Chemical Reaction Engineering: practice problems and exam questions

Reaction rates and rate laws, CSTR and plug-flow reactor sizing, conversion and equilibrium limits.

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Cram pack (PDF)Formula sheets, method steps and practice problems with full solutions, ready to print.

Topics in this course

  1. Reaction kineticsfirst order · conversion and second order · Arrheniuscalculations
  2. Reactor sizing (CSTR & PFR)CSTR first order · PFR first order · conversion from volumecalculations
  3. Chemical equilibriumKc from concentrations · ICE table · ICE table with a quadraticcalculations
  4. Mass balancemixing two streams · blending to a target · evaporatorcalculations

Exam tips for Chemical Reaction Engineering

  • Write the design equation for the reactor type before you substitute the rate law.
  • For the same conversion, a PFR needs less volume than a CSTR for positive-order reactions.
  • Check that the conversion you aim for is below the equilibrium conversion.

Worked examples

Reaction kineticsEasy
t (min)C (mol/L)60 minC = ?

A zero-order reaction A → products has a rate constant of 0.01 mol/(L·min). The initial concentration of A is 0.8 mol/L. Find the concentration CA after 60 min.

k = 0.01 mol/(L·min)CA0 = 0.8 mol/Lt = 60 min

Find CA (mol/L)

Show hints
  1. Zero order: the rate −dC/dt = k does not depend on the concentration.
  2. Integrating gives C = C₀ − kt (valid until A runs out).
  3. kt = 0.6 mol/L.
Show the answer and the step-by-step solution

Integrated rate laws: zero order: C = C₀ − kt (straight line, t½ = C₀/(2k)); first order: ln(C₀/C) = kt (t½ = ln 2/k); second order: 1/C − 1/C₀ = kt (t½ = 1/(kC₀)). Conversion X means C = C₀(1 − X).

Integrated zero-order law

CA = CA0 − kt = 0.8 − 0.01·60 = 0.2 mol/L

Answer

CA = 0.2 mol/L
Reactor sizing (CSTR & PFR)Medium
Q = 20 L/minCA0​ = 2.5 mol/LCA​ = ?V = 200 L, k = 0.25 min⁻¹

A liquid-phase first-order reaction A → B (k = 0.25 min⁻¹) runs in a 200 L plug-flow reactor (PFR). The feed enters at 20 L/min with CA0 = 2.5 mol/L. The density is constant and the reactor is at steady state. Find the outlet concentration CA.

V = 200 LQ = 20 L/mink = 0.25 min⁻¹CA0 = 2.5 mol/L

Find CA (mol/L)

Show hints
  1. Space time: τ = V/Q = 10 min.
  2. PFR, first order: CA = CA0·e^(−kτ).
  3. kτ = 2.5.
Show the answer and the step-by-step solution

Ideal reactors, first-order reaction (−rA = k·CA) at steady state, with space time τ = V/Q. A CSTR is perfectly mixed, so the whole volume reacts at the low outlet concentration: τ = X/(k·(1 − X)) and CA = CA0/(1 + k·τ). In a PFR each slice of fluid reacts like a small batch reactor: τ = ln(1/(1 − X))/k and CA = CA0·e−k·τ. For the same conversion a CSTR always needs more volume than a PFR.

Space time

τ = V/Q = 200/20 = 10 min

Outlet concentration

CA = 2.5·e−0.25·10 = 0.2052 mol/L

Answer

CA = 0.2052 mol/L

Conversion: X = 91.79%.

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

CSTR and PFR volume calculator

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