Practice Problems: Reactor Design

Table of Contents
1. Question 1
2. Question 2
3. Question 3
4. Question 4
5. Question 5
6. Question 6
7. Question 7
8. Question 8
9. Question 9
10. Question 10
11. Question 11
12. Question 12
13. Question 13
14. Question 14
15. Question 15
16. Question 16
17. Question 17
18. Question 18
19. Question 19
20. Question 20
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Question 1

A chemical engineer is designing a continuous stirred tank reactor (CSTR) for the liquid-phase reaction A → B. The reaction is first-order with respect to A with a rate constant of 0.15 min⁻¹. The feed stream contains reactant A at a concentration of 2.5 mol/L and enters at a volumetric flow rate of 100 L/min. If the desired conversion is 80%, what reactor volume is required?
(a) 2130 L
(b) 2667 L
(c) 3200 L
(d) 1780 L

Question 2

A process engineer is evaluating a plug flow reactor (PFR) for a second-order irreversible reaction 2A → B. The rate constant is 0.25 L/(mol·min) and the feed contains 3.0 mol/L of A with a flow rate of 50 L/min. To achieve 75% conversion, what reactor volume is needed?
(a) 300 L
(b) 450 L
(c) 600 L
(d) 750 L

Question 3

A chemical plant operates a batch reactor for the first-order decomposition reaction A → Products with a rate constant of 0.08 min⁻¹. The initial concentration of A is 4.0 mol/L. How long must the reaction proceed to achieve 90% conversion?
(a) 18.4 min
(b) 23.0 min
(c) 28.8 min
(d) 32.5 min

Question 4

A reactor design team is comparing a CSTR and a PFR for a first-order reaction with k = 0.20 min⁻¹. Both reactors have a volume of 1500 L and receive feed at 150 L/min with C_A0 = 2.0 mol/L. What is the difference in conversion between the PFR and CSTR?
(a) 0.12
(b) 0.18
(c) 0.24
(d) 0.30

Question 5

An engineer designs a mixed flow reactor for the elementary liquid-phase reaction A + B → C. The reaction is first-order in both A and B with k = 0.10 L/(mol·min). Feed streams containing A (4.0 mol/L) and B (4.0 mol/L) are mixed and fed at a combined rate of 80 L/min. For 70% conversion of A, what reactor volume is required?
(a) 1867 L
(b) 2240 L
(c) 2800 L
(d) 3200 L

Question 6

A pharmaceutical company operates a semi-batch reactor where reactant A (initially 500 L at 2.0 mol/L) reacts with B continuously fed at 50 L/min with concentration 3.0 mol/L. The reaction A + B → C is first-order in A with k = 0.05 min⁻¹. Assuming constant density and excess B, what is the conversion of A after 20 minutes?
(a) 0.48
(b) 0.55
(c) 0.63
(d) 0.70

Question 7

A refinery engineer is designing a tubular reactor (PFR) for the gas-phase decomposition A → 2B with a first-order rate constant of 0.30 s⁻¹ at operating temperature. The feed is pure A at 5 atm and 400°C with a molar flow rate of 10 mol/s. For 85% conversion and assuming isothermal operation, what reactor volume is needed?
(a) 45.2 L
(b) 63.1 L
(c) 78.5 L
(d) 92.3 L

Question 8

A process engineer needs to select between two CSTRs in series versus one large CSTR for a first-order reaction with k = 0.12 min⁻¹. The total volume available is 3000 L and feed rate is 200 L/min with C_A0 = 1.5 mol/L. What is the conversion achieved with two equal-volume CSTRs in series?
(a) 0.69
(b) 0.75
(c) 0.81
(d) 0.87

Question 9

A biochemical engineer operates a continuous reactor for an enzymatic reaction following Michaelis-Menten kinetics: r = (0.8 C_S)/(2 + C_S) mol/(L·min) where C_S is substrate concentration. The feed substrate concentration is 10 mol/L at 100 L/min. What CSTR volume is needed for 80% conversion?
(a) 850 L
(b) 1100 L
(c) 1350 L
(d) 1600 L

Question 10

A chemical engineer designs a PFR for the exothermic reversible reaction A ⇌ B with forward rate constant k_f = 0.25 min⁻¹ and reverse rate constant k_r = 0.05 min⁻¹ at operating temperature. Feed is pure A at 3.0 mol/L with flow rate 60 L/min. What reactor volume achieves 70% of equilibrium conversion?
(a) 420 L
(b) 560 L
(c) 680 L
(d) 750 L

Question 11

A petrochemical plant operates a fluidized bed reactor (assumed as CSTR) for catalytic cracking. The reaction follows first-order kinetics with k = 5.0 s⁻¹. The feed enters at 800 kg/h with reactant concentration of 0.5 kmol/m³. For 95% conversion and feed density of 750 kg/m³, what reactor volume is required?
(a) 0.071 m³
(b) 0.142 m³
(c) 0.213 m³
(d) 0.284 m³

Question 12

A reactor engineer evaluates an autocatalytic reaction A + R → 2R with rate r = k C_A C_R where k = 0.15 L/(mol·min). The feed contains C_A0 = 4.0 mol/L and C_R0 = 0.5 mol/L at 75 L/min. What CSTR volume gives 80% conversion of A?
(a) 975 L
(b) 1250 L
(c) 1580 L
(d) 1850 L

Question 13

A chemical facility operates a non-isothermal PFR for reaction A → B with activation energy E_a = 80 kJ/mol. At 350 K, k = 0.10 min⁻¹. Due to heat effects, temperature increases linearly to 370 K along the reactor. What is the average rate constant if the inlet concentration is 2.5 mol/L?
(a) 0.165 min⁻¹
(b) 0.198 min⁻¹
(c) 0.223 min⁻¹
(d) 0.251 min⁻¹

Question 14

A process engineer designs a recycle reactor for a first-order reaction with k = 0.08 min⁻¹. The PFR volume is 2000 L with fresh feed at 100 L/min. A recycle ratio R = 2 (recycle flow/fresh feed flow) is used. What is the overall conversion achieved?
(a) 0.58
(b) 0.64
(c) 0.70
(d) 0.76

Question 15

A polymer engineer operates a batch reactor for polymerization with second-order kinetics: r = k C_A² where k = 0.04 L/(mol·min). Initial monomer concentration is 5.0 mol/L. How long does it take to achieve 88% conversion?
(a) 73 min
(b) 88 min
(c) 110 min
(d) 125 min

Question 16

A chemical plant uses three CSTRs in series with volumes V₁ = 800 L, V₂ = 1200 L, and V₃ = 1600 L for a first-order reaction with k = 0.10 min⁻¹. Feed rate is 200 L/min with C_A0 = 2.0 mol/L. What is the final outlet concentration of A?
(a) 0.18 mol/L
(b) 0.24 mol/L
(c) 0.31 mol/L
(d) 0.38 mol/L

Question 17

A refinery engineer designs a packed bed catalytic reactor (PFR) for the hydrogenation reaction A + H₂ → B. The reaction is first-order in A with k = 2.5 min⁻¹ (based on catalyst weight). Catalyst bulk density is 1200 kg/m³. For feed rate of 150 L/min and 90% conversion, what reactor volume is needed?
(a) 0.46 m³
(b) 0.61 m³
(c) 0.76 m³
(d) 0.92 m³

Question 18

A biochemical engineer evaluates a CSTR for cell growth with specific growth rate μ = 0.4 h⁻¹ and yield coefficient Y_X/S = 0.5 g cells/g substrate. Feed substrate concentration is 20 g/L at 10 L/h. For 90% substrate conversion and negligible death rate, what reactor volume maintains steady-state cell concentration of 9 g/L?
(a) 51 L
(b) 68 L
(c) 85 L
(d) 102 L

Question 19

A chemical engineer designs a thermal cracking furnace (PFR) for the first-order decomposition of ethane to ethylene with k = 0.8 s⁻¹ at 850°C. The residence time distribution shows 10% of material bypasses with zero reaction. For 80% nominal conversion in an ideal PFR, what is the actual overall conversion with bypassing?
(a) 0.68
(b) 0.72
(c) 0.76
(d) 0.80

Question 20

A process engineer optimizes a series-parallel reactor system: two CSTRs (each 1000 L) can be arranged in series or parallel for a first-order reaction with k = 0.15 min⁻¹. Feed is 100 L/min with C_A0 = 3.0 mol/L. What is the percentage increase in conversion when switching from parallel to series configuration?
(a) 12.5%
(b) 18.3%
(c) 24.7%
(d) 31.2%