Chemical, Process & Catalysis Engineering
Eley-Rideal Catalytic Rate Law Formula & Apparent Reaction Order Diagnostic
Compute Daniel Eley and Eric Rideal’s (1940) gas-surface collision rate r_ER = k_ER * K_A * P_A * P_B / (1 + K_A * P_A) and Apparent Reaction Order n_app,A = 1 / (1 + K_A * P_A) to distinguish Eley-Rideal from Langmuir-Hinshelwood kinetics.
How high-pressure saturation distinguishes Eley-Rideal from Langmuir-Hinshelwood mechanisms!
Proposed by D. D. Eley and E. K. Rideal (1940) for ortho-para hydrogen conversion and gas-surface recombination, the Eley-Rideal mechanism reacts chemisorbed species A* (at Langmuir coverage theta_A = K_A * P_A / (1 + K_A * P_A)) directly upon collision with gas-phase molecule B(g) without B ever occupying a surface site: r_ER = k_ER * theta_A * P_B = k_ER * K_A * P_A * P_B / (1 + K_A * P_A)!
This yields the textbook mechanistic discrimination test in heterogeneous catalysis: as P_A -> infinity at fixed P_B, Eley-Rideal saturates monotonically at plateau rate k_ER * P_B with strictly positive-to-zero apparent order n_app,A = d(LN r) / d(LN P_A) = 1 - theta_A = 1 / (1 + K_A * P_A) >= 0 (and exact 1st order in P_B everywhere), whereas competitive Langmuir-Hinshelwood turns OVER and exhibits negative order (-1) at high P_A!
| P_A Pressure (k_ER = 1.80, K_A = 3.0 bar^-1, P_B = 0.60 bar) | Coverage theta_A | Apparent Order n_app,A = 1 - theta_A | Rate r_ER |
|---|---|---|---|
| Low P_A = 0.05 bar | 0.1304 | +0.8696 (Near 1st Order) | 0.1409 |
| Moderate P_A = 1.00 bar | 0.7500 | +0.2500 | 0.8100 |
| High P_A = 19.00 bar (Saturation) | 0.9828 | +0.0172 (Zero-Order Plateau -> 1.08) | 1.0614 |
Eley-Rideal Catalytic Reaction Rate r_ER = k_ER * K_A * P_A * P_B / (1 + K_A * P_A)
Evaluates gas-adsorbate collision rate for rate constant B2, chemisorption constant B3, adsorbing gas pressure B4, and impinging gas pressure B5.
=IF(OR(B2 <= 0, B3 <= 0, B4 < 0, B5 < 0), "Requires k_ER > 0, K_A > 0, and Partial Pressures >= 0", ROUND((B2 * B3 * B4 * B5) / (1 + B3 * B4), 4))Apparent Reaction Order in Adsorbing Reactant A: n_app,A = 1 / (1 + K_A * P_A)
Returns 1 - theta_A = 1 / (1 + K_A * P_A), bounded cleanly in (0, 1].
=IF(OR(B3 <= 0, B4 < 0), "Requires K_A > 0 and P_A >= 0", ROUND(1 / (1 + B3 * B4), 4))Try the example
Use the original values or change them to test your understanding.