Heterogeneous Catalysis: Surface Kinetics and Langmuir-Hinshelwood Mechanism

The classical Langmuir-Hinshelwood model makes idealized physical assumptions: (1) Energetic site uniformity: Real heterogeneous catalysts possess stepped facets, edges, corners, and defect sites with differing adsorption energies, whereas the Langmuir isotherm assumes an energetically homogeneous surface. (2) Absence of lateral adsorbate-adsorbate interactions: At high surface coverages, dipole-dipole repulsion or steric crowding between neighboring adsorbed molecules causes adsorption enthalpy to decrease with coverage (better described by Temkin or Freundlich isotherms). (3) Internal mass transfer: For large catalyst porous pellets, intraparticle Knudsen diffusion limitations (quantified by the Thiele modulus) can depress observed rates; fine powder slurries (< 50 μm) are used here to ensure effectiveness factors η ≈ 1.0. (4) Product inhibition: If decomposition products adsorb competitively on surface sites, an additional term (1 + K_P [P]) must be incorporated into the rate denominator. The Langmuir-Hinshelwood (L-H) mechanism describes heterogeneous catalytic surface reactions where reactant molecules first undergo rapid, reversible chemisorption onto active catalytic surface sites (S) to form an adsorbed monolayer intermediate (AS), followed by a rate-determining unimolecular or bimolecular transformation of the adsorbed species on the solid surface: A(aq) + S ⇄ AS (adsorption equilibrium constant K_A), followed by AS ⟶ Products + S (surface reaction rate constant k_r). Assuming ideal Langmuir chemisorption—where all surface active sites are energetically uniform, each site binds at most one substrate molecule, and lateral adsorbate-adsorbate interactions are negligible—the fractional surface coverage θ_A at steady-state adsorption equilibrium obeys θ_A = K_A [A] / (1 + K_A [A]). The rate of catalytic turnover r is directly proportional to fractional surface coverage: r = k_r · θ_A = (k_r · K_A · [A]) / (1 + K_A · [A]). At low substrate concentrations (K_A [A] ≪ 1), fractional coverage is linear (θ_A ≈ K_A [A]) and the reaction exhibits apparent first-order kinetics with rate r ≈ k_r K_A [A]. At high substrate concentrations (K_A [A] ≫ 1), the active catalyst surface reaches monolayer saturation (θ_A → 1) and the reaction collapses to zero-order kinetics independent of substrate concentration: r → k_r. Linearizing the Langmuir-Hinshelwood hyperbolic rate expression into double-reciprocal coordinates yields: 1/r₀ = [1 / (k_r · K_A)] · (1 / [A]) + 1 / k_r. Plotting 1/r₀ versus 1/[A] produces a straight line where the Y-intercept b = 1/k_r yields the maximum surface reaction rate constant k_r = 1/b, and the slope m = 1/(k_r · K_A) enables evaluation of the adsorption equilibrium constant K_A = b / m.