Chemical Reaction Engineering
Reaction engineering turns kinetics into reactor volume and product distribution. GATE CH tests design equations for batch, CSTR and PFR, multiple-reaction selectivity, non-isothermal energy balances, heterogeneous catalysis with pore diffusion, and residence-time distributions.
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). Space time τ = V/v₀ equals the true residence time only for constant density.
- Reactor choice. For positive-order kinetics and a given conversion, a PFR always needs less volume than a single CSTR; the gap widens as conversion rises.
- Multiple reactions. Instantaneous selectivity is the ratio of rates, not of concentrations alone; for parallel reactions of orders a and b, raising C_A favours the higher-order path; for series reactions, use a CSTR or keep conversion low to avoid over-reaction.
- Catalysis. Thiele modulus φ compares reaction to diffusion rate; effectiveness factor η = actual rate/rate at surface conditions, η ≤ 1 for a single first-order reaction. Strong pore diffusion gives η ≈ 1/φ and an apparent order of (n+1)/2.
- RTD. E(t) integrates to 1, mean t̄ = ∫tE dt, variance σ² = ∫t²E dt − t̄²; the dispersion number and tanks-in-series model quantify axial mixing.
Worked example
First-order reaction, k = 0.1 min⁻¹, v₀ = 10 L/min, target conversion 90%. CSTR: V = v₀X/[k(1−X)] = 10(0.9)/(0.1 × 0.1) = 900 L. PFR: V = (v₀/k)ln[1/(1−X)] = 100 × 2.303 = 230 L. The CSTR needs about four times the volume because it runs at the low outlet concentration the whole time.
Traps
- Using −r_A = kC_A0(1−X) without applying the density-change factor ε for gas-phase reactions.
- Reading a Levenspiel plot area as the reactor volume directly without the F_A0 multiplier.
- Confusing space time with mean residence time in a variable-density system.
- Assuming η > 1 is impossible - it is, for certain autocatalytic or inhibition cases, so check the kinetics.