Case Studies
Three worked problems applying the 6-step framework — from Foundation to Advanced. Expand each solution step-by-step.
Isothermal Liquid-Phase CSTR — Bimolecular Reaction
A 50 L CSTR is used to carry out the bimolecular reaction A + B → C. The rate law is r = kC_AC_B with k = 0.2 L/(mol·min). The feed conditions are: volumetric flow rate Q = 5 L/min, inlet concentrations C_{Af} = C_{Bf} = 2 mol/L, C_{Cf} = 0.
Find: (a) Write the SS mole balance for A. (b) Express C_B in terms of C_A using stoichiometry. (c) Calculate the steady-state outlet concentration of A. (d) Find C_B and C_C at the outlet. (e) What is the conversion of A?
Isothermal Gas-Phase PFR with Molar Expansion
Pure A undergoes the gas-phase decomposition A → B + C in a plug flow reactor at T = 500 K and P = 2 atm. The first-order rate law is r = kC_A with k = 0.5 min⁻¹. The feed is pure A at a volumetric flow rate Q₀ = 10 L/min.
Find: What PFR volume V is required to achieve approximately 60% conversion of A?
Adiabatic Liquid-Phase CSTR with Arrhenius Kinetics
A 500 L adiabatic CSTR carries out the first-order liquid-phase reaction A → B with rate r = k(T)C_A. The Arrhenius parameters are: E_a = 50{,}000 J/mol, k_ref = 0.01 min⁻¹ at T_ref = 300 K.
Feed conditions: Q = 2 L/min, C_{Af} = 4 mol/L, T_f = 300 K. Thermodynamic data: ΔH_R = −40{,}000 J/mol, ρ = 1000 kg/m³ (≡ 1 kg/L), Ĉ_p = 4000 J/(kg·K).
Find the steady-state outlet temperature T, concentration C_A, and conversion X_A.