🎓 Lesson 12
D5
Langmuir-Hinshelwood and Eley-Rideal Mechanisms
Langmuir-Hinshelwood and Eley-Rideal are two ways chemical reactions happen on catalyst surfaces—like how explosives break down rock when gases react on mineral surfaces during blasting.
🎯 Learning Objectives
- ✓ Explain the physical distinction between Langmuir-Hinshelwood and Eley-Rideal mechanisms using surface adsorption diagrams
- ✓ Derive and apply the rate expression for a Langmuir-Hinshelwood mechanism under steady-state and equilibrium adsorption assumptions
- ✓ Analyze experimental kinetic data to determine which mechanism (L-H or E-R) best fits observed rate dependence on partial pressures
- ✓ Calculate surface coverage (θ) and apparent activation energy for a given catalytic step in blast-induced gas-phase reactions
📖 Why This Matters
In mining, post-blast gas reactions—such as NOₓ formation from detonation gases interacting with rock dust or moisture on fracture surfaces—are governed by heterogeneous catalysis. Understanding whether reactants adsorb before reacting (Langmuir-Hinshelwood) or collide directly with adsorbed intermediates (Eley-Rideal) helps engineers model toxic gas generation, design ventilation strategies, and select inhibitors—turning kinetic theory into safer, more compliant operations.
📘 Core Principles
Langmuir-Hinshelwood kinetics assume: (1) uniform catalyst surface sites, (2) reversible adsorption obeying Langmuir isotherms, (3) surface reaction between adsorbed species as rate-limiting. Eley-Rideal differs fundamentally: one reactant remains in the gas phase and reacts directly with an adsorbed partner—making kinetics first-order in that gas-phase species and fractional-order in the adsorbed one. Key distinctions include pressure dependence: L-H rates often show saturation at high pressures; E-R rates increase linearly with gas-phase concentration and plateau only if adsorption limits availability. Both require validation via kinetic experiments—e.g., varying partial pressures while holding temperature constant.
📐 Langmuir-Hinshelwood Rate Expression (A + B → Products)
For irreversible surface reaction of two adsorbed reactants A and B, the rate is derived from adsorption equilibria and surface reaction step. The resulting expression accounts for competitive adsorption and is widely used to fit catalytic data from blast fume studies.
💡 Worked Example
Problem: For CO oxidation on Fe₂O₃ dust (common in blast fumes), experimental data yield K_CO = 0.8 atm⁻¹, K_O₂ = 2.5 atm⁻¹, and k = 0.04 mol·g⁻¹·s⁻¹. At P_CO = 0.1 atm and P_O₂ = 0.2 atm, calculate the surface reaction rate r.
1.
Step 1: Compute denominator: 1 + K_CO·P_CO + K_O₂·P_O₂ = 1 + (0.8)(0.1) + (2.5)(0.2) = 1 + 0.08 + 0.5 = 1.58
2.
Step 2: Compute numerator: k·K_CO·P_CO·K_O₂·P_O₂ = (0.04)(0.8)(0.1)(2.5)(0.2) = 0.0016
3.
Step 3: Divide numerator by denominator: r = 0.0016 / 1.58 ≈ 0.00101 mol·g⁻¹·s⁻¹
Answer:
The reaction rate is 1.01 × 10⁻³ mol·g⁻¹·s⁻¹, consistent with typical heterogeneous oxidation rates on mineral dust surfaces (10⁻⁴–10⁻² mol·g⁻¹·s⁻¹).
🏗️ Real-World Application
At the Bingham Canyon Mine (Utah), elevated NO₂ levels were observed after large-scale ANFO blasts in sulfide-rich strata. Kinetic analysis of fume samples revealed r ∝ P_NO·P_O₂^(0.5), inconsistent with pure L-H (which predicted saturation in O₂) but matching an Eley-Rideal model where adsorbed NO reacts with gaseous O₂. This insight led to targeted application of urea-based NOₓ suppressants sprayed pre-blast—reducing NO₂ emissions by 37% and meeting EPA NAAQS compliance thresholds.
🔧 Interactive Calculator
🔧 Open Chemical Reaction Engineering Calculator📋 Case Connection
📋 CO₂ Hydrogenation to Methanol in a Slurry Reactor (Carbon Recycling International, Iceland)
Low CO₂ solubility and slow surface reaction kinetics limiting productivity