Surface Chemistry in Heterogeneous Catalysis — Coverage, Turnover Frequency and Activation Energy
A heterogeneous catalyst is a solid that speeds up a reaction of gases or liquids without being consumed. Most of the world's large-scale chemical manufacturing depends on them, and yet the whole subject reduces to three quantitative ideas you already meet in your syllabus: how much of the surface is covered, how fast each covered site turns over, and how much the activation barrier has been lowered. This article works those three through with real arithmetic, and then describes honestly what the research field does with them.
What actually happens, in order
Catalysis on a surface is a sequence, and any one step can be the slow one:
- Reactant diffuses from the bulk fluid to the outside of the catalyst particle.
- It diffuses into the pores, since almost all real catalysts are porous.
- It adsorbs onto an active site.
- The surface reaction occurs between adsorbed species.
- The product desorbs.
- The product diffuses back out and away.
Steps 3 to 5 are the chemistry; steps 1, 2 and 6 are mass transport. A common experimental finding is that a catalyst which looks slow is actually limited by transport, not by chemistry — which is why particle size and pore structure are treated as seriously as composition.
Adsorption: the two kinds, and why the difference matters
| Physisorption | Chemisorption | |
|---|---|---|
| Force involved | van der Waals | a genuine chemical bond to the surface |
| Enthalpy released | small, comparable with a heat of condensation | large, comparable with a bond enthalpy |
| Specificity | non-specific — any gas on any solid | specific — this adsorbate on this surface |
| Layers | multilayer possible | monolayer only |
| Reversibility | easily reversed by lowering pressure | often needs heating; may be irreversible |
| Effect of temperature | falls as temperature rises | rises with temperature at first, since it has its own activation barrier |
| Role in catalysis | mostly a route to the surface, and the basis of surface-area measurement | the step that activates the molecule — bonds are weakened or broken |
Only chemisorption catalyses. Physisorption matters for a different reason: multilayer physisorption of an inert gas at low temperature is how the surface area of a catalyst is measured in the first place, through the BET treatment, which extends Langmuir's monolayer picture to several layers.
The Langmuir isotherm
- θ — fraction of sites occupied, between 0 and 1
- P — pressure of the adsorbing gas
- K — adsorption equilibrium constant, units reciprocal to pressure
- V — volume adsorbed at pressure P; Vm the volume needed for a complete monolayer
Its assumptions are stated openly, and every one of them is an approximation: the surface is uniform so all sites are equivalent; adsorption stops at one monolayer; adsorbed molecules do not interact with their neighbours; and adsorption is a dynamic equilibrium. Real surfaces have edges, corners, steps and defects that bind differently, which is precisely why the linearised plot is used — a straight line is evidence the model is adequate for that system, and curvature is evidence that it is not.
Worked example 1 — surface coverage across three pressures
A gas adsorbs on a metal with K = 0.50 kPa⁻¹.
At P = 0.20 kPa: KP = 0.50 × 0.20 = 0.10
θ = 0.10 ÷ (1 + 0.10) = 0.10 ÷ 1.10 = 0.091
At P = 4.0 kPa: KP = 0.50 × 4.0 = 2.0
θ = 2.0 ÷ (1 + 2.0) = 2.0 ÷ 3.0 = 0.667
At P = 20 kPa: KP = 0.50 × 20 = 10
θ = 10 ÷ (1 + 10) = 10 ÷ 11 = 0.909
Look at the pattern. At low pressure θ is nearly proportional to P, so a reaction whose rate depends on coverage looks first order in that gas. At high pressure θ approaches 1 and stops responding, so the same reaction looks zero order. The Langmuir isotherm therefore explains, in one line of algebra, why the measured order of a surface reaction changes with pressure. That is a favourite examination point.
Worked example 2 — how much faster does the catalyst make it?
A catalyst does not change ΔG or the equilibrium constant. It provides a different mechanism with a lower activation energy, so both forward and reverse rates rise by the same factor and equilibrium arrives sooner at the same place.
Uncatalysed Ea = 180 kJ mol⁻¹, catalysed Ea = 90 kJ mol⁻¹, at T = 500 K.
ΔEa = 180 − 90 = 90 kJ mol⁻¹
= 90000 J mol⁻¹
RT = 8.314 × 500 = 4157 J mol⁻¹
ΔEa/RT = 90000 ÷ 4157 = 21.65
ratio = e21.65
21.65 ÷ 2.3026 = 9.403, so the ratio = 109.403
= 2.5 × 10⁹
Halving the barrier speeds the reaction up by a factor of about two and a half billion at this temperature. State the assumption honestly, though: this calculation holds the pre-exponential factor constant, and in reality A differs between the two mechanisms — a surface route usually has a smaller A because the adsorbed reactants have lost translational and rotational freedom. The exponential term still dominates, so the conclusion survives, but the exact factor should not be quoted as though it were measured.
Worked example 3 — turnover frequency, the fair way to compare catalysts
A rate quoted "per gram of catalyst" mixes up how good the material is with how much of it is exposed. Turnover frequency removes that confusion:
0.20 g of catalyst has an active-site density of 1.5 × 10⁻⁴ mol of sites per gram, and converts 6.0 × 10⁻⁴ mol of reactant in 10.0 minutes.
sites = 0.20 × 1.5 × 10⁻⁴
= 3.0 × 10⁻⁵ mol
rate = 6.0 × 10⁻⁴ ÷ 600 s
= 1.0 × 10⁻⁶ mol s⁻¹
TOF = 1.0 × 10⁻⁶ ÷ 3.0 × 10⁻⁵
= 0.033 s⁻¹, that is 2.0 conversions per site per minute
The honest difficulty is in the denominator. Counting active sites is genuinely hard, because not every surface atom is active and the number can change while the reaction runs. Any TOF should therefore be read together with a statement of how the sites were counted.
Two surface mechanisms worth knowing by name
- Langmuir–Hinshelwood — both reactants adsorb, then react on the surface. Its rate law contains the coverages of both, so raising the pressure of one reactant too far can reduce the rate by crowding the other off the surface. That counter-intuitive maximum in the rate is the signature of this mechanism, and it is a standard examination question.
- Eley–Rideal — one reactant adsorbs and the other strikes it directly from the gas phase. Here the rate rises with the pressure of the gas-phase partner without any such maximum.
The Sabatier principle — why the best catalyst binds moderately
If the surface binds the reactant too weakly, coverage stays near zero (Example 1, first line) and nothing happens. If it binds too strongly, the reactant is activated but the product will not leave, and the surface stays blocked. The best catalyst binds in between. Plotting activity against binding strength therefore gives a peak — the "volcano" shape — and the whole search for new catalysts can be framed as the search for a material sitting at the top of that curve. Promoters, alloying and choice of support are all ways of shifting a material's binding strength towards the peak.
How catalysts die
- Poisoning — a species chemisorbs so strongly that it never leaves, and that site is gone. Sulfur compounds are the classic example, which is why feedstocks are desulfurised before they reach a sensitive catalyst.
- Sintering — at high temperature small metal particles merge into larger ones. Total mass is unchanged but exposed surface falls, so activity falls with it.
- Coking — carbon deposits block pores. Often reversible by controlled burn-off, which is why some processes run with continuous catalyst regeneration.
- Fouling and attrition — physical blocking and mechanical breakup in a moving bed.
Research in this field, described generically, concentrates on watching the surface while it works — spectroscopic and diffraction methods applied under reaction conditions rather than on a cold sample afterwards — on making every metal atom count by dispersing the active phase as finely as possible, and on computational screening of binding energies to predict where a material sits on the volcano before it is ever made.
Mistakes that cost marks
- Saying a catalyst shifts the equilibrium. It does not. It changes neither ΔG nor K, only the rate at which equilibrium is reached. This is the single most penalised error in the topic.
- Saying a catalyst lowers the activation energy of the reaction. Strictly it offers a different pathway with its own lower barrier. The original pathway is unchanged and still available.
- Mixing up the two adsorptions. Large enthalpy, specific, monolayer, activated means chemisorption; small enthalpy, non-specific, multilayer means physisorption.
- Applying Langmuir where its assumptions fail. On a heterogeneous surface with strong lateral interactions, the isotherm will not be linear when plotted in the linearised form — and that curvature is data, not experimental error.
- Comparing rates per gram. Two catalysts can differ in rate per gram purely because of surface area. Compare TOF, and say how sites were counted.
- Assuming more surface area is always better. Very fine pores can make internal diffusion the slow step, so added area goes unused.
- Reporting an apparent activation energy as a true one. The Ea measured for an overall catalytic reaction usually contains adsorption enthalpies as well as the surface-step barrier.
Where this appears in your exam
| Exam | How it is asked |
|---|---|
| IIT-JAM | Physisorption versus chemisorption, Langmuir and Freundlich isotherms, coverage numericals |
| GATE | Surface reaction rate laws, order changing with pressure, BET surface area, catalyst deactivation |
| CSIR-NET | Langmuir–Hinshelwood versus Eley–Rideal, colloids and surfaces, catalyst characterisation methods |
| CUET-PG | Definitions, adsorption isotherm shapes and straightforward θ calculations |
Try the barrier arithmetic yourself. Change the two activation energies or the temperature in Example 2 and watch the rate ratio move — it is the fastest way to feel how violently an exponential responds to a change in Ea.
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