Chemical, Process & Catalysis Engineering
Mars-van Krevelen Redox Catalytic Rate Law & Oxidized Lattice Fraction theta_ox
Model selective hydrocarbon oxidation over reducible metal oxides (V2O5, MoO3, CeO2) using Pieter Mars and Dirk Willem van Krevelen’s (1954) redox rate law r_R = (k_red * P_R * k_ox * P_O2^n) / (nu * k_red * P_R + k_ox * P_O2^n).
In selective oxide catalysis, the solid crystal lattice ITSELF is the oxygen shuttle!
Formulated by P. Mars and D. W. van Krevelen (1954, Chem. Eng. Sci.) for naphthalene/aromatics oxidation over V2O5, the Mars-van Krevelen (MvK) redox cycle recognizes that gas-phase O2 does not react directly with adsorbed hydrocarbon R: instead, R reduces oxidized lattice sites [O_lat] at rate r_red = k_red * P_R * theta_ox (creating oxygen vacancies [V_O]), while gas-phase O2 re-oxidizes those vacancies at rate r_ox = k_ox * (P_O2^n) * (1 - theta_ox) (with n = 0.5 for dissociative O2 or n = 1 for molecular O2 re-oxidation)!
Setting steady-state oxygen stoichiometry nu * r_red = r_ox (where nu moles of O2 replenish the lattice oxygen consumed per mole of R) yields steady-state oxidized site fraction theta_ox = (k_ox * P_O2^n) / (nu * k_red * P_R + k_ox * P_O2^n) and overall harmonic-resistance rate 1 / r_R = 1 / (k_red * P_R) + nu / (k_ox * P_O2^n) — warning process engineers immediately when theta_ox drops too low and irreversible over-reduction / coking threatens the catalyst bed!
| MvK Quantity (k_red = 0.40, P_R = 0.25 bar, k_ox = 0.80, P_O2 = 0.20 bar, n = 0.5, nu = 1.5) | Formula | Evaluated Value |
|---|---|---|
| Lattice Reduction Flux k_red * P_R | =B2 * B3 | 0.1000 |
| Vacancy Re-Oxidation Flux k_ox * P_O2^n | =B4 * (B5 ^ B6) | 0.3578 |
| Steady-State Oxidized Lattice Fraction theta_ox | (k_ox * P_O2^n) / (nu * k_red * P_R + k_ox * P_O2^n) | 0.7046 (70.5% Oxidized) |
| Net Reductant Oxidation Rate r_R | k_red * P_R * theta_ox | 0.0705 mol/(g·s) |
Steady-State Oxidized Catalyst Lattice Fraction theta_ox
Computes (k_ox * P_O2^n) / (nu * k_red * P_R + k_ox * P_O2^n) across k_red (B2), P_R (B3), k_ox (B4), P_O2 (B5), O2 order n (B6), and stoichiometry nu (B7).
=IF(OR(B2 <= 0, B3 < 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid MvK Redox Inputs", ROUND((B4 * (B5 ^ B6)) / (B7 * B2 * B3 + B4 * (B5 ^ B6)), 4))Mars-van Krevelen Net Reductant Consumption Rate r_R
Evaluates (k_red * P_R * k_ox * P_O2^n) / (nu * k_red * P_R + k_ox * P_O2^n).
=IF(OR(B2 <= 0, B3 < 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid MvK Redox Inputs", ROUND((B2 * B3 * B4 * (B5 ^ B6)) / (B7 * B2 * B3 + B4 * (B5 ^ B6)), 4))Try the example
Use the original values or change them to test your understanding.