Study notes

Qwestrum Engineering360 · Chemical Engineering · Chemical Reaction Engineering

Reaction Kinetics

Reaction kinetics quantifies how fast a reaction proceeds through a rate law −r_A = k·C_A^a…; the rate constant follows Arrhenius temperature dependence, and orders are determined experimentally, not from stoichiometry unless the step is elementary.

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.

Reaction order ≠ stoichiometry unless the step is elementary
$Half-life t_\frac{1}{2} = ln \frac{2}{k} for a first-order reaction$
$Reversible: -r_{A} = k_{f} f(C) - k_{r} g(C); rate is zero at equilibrium$

Topic details

Introduction

This foundational Levenspiel topic gives the rate expression that every reactor design consumes. You learn to determine reaction order and rate constant from batch data (integral or differential methods), apply the Arrhenius equation to capture temperature effects, and recognise reversible kinetics that vanish at equilibrium.

Key relations & formulas

-r_{A} = -(\frac{1}{V}) \frac{dN_{A}}{dt}

(rate definition, Levenspiel)

-r_{A} = k C_{A}^a C_{B}^b

(power-law rate law)

k = k_{0} exp(-\frac{E}{RT})

(Arrhenius equation)

Notation and sign conventions

Relation 1 —

-r_{A} = -

-r_{A} = -(\frac{1}{V}) \frac{dN_{A}}{dt}

(rate definition, Levenspiel)

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 —

-r_{A} = k C_{A}^a C_{B}^b

-r_{A} = k C_{A}^a C_{B}^b

(power-law rate law)

Relation 3 —

k = k_{0} exp

k = k_{0} exp(-\frac{E}{RT})

(Arrhenius equation)

Concept in depth

The rate law connects the disappearance of a reactant to concentrations raised to their orders. Orders reflect the reaction mechanism and must be found by experiment; only for an elementary single-step reaction do they equal the stoichiometric coefficients. The Arrhenius relation shows the rate constant rising exponentially with temperature because a larger fraction of molecular collisions exceed the activation energy — a 10 °C rise often roughly doubles the rate. For reversible reactions the net rate is the forward minus the reverse term, so it falls to zero as the system approaches equilibrium, which caps conversion regardless of time.

Assumptions and validity limits

State assumptions explicitly before using any relation for reaction kinetics — 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 reaction kinetics.
4. Use equation 1:

-r_{A} = -

.
5. Use equation 2:

-r_{A} = k C_{A}^a C_{B}^b

.
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

Reaction Kinetics 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 reaction kinetics with earlier units — revise prerequisites before attempting mixed problems.

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

Common mistakes in exams

The classic error is equating reaction order with stoichiometric coefficients for non-elementary reactions. Others include using temperature in Celsius in the Arrhenius exponent, mismatching rate-constant units with the reaction order, and forgetting that a reversible reaction cannot exceed its equilibrium conversion.

Quick revision checklist

Before attempting reaction kinetics problems, confirm you can:

1. Reaction order ≠ stoichiometry unless the step is elementary
2.

Half-life t_\frac{1}{2} = ln \frac{2}{k} for a first-order reaction

Reversible: -r_{A} = k_{f} f(C) - k_{r} g(C); rate is zero at equilibrium

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.

First-order half-life

Problem

A first-order reaction has k = 0.05 min⁻¹. Find the half-life and the time for 90% conversion.

Solution

t_½ = ln2/k = 0.693/0.05 = 13.9 min. For 90%: t = ln(1/(1−0.9))/k = ln10/0.05 = 2.303/0.05 = 46.1 min.

Conceptual check — Reaction Kinetics

Problem

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

Exams & GATE

Levenspiel Ch. 3 — integrate the rate law with stoichiometry for batch.

📖 Standard books (India)

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

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📚Key formulas & points