Heterogeneous catalysis

Result

Heterogeneous catalysis

T-122Home CU-403Threads kinetics · energy

Statement

Adsorption, surface reaction and desorption.

Why it matters

catalysis-activation-energy established that a catalyst works by opening a lower-activation-energy pathway without being consumed; heterogeneous catalysis is the specific, industrially dominant case where that pathway runs on a solid surface while reactants approach from a separate gas or liquid phase. Nearly every large-scale industrial chemical process — ammonia synthesis, catalytic converters, petroleum refining — relies on a heterogeneous catalyst, and understanding the surface mechanism (adsorption, surface reaction, desorption) is what lets chemists rationally design catalysts rather than discover them purely by trial and error. langmuir-isotherm, developed alongside this result, supplies the quantitative surface-coverage machinery that the rate law derived here depends on directly.

Hypotheses

The catalytic cycle proceeds through a well-defined sequence of surface steps: adsorption of reactant(s) onto active sites, reaction while adsorbed, and desorption of product to free the site again.This staged picture is what allows each step to be analysed and rate-limited separately; if adsorption, surface reaction, and desorption were not cleanly separable steps (for instance, in some concerted, non-stepwise surface mechanisms), the simple rate-determining-step analysis below would not apply directly. The solid surface offers a finite number of active sites, each capable of adsorbing at most one reactant species at a time.This is exactly the Langmuir-isotherm assumption (uniform, non-interacting, singly-occupiable sites) carried over into the kinetic picture; real catalyst surfaces can have heterogeneous site energies and lateral adsorbate–adsorbate interactions that this idealisation neglects, refined further in more advanced surface-kinetics treatments.

Proof

\text{A(g)} + \text{site} \rightleftharpoons \text{A(ads)}

Gas-phase reactant molecules strike and adsorb reversibly onto available surface sites, with the fraction of sites occupied, \(\theta\), governed at equilibrium by the Langmuir adsorption isotherm (langmuir-isotherm) as a function of the reactant's gas-phase pressure. A

\text{A(ads)} \to \text{B(ads)}\ \text{(surface reaction, often rate-determining)}

While bound to the surface, the adsorbed reactant undergoes chemical transformation, frequently the slowest step in the overall cycle because it requires overcoming the reaction's intrinsic activation barrier while confined to the two-dimensional surface geometry; when this step is rate-determining, the overall observed rate is directly proportional to the surface coverage \(\theta\) of the reacting species. A

\text{B(ads)} \to \text{B(g)} + \text{site}

The product desorbs from the surface, releasing the active site to participate in another catalytic cycle; if desorption were slow or incomplete, sites would become progressively blocked by adsorbed product, a form of self-poisoning distinct from poisoning by an unrelated impurity species. A

\text{rate} = k\,\theta_A = k\,\frac{K_A P_A}{1+K_A P_A}\ \text{(Langmuir–Hinshelwood, single-reactant case, surface reaction rate-determining)}

Combining the rate-determining surface-reaction step (Step 2) with the Langmuir isotherm's expression for \(\theta_A\) as a function of pressure \(P_A\) (Step 1) gives the overall observed rate law directly in terms of gas-phase pressure, without needing to track surface concentrations explicitly. B

Result

\text{rate} = k\,\theta \ \text{(surface coverage sets the rate)}; \quad \theta \to 1 \text{ at high } P \Rightarrow \text{rate} \to k\ (\text{zero order in }P)

Reading. Heterogeneous catalytic rate is governed by how much of the surface is covered by reactant, not directly by gas-phase concentration; at low pressure, rate rises roughly linearly with pressure (first order), but at high pressure, once the surface saturates (\(\theta\to1\)), the rate levels off and becomes independent of further pressure increase (zero order) — a signature qualitatively different from any simple homogeneous, gas-phase-only rate law.

Scope. Applies to reactions genuinely proceeding through the adsorb–react–desorb cycle on a finite-site surface (Hypotheses); breaks down under strong lateral adsorbate interactions, multiple simultaneously occupied site types, or when the rate-determining step is adsorption or desorption itself rather than the surface reaction assumed in Step 4.

Corollaries & converses

Catalyst poisoning (a separate, non-reacting species binding strongly and essentially permanently to active sites) reduces the number of sites available for the genuine catalytic cycle, directly lowering the effective rate constant \(k\) in the Result even though the intrinsic surface-reaction chemistry is unaffected.
enzyme-catalysis-mechanism shows a strikingly parallel kinetic signature (Michaelis–Menten kinetics: linear at low substrate concentration, saturating at high concentration) arising from an analogous binding-site-saturation mechanism, despite enzymes being dissolved, homogeneous catalysts rather than solid surfaces — the same underlying site-saturation logic recurs in a chemically very different setting.
catalysis-activation-energy's general principle, that a catalyst lowers the activation barrier of the rate-determining step without appearing in the overall stoichiometry, applies here specifically to Step 2's surface reaction, the step whose barrier the catalyst surface is actually lowering.

Fails without

Drop the finite, uniform-site hypothesis and treat the surface as having unlimited capacity: the saturation behaviour central to the Result (rate levelling off at high pressure, Step 4) disappears entirely, and the predicted rate law would instead rise indefinitely with pressure, contrary to the well-established experimental saturation kinetics of real heterogeneous catalysts.
Assume the surface reaction (Step 2) is always the rate-determining step: if adsorption or desorption is instead rate-limiting, the simple rate law of Step 4 (built specifically assuming surface reaction is rate-determining) no longer describes the system, and a different rate expression, built around whichever step is actually slowest, is required.

Common errors

Assuming heterogeneous catalytic rate is always directly proportional to gas-phase pressure or concentration; the Result shows this holds only at low coverage (low \(P\)), with zero-order behaviour emerging instead at high coverage.
Confusing catalyst poisoning (an unrelated species blocking active sites, Corollaries) with normal product inhibition (the reaction's own product competing for sites, which is a distinct, though related, saturation effect).
Treating the Langmuir–Hinshelwood mechanism (both reactants adsorbed before reacting) as the only possible heterogeneous mechanism, overlooking the Eley–Rideal alternative, in which a gas-phase molecule reacts directly with an already-adsorbed species without itself adsorbing first.
Forgetting that the catalyst surface itself does not appear in the overall balanced chemical equation, even though it is essential to, and explicitly present in, every individual mechanistic step of the Proof.

Discussion

Irving Langmuir's early-20th-century work on gas adsorption at solid surfaces (recognised with the 1932 Nobel Prize in Chemistry) provided both the isotherm used in Step 1 and much of the conceptual foundation for treating heterogeneous catalytic kinetics quantitatively; Cyril Hinshelwood's subsequent kinetic analysis, combining Langmuir's adsorption picture with explicit surface-reaction rate laws, gives the mechanism its common Langmuir–Hinshelwood name.

The industrial Haber process (ammonia synthesis over an iron catalyst) and the automotive catalytic converter (oxidising CO and unburned hydrocarbons, reducing \(\text{NO}_x\), over platinum-group-metal surfaces) are both large-scale, everyday illustrations of exactly the adsorb–react–desorb cycle developed here; catalyst poisoning by trace impurities (sulfur compounds are a classic industrial poison for many metal catalysts) is a genuine, economically significant practical concern in both settings.

Common misconception: that a catalyst's only job is to lower the overall reaction's activation energy in some generic sense. More precisely, per Step 2, it provides an entirely alternative reaction pathway — via surface adsorption and a different, lower-barrier transition state accessible only on the surface — not a modification of the original, uncatalysed gas-phase or solution pathway at all.

Worked examples

\text{Low pressure limit: } K_AP_A\ll1 \Rightarrow \theta_A\approx K_AP_A \Rightarrow \text{rate}\approx kK_AP_A

At sufficiently low reactant pressure, the Langmuir isotherm's denominator is dominated by the constant \(1\), so coverage rises linearly with pressure, and the Result's rate law reduces to simple first-order (apparent) kinetics in gas-phase pressure. A

\text{High pressure limit: } K_AP_A\gg1 \Rightarrow \theta_A\approx1 \Rightarrow \text{rate}\approx k

At sufficiently high pressure, essentially every active site is occupied, so further increasing the pressure cannot increase the rate any further; the reaction becomes zero order in \(P_A\), a distinctive experimental signature used to confirm a genuinely heterogeneous, surface-saturation-limited mechanism. A

\text{low }P:\ \text{rate}\propto P;\qquad \text{high }P:\ \text{rate}\to\text{constant (zero order)}

Reading. The transition from first-order to zero-order kinetics as pressure rises is the experimental fingerprint of a surface-saturation mechanism, distinguishing heterogeneous catalytic kinetics from simple homogeneous gas-phase kinetics.

Scope. This full pressure dependence, interpolating smoothly between the two limits, is exactly the Langmuir-isotherm-based rate law of Step 4, valid across the entire pressure range for a single-reactant, surface-reaction-limited mechanism.

Problems

A heterogeneously catalysed reaction shows a rate that doubles when reactant pressure is doubled at low pressure, but is unaffected by a further pressure increase at high pressure. Explain both observations using the Result.
Solution
At low pressure, \(K_AP_A\ll1\), so \(\theta_A\approx K_AP_A\) (Worked Example 1) and the rate is directly proportional to \(P_A\); doubling \(P_A\) doubles the rate. At high pressure, \(K_AP_A\gg1\), so \(\theta_A\to1\) (Worked Example 2) and the rate saturates at \(k\), independent of further pressure changes — the surface is already essentially fully covered, so additional reactant pressure cannot increase the number of occupied sites any further.
A catalyst is exposed to a trace impurity that binds irreversibly and strongly to a fraction of its active sites. Predict, using the Result, how this affects the observed rate at high reactant pressure versus at low reactant pressure.
Solution
Irreversible binding of the impurity permanently removes those sites from the catalytic cycle, effectively reducing the total number of active sites (and hence the effective rate constant \(k\) in the Result) rather than changing the surface chemistry of the remaining sites. At high pressure (already saturated, rate \(\approx k\)), the rate would drop roughly in proportion to the fraction of sites poisoned. At low pressure (rate \(\approx kK_AP_A\)), the rate would also drop proportionally, since \(k\) appears as a simple multiplicative factor in both limits — poisoning reduces the observed rate at any pressure, though the underlying adsorption equilibrium constant \(K_A\) itself is unaffected for the remaining, unpoisoned sites.
Distinguish the Langmuir–Hinshelwood mechanism from the Eley–Rideal mechanism in one or two sentences, referencing Step 1 of the Proof.
Solution
In the Langmuir–Hinshelwood mechanism (the case developed in the Proof), both reacting species adsorb onto the surface (Step 1) before reacting together while both are surface-bound. In the Eley–Rideal mechanism, only one species adsorbs onto the surface; the second species reacts directly from the gas phase with the already-adsorbed species, without itself ever adsorbing, giving a different, generally simpler dependence of rate on the gas-phase reactant's pressure.