per site — a plausible value for a moderately active hydrogenation catalyst (literature TOFs for supported Pd hydrogenation typically span $10^{-3}$ to 1 s⁻¹ depending on temperature and particle size).

Step D — distinguishing mechanism. If, on repeating the experiment at fixed alkene coverage but increasing H₂ pressure ten-fold, TOF increases linearly with $p_{H_2}$ without saturating, that behavior is inconsistent with LH kinetics (which predicts saturation as $K_{H_2}p_{H_2}$ grows) and instead fits

i.e., Eley-Rideal: gas-phase H₂ (or dissociated H atoms with negligible equilibrium coverage) reacting directly with adsorbed alkene. This pressure-dependence test is the standard experimental discriminator between the two mechanisms.

Cyril Norman Hinshelwood built much of the mechanistic framework for surface-catalyzed and chain reactions, sharing the 1956 Nobel Prize in Chemistry with Nikolay Semyonov for work on reaction mechanisms. His collaboration with Irving Langmuir's adsorption theory — applying the isotherm to reacting, not just equilibrating, surfaces — gave the field its first quantitative rate laws. Eric Keightley Rideal, working independently in the same era on gas-surface reaction dynamics, proposed the direct-impact alternative that now bears his name alongside John Eley's later refinements. Together their names label the two idealized limits every real catalytic system is measured against.

Ask the tutor: How would this rate law change if the surface reaction itself, rather than adsorption, involved a rate-limiting dissociation step for a diatomic reactant like H₂ or O₂?