Reaction Engineering and Process Kinetics
What the exam tests
Rate laws, batch/CSTR/PFR design equations, Arrhenius temperature dependence, selectivity and yield in multiple reactions, non-isothermal reactor behaviour and stability, and catalysis with diffusion limitations.
Core rules
- Design equations: batch t = N_A0∫dX/(−r_A V); CSTR V = F_A0 X/(−r_A); PFR V = F_A0∫dX/(−r_A).
- First order: CSTR V = QX/[k(1−X)]; PFR V = (Q/k)ln[1/(1−X)].
- Arrhenius k = A exp(−E/RT); near ambient a 10 K rise roughly doubles to triples k.
- Selectivity: for parallel reactions of different order, the concentration that favours the desired product depends on the order difference; for series reactions, keep conversion per pass low to protect an intermediate.
- Pellet diffusion: Thiele modulus φ = L√(k/D_e); for a slab, η = tanh φ/φ.
- Adiabatic PFR energy balance: dT/dX = (−ΔH)F_A0/ΣF_i Cp_i.
Worked example
A first-order liquid reaction has k = 0.05 min⁻¹, Q = 10 L/min and target X = 0.90. CSTR: V = 10 × 0.90/(0.05 × 0.10) = 1,800 L. PFR: V = (10/0.05) × ln(1/0.10) = 200 × 2.303 = 460 L. The PFR needs roughly a quarter of the volume because the rate stays high along the length; for zero-order kinetics the two volumes are equal, and for autocatalytic kinetics the CSTR can be the smaller unit.
Traps
- Using a rate per catalyst mass where the design equation is per reactor volume.
- Forgetting that a reversible reaction is bounded by the equilibrium conversion.
- Ignoring heat of reaction; an exothermic CSTR can show multiple steady states and runaway.
- Setting η = 1 for a pellet with strong internal diffusion resistance.