Study notes

Qwestrum Engineering360 · Chemical Engineering · Chemical Reaction Engineering

Catalysis Basics

Heterogeneous catalysis proceeds through adsorption, surface reaction and desorption; Langmuir-Hinshelwood kinetics captures site competition, while the Thiele modulus and effectiveness factor quantify how internal pore diffusion can throttle the intrinsic rate.

Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

Thiele modulus φ measures pore-diffusion versus reaction rate
$Effectiveness factor \eta = actual \frac{rate}{rate} without diffusion limit$
Deactivation: activity falls with time on stream

Topic details

Introduction

This topic introduces solid-catalysed reactions central to refining and chemicals. You build a rate law from the Langmuir adsorption isotherm and surface-reaction steps, identify which of the seven physical steps (film diffusion, pore diffusion, adsorption, reaction, desorption, and back) is limiting, and use the Thiele modulus and effectiveness factor to correct the observed rate for diffusion resistance inside the pellet.

Key relations & formulas

-r_{A} = k \frac{C_{A}}{(1 + K_{A} C_{A})}

(Langmuir-Hinshelwood, single site)

\theta_{i} = K_{i} \frac{P_{i}}{(1 + Σ K_{j} P_{j})}

(Langmuir surface coverage)

\eta = tanh\frac{(\phi)}{\phi}

(effectiveness factor, first-order slab, small φ)

Notation and sign conventions

Relation 1 —

-r_{A} = k C_{A} /

-r_{A} = k \frac{C_{A}}{(1 + K_{A} C_{A})}

(Langmuir-Hinshelwood, single site)

Write this relation with symbols exactly as in Chemical Reaction Engineering — Octave Levenspiel before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

\theta_{i} = K_{i} P_{i} /

\theta_{i} = K_{i} \frac{P_{i}}{(1 + Σ K_{j} P_{j})}

(Langmuir surface coverage)

Relation 3 —

\eta = tanh

\eta = tanh\frac{(\phi)}{\phi}

(effectiveness factor, first-order slab, small φ)

Concept in depth

A catalyst offers a lower-energy surface pathway; reactants must reach an active site, adsorb, react, and the products desorb. The Langmuir-Hinshelwood form embodies competition for a finite number of sites, so the rate can saturate at high concentration. Inside a porous pellet, reactant must diffuse to interior sites; when the reaction is fast relative to diffusion (large Thiele modulus), the interior is starved and only the outer shell works, so the effectiveness factor drops well below one. Recognising the rate-limiting step tells you whether to change temperature (reaction-limited) or particle size (diffusion-limited).

Assumptions and validity limits

State assumptions explicitly before using any relation for catalysis basics — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Reaction Engineering viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Reaction Engineering papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to catalysis basics.
4. Use equation 1:

-r_{A} = k C_{A} /

.
5. Use equation 2:

\theta_{i} = K_{i} P_{i} /

.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Catalysis Basics appears in chemical and pharma plants. In Indian chemical curricula this topic is tested because it connects theory to reactor design and kinetics.

GATE and semester exams often combine catalysis basics with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use catalysis basics?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Students assume the reaction is always surface-reaction controlled and ignore pore-diffusion limitation revealed by a large Thiele modulus. Others forget that a large effectiveness factor drop lowers the apparent activation energy (roughly halving it), and confuse adsorption equilibrium constants with rate constants.

Quick revision checklist

Before attempting catalysis basics problems, confirm you can:

1. Thiele modulus φ measures pore-diffusion versus reaction rate
2.

Effectiveness factor \eta = actual \frac{rate}{rate} without diffusion limit

3. Deactivation: activity falls with time on stream

Revise the solved examples in Chemical Reaction Engineering — Octave Levenspiel and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Effectiveness factor at large Thiele modulus

Problem

A first-order catalyst pellet (slab) has Thiele modulus φ = 5. Estimate the effectiveness factor.

Solution

For large φ, η ≈ 1/φ = 1/5 = 0.2. Only about 20% of the catalyst is fully utilised, so the reaction is strongly pore-diffusion limited.

Conceptual check — Catalysis Basics

Problem

In a Reaction Engineering semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of catalysis basics." What should a complete answer include?

Exams & GATE

Identify the rate-limiting step: external film, pore diffusion, or surface reaction.

📖 Standard books (India)

Chemical Reaction Engineering — Octave Levenspiel
Read: Syllabus unit
Reactor design and kinetics

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📚Key formulas & points