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Topic Guide

Chemical Reaction
Engineering Guide

Rate laws, ideal reactor design (batch, CSTR, PFR), multiple reactions, RTD, and catalysis for the GATE Chemical Engineering paper.

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Overview

Chemical Reaction Engineering (CRE) asks a deceptively simple question, how big does a reactor need to be, and what will come out of it?, and builds a complete toolkit to answer it for any rate law, reactor type, and flow pattern. In the GATE CH syllabus it's consistently one of the highest-weightage sections, because it combines kinetics (how fast a reaction goes) with reactor design (how that rate translates into required volume or residence time), and both halves are tested heavily.

The section splits cleanly. Kinetics covers rate laws, reaction order, and the Arrhenius temperature dependence, usually determined from concentration-vs-time data. Reactor design covers the ideal reactor types, batch, CSTR (continuous stirred-tank), and PFR (plug flow), each with its own design equation relating conversion, rate, and either time or volume, plus combinations like reactors in series or with recycle. Non-ideal flow (residence time distribution, or RTD) and heterogeneous/catalytic reactions (external and internal mass-transfer effects, catalyst deactivation) round out the syllabus as the more advanced, GATE-favorite topics.

The standard reference for this section is Fogler's "Elements of Chemical Reaction Engineering," and its design-equation-first approach (write the mole balance, substitute the rate law, integrate) is exactly the method GATE numericals reward. Multiple-reaction problems (parallel and series reactions, selectivity) are a GATE favorite precisely because they test whether you can track more than one species' mole balance at once.

Real GATE CH PYQ Frequency (2024–2026)

2024202520263-Yr Avg
9999

Computed directly from 27 real questions tagged to this topic across our GATE CH 2024–2026 archive, averaging 9 questions/year. Browse the underlying 27 questions for this topic in the PYQ archive, or see the full topic weightage comparison across all topics.

GATE Weightage

Chemical Reaction Engineering typically contributes 6–9 questions (about 10–15 marks) to the GATE CH paper, usually the single highest-weightage section, spread across kinetics, ideal reactor design, non-ideal flow, and catalysis.

Sub-areaApprox. Marks
Kinetics & rate laws~2–3
Ideal reactor design (batch, CSTR, PFR)~3–4
Multiple reactions & reactor networks (series, recycle)~2–3
Non-ideal flow (RTD) & catalysis~2–3

Sub-area split is a directional estimate (our archive doesn't tag marks at this granularity), for the real, computed topic-level total, see "Real GATE CH PYQ Frequency" above.

Key Subtopics

1

Rate laws & reaction order

Power-law kinetics, determining reaction order and rate constant from concentration-time data (integral or differential method), and the Arrhenius equation for temperature dependence.

2

Batch reactor design

The batch reactor design equation (integrating the mole balance over time for constant- and variable-volume systems), used as the basis for determining rate laws from lab data.

3

CSTR design

The continuous stirred-tank reactor design equation, algebraic, not differential, since perfect mixing means the exit concentration equals the tank concentration everywhere.

4

PFR design

The plug flow reactor design equation, integrated along reactor length/volume assuming no axial mixing (a differential mole balance, unlike the CSTR's algebraic one).

5

Reactors in series & recycle

Comparing CSTRs-in-series (approaching PFR performance as N → ∞) and recycle reactors, which behave like a CSTR at high recycle ratio and a PFR at low recycle ratio.

6

Multiple reactions

Parallel and series (consecutive) reaction networks, where selectivity and yield, not just conversion, determine the optimal reactor choice and operating conditions.

7

Non-ideal flow (RTD)

The residence time distribution E(t), used to diagnose deviations from ideal PFR/CSTR behavior via models like the tanks-in-series or dispersion model.

8

Heterogeneous & catalytic reactions

External (film) and internal (pore diffusion, via the Thiele modulus and effectiveness factor) mass-transfer resistances in catalytic reactions, plus catalyst deactivation.

Essential Formulas

Full formula reference →

−rA=kCAn-r_A = k C_A^n

Power-law rate expression; n = reaction order, k = rate constant

k=Ae−Ea/RTk = A e^{-E_a/RT}

Arrhenius equation, temperature dependence of the rate constant

VCSTR=FA0X−rAV_{CSTR} = \dfrac{F_{A0}X}{-r_A}

CSTR design equation, exit conditions apply throughout the whole reactor volume

VPFR=FA0∫0XdX−rAV_{PFR} = F_{A0}\int_0^X \dfrac{dX}{-r_A}

PFR design equation, conditions change continuously along the reactor length

tbatch=NA0∫0XdX(−rA)Vt_{batch} = N_{A0}\int_0^X \dfrac{dX}{(-r_A)V}

Batch reactor design equation, time required for a given conversion

SD/U=rDrUS_{D/U} = \dfrac{r_D}{r_U}

Instantaneous selectivity of a desired product D over an undesired product U in parallel/series reactions

τ=Vv0\tau = \dfrac{V}{v_0}

Space time, the ideal residence time based on volumetric flow rate v0

tˉ=∫0∞t E(t) dt\bar t = \int_0^{\infty} t\,E(t)\,dt

Mean residence time from the residence time distribution E(t)

ϕ=LkDeff\phi = L\sqrt{\dfrac{k}{D_{eff}}}

Thiele modulus, compares reaction rate to internal (pore) diffusion rate in a catalyst pellet

η=actual rate with pore diffusionrate at surface conditions\eta = \dfrac{\text{actual rate with pore diffusion}}{\text{rate at surface conditions}}

Catalyst effectiveness factor, approaches 1 at low Thiele modulus, 1/φ at high Thiele modulus

CA=CA0(1−X)C_{A} = C_{A0}(1-X)

Concentration in terms of conversion for a constant-volume (or constant-density) system

Visual Reference

Conversion, X1/(−rA)PFR: area under curveCSTR: rectangle at exit XX = 0.8
Same rate data, same exit conversion — for this first-order example, PFR needs V/FA0 ≈ 1.61 L·min/mol, CSTR needs ≈ 4.00L·min/mol, the CSTR rectangle always overshoots the curve it's inscribed against.
Small white porous solid beads, packed together
Solid catalyst pellets take exactly this physical form — packed as a fixed bed, with pore-diffusion resistance (the Thiele modulus) governing how much of each bead's interior surface actually participates in the reaction. Desiccants, CC BY-SA 3.0, via Wikimedia Commons.

Derivations & Physical Insight

Why CSTR Volume Is Larger Than PFR Volume for the Same Conversion (Positive-Order Kinetics)

Both reactor design equations integrate the same quantity, F_A0/(−r_A) versus conversion X, but in fundamentally different ways. A PFR integrates continuously along the reactor, so at every point it "sees" the actual local rate, which is higher at low conversion (higher concentration) and decreases smoothly as conversion rises. A CSTR, by contrast, is perfectly mixed, so the entire reactor operates at the single (typically low) rate corresponding to the exit conversion, the highest-conversion, slowest-rate point on the whole curve.

Graphically, PFR volume is the area under the 1/(−r_A) vs. X curve from 0 to X (a Simpson's-rule-style integral that captures the fast, low-conversion rates too), while CSTR volume is a rectangle of height 1/(−r_A) evaluated at the exit X, times the conversion X, a level performance test always shows this rectangle sitting above the curve for any positive-order, concentration-decreasing rate law. That's precisely why a CSTR always requires more volume than a PFR for the same conversion and rate law, the CSTR "wastes" reaction driving force by mixing the low-concentration exit stream back with the high-concentration feed instantaneously.

Deriving the Thiele Modulus and Why It Predicts the Effectiveness Factor

Inside a porous catalyst pellet, reactant must diffuse in through the pores at the same time it's being consumed by reaction, a competition between diffusion rate and reaction rate. Writing a differential mass balance on reactant diffusing into a pellet (Fick's law diffusion term balanced against a first-order reaction consumption term) and non-dimensionalizing the resulting second-order ODE naturally produces a single dimensionless group multiplying the equation, the Thiele modulus φ = L√(k/D_eff), where L is a characteristic pellet dimension.

When φ is small, diffusion is fast relative to reaction, so reactant penetrates the whole pellet before it can react, the entire catalyst volume is used effectively, and the effectiveness factor η ≈ 1. When φ is large, reaction consumes reactant faster than it can diffuse inward, so only a thin outer shell of the pellet actually participates in reaction, most of the expensive catalyst interior sits idle, and η ≈ 1/φ. This is why increasing catalyst pellet size beyond a certain point gives diminishing returns: a larger pellet has more Thiele modulus (bigger L) and a lower effectiveness factor, so total surface-normalized activity per unit catalyst volume actually falls.

Worked Practice Problems

Original practice problems in the GATE CH style, not copied from any question bank. Work them before reading the solution.

1-mark · NAT

PFR Volume for a First-Order Liquid-Phase Reaction

Problem: A first-order liquid-phase reaction (k = 0.2 min⁻¹) is run in a PFR to achieve 80% conversion at a feed rate FA0 corresponding to CA0 = 2 mol/L and volumetric flow v0 = 10 L/min. Find the required PFR volume.

Given: k = 0.2 min⁻¹, X = 0.80, first-order, constant density, v0 = 10 L/min.

VPFR=v0kln⁡ ⁣(11−X)=100.2ln⁡ ⁣(10.2)V_{PFR} = \dfrac{v_0}{k}\ln\!\left(\dfrac{1}{1-X}\right) = \dfrac{10}{0.2}\ln\!\left(\dfrac{1}{0.2}\right)
=50×1.609= 50 \times 1.609

Answer: V ≈ 80.5 L

2-mark · NAT

CSTR vs. PFR Volume Comparison for Second-Order Kinetics

Problem: A second-order liquid-phase reaction (−rA = kCA², k = 0.5 L/mol·min, CA0 = 1 mol/L) is to achieve 75% conversion at v0 = 5 L/min. Compare the required CSTR and PFR volumes.

Given: k = 0.5 L/mol·min, CA0 = 1 mol/L, X = 0.75, v0 = 5 L/min, constant density, second order.

CA=CA0(1−X)=1×0.25=0.25 mol/L,−rA=kCA2=0.5×0.252=0.03125 mol/L⋅minC_A = C_{A0}(1-X) = 1 \times 0.25 = 0.25\ \text{mol/L}, \quad -r_A = kC_A^2 = 0.5 \times 0.25^2 = 0.03125\ \text{mol/L·min}
VCSTR=v0CA0X−rA=5×1×0.750.03125=120 LV_{CSTR} = \dfrac{v_0 C_{A0} X}{-r_A} = \dfrac{5 \times 1 \times 0.75}{0.03125} = 120\ \text{L}
VPFR=v0kCA0[X1−X]=50.5×1[0.750.25]=10×3V_{PFR} = \dfrac{v_0}{kC_{A0}}\left[\dfrac{X}{1-X}\right] = \dfrac{5}{0.5\times1}\left[\dfrac{0.75}{0.25}\right] = 10 \times 3

Answer: V_CSTR = 120 L; V_PFR = 30 L, the CSTR needs 4× the volume of the PFR for the same conversion, as expected for positive-order kinetics.

Topic-wise PYQ Frequency

High

Ideal reactor design (batch, CSTR, PFR sizing)

GATE 2024 Q45 (PFR/CSTR comparison), 2025 Q58 (PFR design), and 2026 Q55 (adiabatic CSTR) show this is tested almost every year.

High

Multiple reactions & selectivity

GATE 2024 Q21 and GATE 2026 Q43 both tested parallel-reaction selectivity, a GATE CRE favorite.

Medium

Residence time distribution (RTD)

A recurring topic, GATE 2024 Q46, GATE 2025 Q23/Q35, and GATE 2026 Q56 (tanks-in-series) all drew on RTD concepts.

Medium

Catalysis & catalyst deactivation

GATE 2025 Q20 and Q29/Q59 (catalyst deactivation) confirm this is tested regularly, often alongside pore-diffusion effects.

Medium

Recycle reactors

GATE 2024 Q54, GATE 2025 Q64, and GATE 2026 Q19/Q64 show recycle-reactor problems recur across years.

Low

Enzyme/bioreactor kinetics

GATE 2024 Q62 and GATE 2025 Q31 tested bioreactor/enzyme kinetics, a less frequent but recurring niche.

Recommended Study Order

  1. 1

    1. Rate laws & the Arrhenius equation

    The foundation for every reactor design calculation, get comfortable extracting k and n from concentration-time data first.

  2. 2

    2. Batch, CSTR & PFR design equations

    The highest-yield subtopic in all of GATE CH, practice deriving and integrating each design equation until it's automatic.

  3. 3

    3. Multiple reactions & selectivity

    A GATE favorite that builds directly on single-reaction design equations, just tracked for two or more species at once.

  4. 4

    4. Reactors in series & recycle

    A natural extension once single-reactor sizing is solid, focus on the high-recycle-ratio limits (CSTR-like) and low-recycle-ratio limits (PFR-like).

  5. 5

    5. Non-ideal flow (RTD)

    Conceptually distinct from ideal reactor sizing, study once ideal reactors are secure, since RTD models are compared against ideal PFR/CSTR behavior.

  6. 6

    6. Catalysis & the Thiele modulus

    The most advanced subtopic, study last, building on both kinetics and diffusion concepts from Mass Transfer.

Common Pitfalls

✗ Using the CSTR design equation (algebraic) when the problem describes a PFR, or vice versa.

✓ CSTR: exit conditions apply everywhere (algebraic equation, no integral). PFR: conditions vary continuously along the reactor (must integrate 1/(−rA) over conversion or length).

✗ Forgetting that conversion X in a variable-volume (gas-phase, mole-number-changing) reaction requires an explicit volume-correction term.

✓ For constant-density (most liquid-phase) systems, CA = CA0(1−X) is exact; for variable-volume gas-phase systems, include the expansion factor ε: CA = CA0(1−X)/(1+εX).

✗ Comparing CSTR and PFR volumes without checking the sign/order of the rate law.

✓ CSTR ≥ PFR volume only holds for positive-order kinetics where rate decreases with conversion; for autocatalytic or negative-order reactions, this can reverse.

✗ Assuming a catalyst effectiveness factor of 1 without checking the Thiele modulus.

✓ Only assume negligible pore-diffusion resistance (η ≈ 1) when the problem gives a small Thiele modulus or explicitly states diffusion is fast, otherwise, compute φ first.

Put It Into Practice

Work through the PFR/CSTR sizing problems above by writing the design equation from scratch each time, then apply the same method to the multiple-reaction and RTD problems in the full GATE previous-year test set.

Take a Practice Test →Browse Solved PYQs →

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