Practice Problems: Chemical Reactions
Question 1
A process engineer is designing a continuous stirred tank reactor (CSTR) for a first-order irreversible liquid-phase reaction A → B. The feed stream contains reactant A at a concentration of 2.5 mol/L and flows at 150 L/min. The reaction rate constant is 0.35 min⁻¹. To achieve 80% conversion of A, what reactor volume is required?
(a) 1,371 L
(b) 1,714 L
(c) 2,057 L
(d) 2,400 L
Question 2
A chemical plant operates a plug flow reactor (PFR) for the decomposition of compound C following first-order kinetics with k = 0.25 s⁻¹. The volumetric flow rate is 0.08 m³/s and the inlet concentration is 4.2 mol/L. If 90% conversion is required, what is the necessary reactor volume?
(a) 0.54 m³
(b) 0.68 m³
(c) 0.74 m³
(d) 0.82 m³
Question 3
A reactor engineer is evaluating a batch reactor for a second-order irreversible reaction 2A → P. The initial concentration of A is 3.0 mol/L and the rate constant is 0.15 L/(mol·min). How long will it take to achieve 75% conversion?
(a) 5.33 min
(b) 6.67 min
(c) 8.00 min
(d) 9.33 min
Question 4
A petrochemical facility operates a CSTR for an exothermic reaction. The reaction rate constant follows the Arrhenius equation with activation energy Ea = 85 kJ/mol and pre-exponential factor A = 2.5 × 10⁸ min⁻¹. At what temperature (in °C) will the rate constant equal 4.2 min⁻¹? (R = 8.314 J/(mol·K))
(a) 127°C
(b) 142°C
(c) 157°C
(d) 172°C
Question 5
A production engineer is comparing reactor volumes for 85% conversion of a first-order reaction with k = 0.42 min⁻¹ and feed flow rate of 200 L/min. What is the ratio of the required CSTR volume to the required PFR volume?
(a) 2.98
(b) 3.50
(c) 4.02
(d) 4.55
Question 6
A process development engineer is studying a reversible reaction A ⇌ B in a batch reactor. The forward rate constant is kf = 0.28 min⁻¹ and the reverse rate constant is kr = 0.12 min⁻¹. Starting with pure A at 5.0 mol/L, what is the equilibrium concentration of A?
(a) 1.50 mol/L
(b) 1.75 mol/L
(c) 2.00 mol/L
(d) 2.25 mol/L
Question 7
A reaction engineer operates two equal-volume CSTRs in series, each with volume 800 L, for a first-order reaction with k = 0.18 min⁻¹. The feed rate is 120 L/min with inlet concentration 3.5 mol/L. What is the overall conversion achieved?
(a) 65.8%
(b) 71.2%
(c) 76.5%
(d) 81.9%
Question 8
A specialty chemicals manufacturer operates a semi-batch reactor where reactant A (initially 400 L at 2.8 mol/L) reacts with B being fed continuously at 25 L/min and 4.0 mol/L. The reaction A + B → C is first-order in each reactant with k = 0.055 L/(mol·min). Assuming steady-state and constant volume, what is the consumption rate of A at t = 0?
(a) 61.6 mol/min
(b) 75.3 mol/min
(c) 88.9 mol/min
(d) 102.5 mol/min
Question 9
A pilot plant engineer tests a catalyst in a packed bed reactor (PFR) for the reaction A → B. The catalyst weight is 45 kg, feed rate of A is 18 mol/min at concentration 1.2 mol/L with volumetric flow 15 L/min. The reaction rate is -rA = 0.32 × CA mol/(kg·min). What conversion is achieved?
(a) 72.0%
(b) 80.0%
(c) 88.0%
(d) 96.0%
Question 10
A biochemical engineer designs a reactor for an enzymatic reaction following Michaelis-Menten kinetics with Vmax = 12 mmol/(L·min) and Km = 3.5 mmol/L. At a substrate concentration of 14 mmol/L, what is the reaction rate?
(a) 8.0 mmol/(L·min)
(b) 9.6 mmol/(L·min)
(c) 10.4 mmol/(L·min)
(d) 11.2 mmol/(L·min)
Question 11
A refinery engineer analyzes a complex reaction network where A undergoes parallel reactions: A → B (desired, k₁ = 0.45 min⁻¹) and A → C (undesired, k₂ = 0.18 min⁻¹). In a PFR with residence time of 4.5 min, what is the selectivity of B to C at the reactor exit?
(a) 1.85
(b) 2.15
(c) 2.50
(d) 2.85
Question 12
A polymer production facility operates a CSTR at 95°C for a reaction with activation energy 72 kJ/mol. Due to cooling system failure, the temperature increases to 110°C. By what factor does the reaction rate constant increase? (Assume pre-exponential factor remains constant)
(a) 2.12
(b) 2.48
(c) 2.84
(d) 3.20
Question 13
A reactor design engineer evaluates a gas-phase reaction A → 2B in a PFR operating at 450 K and 5 atm. The feed is pure A at 100 mol/min. The first-order rate constant is 0.65 min⁻¹ and 75% conversion is required. Assuming isothermal operation and ideal gas behavior, what reactor volume is needed?
(a) 178 L
(b) 213 L
(c) 248 L
(d) 283 L
Question 14
A process engineer investigates a series-parallel reaction scheme: A → B → C, where k₁ = 0.80 min⁻¹ and k₂ = 0.32 min⁻¹ (both first-order). In a batch reactor starting with pure A at 4.0 mol/L, what is the maximum concentration of intermediate B achieved?
(a) 1.85 mol/L
(b) 2.13 mol/L
(c) 2.41 mol/L
(d) 2.69 mol/L
Question 15
A safety engineer analyzes a runaway exothermic reaction in a batch reactor. The reaction has a half-life of 25 minutes at 80°C and 6.25 minutes at 100°C. Assuming first-order kinetics, what is the activation energy?
(a) 55.2 kJ/mol
(b) 62.8 kJ/mol
(c) 69.4 kJ/mol
(d) 76.0 kJ/mol
Question 16
A production manager evaluates replacing a single CSTR (V = 2,400 L) with two smaller CSTRs in series (each 1,200 L) for a first-order reaction with k = 0.22 min⁻¹ and feed rate 180 L/min. By how much does the conversion improve with the two-reactor system?
(a) 8.5 percentage points
(b) 10.2 percentage points
(c) 11.9 percentage points
(d) 13.6 percentage points
Question 17
A chemical engineer designs a fluidized bed reactor for the catalytic oxidation of SO₂ to SO₃. The reaction is second-order in SO₂ with k = 1.8 m³/(kmol·s) at reactor conditions. The feed gas contains 8% SO₂ (by volume) at 2.5 bar and 450°C, flowing at 1,200 m³/h (at STP). For 95% conversion, what catalyst mass is required if -rA = k × C²SO₂ per kg catalyst?
(a) 3,250 kg
(b) 4,180 kg
(c) 5,110 kg
(d) 6,040 kg
Question 18
A research engineer studies the liquid-phase dimerization reaction 2A → A₂ in an isothermal batch reactor. The reaction is second-order with k = 0.28 L/(mol·min). Starting with CA0 = 2.5 mol/L, what time is required to reduce the concentration to 0.5 mol/L?
(a) 11.4 min
(b) 14.3 min
(c) 17.2 min
(d) 20.1 min
Question 19
A membrane reactor engineer designs a system where product B is continuously removed from the reaction A → B + C (first-order, k = 0.38 min⁻¹). The reactor volume is 600 L with feed flow of 75 L/min. If 50% of product B is removed instantaneously, what conversion of A is achieved compared to 70% in a conventional PFR?
(a) 78%
(b) 82%
(c) 86%
(d) 90%
Question 20
A pharmaceutical engineer operates an autoclave batch reactor for a zero-order decomposition reaction with rate constant k = 0.085 mol/(L·min). The initial concentration is 6.5 mol/L in a 250 L reactor. If 90% conversion is required, what batch time is needed?
(a) 58.2 min
(b) 68.8 min
(c) 79.4 min
(d) 90.0 min
