Visualise the Langmuir-Hinshelwood mechanism, in which reactants A and B compete for the same adsorption sites on a catalyst surface and react between adjacent sites. Change the adsorption equilibrium constants or the partial pressures and watch the surface coverages and reaction rate update in real time, including the rate maximum that is unique to LH kinetics.
Parameters
Surface rate constant k
Intrinsic speed at which an adjacent A-B pair reacts
Adsorption sites are filled with A (blue), B (orange) and vacancies (dark) in proportion to the coverages. Adjacent A-B pairs occasionally react and desorb, leaving as product.
The Langmuir-Hinshelwood rate law. r: reaction rate, k: surface rate constant, K: adsorption equilibrium constant, P: partial pressure. The rate is proportional to the product of both coverages.
Coverage of A, θA, and the vacant-site fraction θv. θA+θB+θv=1. Because the denominator (where A and B share the same sites) is squared, the rate has a maximum versus partial pressure.
What is the Langmuir-Hinshelwood Mechanism?
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The "Langmuir-Hinshelwood mechanism" is about reactions on a catalyst surface, right? How is it different from ordinary reaction kinetics?
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Roughly speaking, the difference is that the stage is not "inside a gas or a liquid" but "the surface of a solid catalyst". Think of the catalytic converter in a car, or the iron catalyst in ammonia synthesis. A reactant molecule first sits down on one of the limited "seats" — the adsorption sites — on the surface. In the LH mechanism, both A and B have to sit down first, and they react only once they happen to be next to each other.
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So both of them have to take a seat. Does that mean A and B fight over the seats?
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That is exactly the key point. The number of seats — the adsorption sites — is finite, so A and B compete for the same sites. Try raising KA on the left. A adsorbs more strongly and θA, the coverage of A, climbs sharply, but B loses seats and θB drops. The reaction rate is r = k·θA·θB, the product of both coverages, so increasing only one of them does not speed things up.
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Wait — so even if I keep raising the partial pressure of A, the rate does not just keep climbing?
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Right, and this is the most interesting thing about the LH mechanism. Look at the "Reaction rate vs PA" chart below. While PA is low, A increases and the rate rises. But past a certain point, A occupies so much of the surface that it pushes B off its seats. θB falls, so the rate actually goes down. That is why the curve is hill-shaped, with a maximum somewhere. In ordinary reactions "raise the concentration to go faster" is common sense, so this surprises people the first time they see it.
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When I want the rate to be as high as possible, how should I choose the partial pressures?
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The trick is to balance θA and θB. See the "rate-limiting factor" in the results card? That is whichever reactant has the smaller coverage — the bottleneck, in effect. If θB is small, B is limiting, so raising the partial pressure of B or slightly lowering that of A increases the rate. In real catalytic processes, engineers optimise the feed ratio (the A:B ratio) precisely to hit this coverage balance.
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I see. So a catalyst that adsorbs more strongly is not necessarily better.
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Exactly. This connects to a famous principle of catalyst design, the Sabatier principle: if adsorption is too weak the molecules never reach the surface, and if it is too strong they never leave and they push the partner off. The activity is highest at a "moderate, just-right" adsorption strength. Push KA to an extreme value and you will see θA approach 1, θB drop to almost 0, and the rate collapse. The LH rate law expresses this "harm of over-strong adsorption" cleanly in a single equation.
Frequently Asked Questions
The Langmuir-Hinshelwood (LH) mechanism describes a heterogeneous catalytic reaction in which both reactants A and B adsorb onto the catalyst surface and react between adjacent adsorption sites. The reaction rate is proportional to the product of both coverages, r = k·θA·θB. Unlike the Eley-Rideal mechanism, where a gas-phase molecule strikes an adsorbed molecule directly, in the LH mechanism both reactants must first adsorb on the surface before they react.
In the LH rate law r = k·KA·PA·KB·PB / (1+KA·PA+KB·PB)², the denominator is squared. Raising the partial pressure of A, PA, increases the rate at low pressure because the numerator term KA·PA grows, but at high pressure A crowds the surface and displaces B, so θB falls and the rate drops. This rise-then-fall, non-monotonic behaviour is the signature of LH kinetics and is characteristic of reactions with competitive adsorption.
The adsorption equilibrium constant K measures how strongly a reactant binds to the catalyst surface. A large K (strong adsorption) means the reactant occupies much of the surface even at low partial pressure, but it also takes sites away from the other reactant and lowers its coverage. In an LH reaction, if one species adsorbs too strongly the other cannot reach the surface and the rate actually falls. The maximum rate is reached when the coverages of A and B are balanced.
The rate-limiting factor is whichever of A and B has the smaller coverage. Because r = k·θA·θB is the product of both coverages, the smaller coverage is the bottleneck of the reaction rate. For example, if θA is large and θB is small, B is limiting, and raising the partial pressure of B or lowering that of A improves the rate. Raising the partial pressure of the species that already has the larger coverage only displaces the other and does not increase the rate.
Real-World Applications
Automotive exhaust catalysts: The oxidation of carbon monoxide, CO + O, on a three-way catalyst (Pt/Pd/Rh) is a textbook Langmuir-Hinshelwood reaction. CO and atomic oxygen adsorb competitively on the surface and react when they are adjacent to form CO₂. At low temperature, CO can occupy so much of the surface that oxygen cannot adsorb and the reaction stalls — "CO poisoning" — which corresponds exactly to the rate falling in this tool when KA is large and PA is high.
Ammonia synthesis and hydrogenation: The reaction of nitrogen and hydrogen on the iron catalyst of the Haber-Bosch process, and the hydrogenation of fats and oils, are among the many industrial catalytic reactions described by LH-type rate laws. When optimising the partial-pressure ratio of the feed, engineers choose the N₂:H₂ ratio with the coverage balance in mind. The intuition this tool gives — that raising a partial pressure too far backfires — is the starting point for such process design.
Solid-catalyst reactor design: In packed-bed and fluidised-bed reactors the partial pressures change with position in the catalyst bed. Building the LH rate law into a reactor model lets you predict counter-intuitive situations, such as the rate near the inlet already being past its maximum because the partial pressure is too high. Wrongly assuming the rate is simply proportional to concentration leads to a large error in the estimated reactor size.
Catalyst screening and mechanism discrimination: When you plot a measured reaction rate against partial pressure, a rate that rises to a maximum and then falls points to an LH mechanism (competitive adsorption), whereas a rate that simply saturates monotonically suggests an Eley-Rideal mechanism or non-competitive adsorption. Understanding the behaviour of rate laws like the one in this tool helps you infer the reaction mechanism from experimental data.
Common Misconceptions and Pitfalls
The most common misconception is the assumption that "raising the partial pressure (concentration) of a reactant always increases the reaction rate". For homogeneous elementary reactions this is usually true, but it does not hold for the Langmuir-Hinshelwood mechanism. Sweep PA from 0 to 10 in this tool and you will see a "hill" — the rate rises and then falls. This is the harm of competitive adsorption, with A occupying the surface and displacing B, so blindly raising a partial pressure to speed things up can backfire. The correct move is to raise the partial pressure of the limiting species, the one with the smaller coverage.
Next is the misconception that "the more strongly a catalyst adsorbs, the more active it is". A larger adsorption equilibrium constant K raises the coverage, but adsorption that is too strong takes sites from the partner and also makes the product slow to desorb, blocking the surface. The fact that catalytic activity follows a volcano-shaped curve against adsorption strength is known as the Sabatier principle, and the LH rate law captures one facet of it quantitatively. Push KA to its maximum in this tool and confirm that θA≈1, θB≈0 and the rate drops sharply.
Finally, do not over-trust the idea that "the LH rate law alone can correctly predict a real catalyst". This tool deals with an idealised dual-site model: a uniform surface, ideal Langmuir adsorption, and a rate-limiting surface reaction. A real catalyst involves heterogeneity of surface sites, interactions between adsorbed molecules, mass-transfer limitations, deactivation by poisoning or sintering, and multiple reaction pathways. The LH model is an excellent skeleton for understanding the mechanism and getting the direction of a design right, but quantitative design requires correction with measured rate parameters and an analysis of mass and heat transfer at reactor scale.
How to Use
Set forward reaction rate constant (kNum, kRange) in mol/(m²·s) for the surface-catalyzed step
Input Langmuir adsorption coefficients: kaNum/kaRange for reactant A (Pa⁻¹) and kbNum/kbRange for reactant B (Pa⁻¹)
Specify partial pressures paNum/paRange (Pa) and pbNum/pbRange; simulator calculates θA, θB, θv and reaction rate r automatically
Observe coverage fractions that must sum to unity and identify the rate-limiting factor (adsorption vs. surface reaction)
Worked Example
CO oxidation on Pt catalyst: kNum=0.85 mol/(m²·s), kaNum=2.5×10⁻⁵ Pa⁻¹ (CO), kbNum=1.2×10⁻⁵ Pa⁻¹ (O₂), paCO=1000 Pa, pbO₂=500 Pa. Results: θA=0.18, θB=0.06, θv=0.76, r=0.042 mol/(m²·s). The high vacant fraction indicates weak competitive adsorption; increasing kaNum to 8.0×10⁻⁵ shifts θA to 0.48 and r to 0.068 mol/(m²·s), demonstrating surface reaction rate limitation.
Practical Notes
When θA+θB>0.85, adsorption saturation dominates kinetics; reduce partial pressures or increase temperature to desorb
Compare rate-limiting factors between reactants: if one ka is 10× larger, that species blocks active sites preferentially in competitive kinetics
Validate against experimental Langmuir isotherm data before scaling to industrial reactor models