Practice Problems: Steady-State Systems
Question 1
A chemical engineer is designing a continuous stirred tank reactor (CSTR) for a first-order liquid-phase reaction A → B. The reaction rate constant is 0.25 min⁻¹, and the desired conversion is 80%. The volumetric flow rate into the reactor is 100 L/min with an inlet concentration of 2.0 mol/L. What reactor volume is required to achieve this conversion?
(a) 320 L
(b) 400 L
(c) 640 L
(d) 800 L
Question 2
A process engineer is evaluating a heat exchanger operating at steady state. Hot oil enters at 150°C and exits at 90°C with a mass flow rate of 2000 kg/h. The specific heat of the oil is 2.5 kJ/(kg·K). Cold water enters at 25°C with a mass flow rate of 3000 kg/h and specific heat of 4.18 kJ/(kg·K). Assuming no heat losses, what is the exit temperature of the water?
(a) 45.2°C
(b) 48.9°C
(c) 52.1°C
(d) 55.7°C
Question 3
A distillation column operating at steady state separates a binary mixture of benzene and toluene. The feed rate is 1000 kg/h containing 40% benzene by mass. The distillate contains 95% benzene and the bottoms contain 5% benzene. What is the mass flow rate of the distillate product?
(a) 350 kg/h
(b) 389 kg/h
(c) 420 kg/h
(d) 455 kg/h
Question 4
A chemical plant operates a compressor at steady state that handles 500 kg/h of air (ideal gas, MW = 29 g/mol, k = 1.4). The inlet conditions are 100 kPa and 25°C, and the outlet pressure is 600 kPa. Assuming isentropic compression with 75% efficiency, what is the power requirement?
(a) 28.5 kW
(b) 35.2 kW
(c) 42.8 kW
(d) 48.6 kW
Question 5
An absorption column operates at steady state to remove CO₂ from a gas stream using water as the solvent. The inlet gas flow rate is 1000 kmol/h containing 10 mol% CO₂. The exit gas contains 1 mol% CO₂. The liquid inlet is pure water at 500 kmol/h. What is the mole fraction of CO₂ in the exit liquid stream?
(a) 0.152
(b) 0.162
(c) 0.172
(d) 0.182
Question 6
A plug flow reactor (PFR) is used for a second-order reaction 2A → B with rate constant k = 0.15 L/(mol·min). The inlet concentration is 4.0 mol/L and the volumetric flow rate is 50 L/min. To achieve 75% conversion, what reactor volume is required?
(a) 250 L
(b) 375 L
(c) 500 L
(d) 625 L
Question 7
A process steam generator operates at steady state producing saturated steam at 20 bar from feedwater at 40°C. The steam production rate is 5000 kg/h. At 20 bar, the enthalpy of saturated liquid is 909 kJ/kg and the enthalpy of saturated vapor is 2799 kJ/kg. The enthalpy of feedwater at 40°C is 168 kJ/kg. What is the required heat input?
(a) 11.2 MW
(b) 13.2 MW
(c) 3.65 MW
(d) 2.62 MW
Question 8
A chemical engineer designs a flash drum operating at 5 bar and 100°C. A liquid mixture containing 50 mol% n-hexane and 50 mol% n-octane enters at 100 kmol/h. At the operating conditions, the equilibrium K-values are K_hexane = 1.8 and K_octane = 0.6. What is the vapor flow rate leaving the drum?
(a) 35.7 kmol/h
(b) 41.7 kmol/h
(c) 47.6 kmol/h
(d) 52.4 kmol/h
Question 9
A crystallizer operates at steady state with a feed solution entering at 10,000 kg/h containing 30 wt% salt. Crystals leave as a slurry with the mother liquor containing 10 wt% salt. If 1800 kg/h of pure salt crystals are produced, what is the total mass flow rate of the slurry?
(a) 8200 kg/h
(b) 9100 kg/h
(c) 10,000 kg/h
(d) 11,800 kg/h
Question 10
A membrane separation unit operates at steady state to purify hydrogen from a gas mixture. The feed contains 60 mol% H₂ and 40 mol% N₂ at 1000 kmol/h. The permeate stream contains 95 mol% H₂ and the retentate contains 20 mol% H₂. What is the permeate flow rate?
(a) 520 kmol/h
(b) 560 kmol/h
(c) 600 kmol/h
(d) 640 kmol/h
Question 11
A vertical cylindrical storage tank has a diameter of 4 m and is filled with liquid benzene (density = 876 kg/m³) to a height of 6 m. An outlet pipe at the bottom of the tank has an inside diameter of 50 mm. Assuming negligible friction losses and using the Bernoulli equation, what is the initial discharge velocity through the outlet when the valve is fully opened?
(a) 8.5 m/s
(b) 10.3 m/s
(c) 10.8 m/s
(d) 12.2 m/s
Question 12
An evaporator concentrates a fruit juice solution from 12 wt% solids to 45 wt% solids at a feed rate of 2000 kg/h. The concentrated product is then mixed with a bypass stream of the original feed to produce a final product containing 30 wt% solids. What is the mass flow rate of the bypass stream?
(a) 532 kg/h
(b) 638 kg/h
(c) 745 kg/h
(d) 850 kg/h
Question 13
A gas turbine power plant operates with air entering the compressor at 100 kPa and 25°C. The compressor pressure ratio is 10:1. After combustion, gases enter the turbine at 1200°C. Assuming ideal gas behavior with c_p = 1.005 kJ/(kg·K) for air and 1.15 kJ/(kg·K) for combustion gases, and isentropic efficiencies of 85% for both compressor and turbine, what is the thermal efficiency of the cycle?
(a) 32.5%
(b) 37.8%
(c) 42.1%
(d) 45.3%
Question 14
A continuous dryer removes moisture from a wet solid feed. The feed rate is 1500 kg/h with 30 wt% moisture. The product contains 5 wt% moisture. Air enters the dryer at 25°C with 0.01 kg H₂O/kg dry air and exits at 60°C saturated. The latent heat of vaporization at average conditions is 2400 kJ/kg. What is the heat input required (excluding air heating)?
(a) 285 kW
(b) 320 kW
(c) 355 kW
(d) 390 kW
Question 15
A mixing tank at steady state receives three inlet streams. Stream 1: 500 kg/h at 20°C with 10 wt% NaCl. Stream 2: 300 kg/h at 60°C with 25 wt% NaCl. Stream 3: 200 kg/h at 40°C with 5 wt% NaCl. Assuming the specific heat of all solutions is 3.8 kJ/(kg·K) and the mixing process is adiabatic, what is the outlet temperature?
(a) 34.0°C
(b) 36.2°C
(c) 38.8°C
(d) 41.5°C
Question 16
A spray dryer operates at steady state with a slurry feed containing 40 wt% solids at 2500 kg/h. Hot air at 200°C enters at 15,000 kg/h with absolute humidity of 0.005 kg H₂O/kg dry air. The outlet air exits at 90°C with absolute humidity of 0.055 kg H₂O/kg dry air. What is the moisture content in the dried product (wt%)?
(a) 3.2%
(b) 4.5%
(c) 5.8%
(d) 7.1%
Question 17
A counter-current extraction unit separates acetic acid from water using ethyl acetate as solvent. The aqueous feed contains 30 wt% acetic acid at 1000 kg/h. Pure solvent enters at 1500 kg/h. The raffinate exits with 5 wt% acetic acid and 10 wt% ethyl acetate. What is the mass flow rate of acetic acid in the extract?
(a) 245 kg/h
(b) 268 kg/h
(c) 282 kg/h
(d) 295 kg/h
Question 18
A parallel reaction system operates in a CSTR at steady state: A → B (desired, k₁ = 0.8 min⁻¹) and A → C (undesired, k₂ = 0.2 min⁻¹). The volumetric flow rate is 200 L/min with inlet concentration C_A0 = 3.0 mol/L. To maximize selectivity while achieving 70% conversion of A, what reactor volume is required?
(a) 420 L
(b) 467 L
(c) 525 L
(d) 583 L
Question 19
A refrigeration system operates between -20°C (evaporator) and 40°C (condenser) using R-134a as refrigerant. The cooling load is 50 kW. The enthalpy values are: evaporator inlet h₁ = 256 kJ/kg, evaporator outlet h₂ = 398 kJ/kg, compressor outlet h₃ = 435 kJ/kg, condenser outlet h₄ = 256 kJ/kg. What is the coefficient of performance (COP)?
(a) 2.84
(b) 3.16
(c) 3.84
(d) 4.25
Question 20
A packed bed adsorption column operates at steady state to remove VOCs from an air stream. The column is 2 m tall with 0.5 m diameter, packed with activated carbon (bulk density = 450 kg/m³, void fraction = 0.40). Air flows at 500 m³/h (at operating conditions). The inlet VOC concentration is 1000 ppm and outlet is 50 ppm. If the adsorption capacity is 0.25 kg VOC/kg carbon, what is the breakthrough time assuming the mass transfer zone is negligible?
(a) 12.5 h
(b) 16.8 h
(c) 20.3 h
(d) 24.7 h
