Reaction Kinetics & Reactor Design (Batch, PFR, CSTR)
Arrhenius temperature dependence, order-of-reaction analysis, residence-time design and the batch/PFR/CSTR comparison interviewers build on.
Key formulas
Batch: t = (1/k)·ln(C0/C); PFR: V/FA0 = (1/kCA0)·ln(1/(1−X)); CSTR: V/FA0 = X/(k·CA0·(1−X))
First-order design equations: Same X from PFR needs the CSTR volume that the PFR needs at its highest (exit) rate everywhere — hence CSTR bigger for n>0.
d(ln k)/dT = Ea/(RT²)
Arrhenius sensitivity: High Ea ⇒ temperature is a powerful lever but also a runaway risk in exothermic systems — link to heat-removal design.
Cheat sheet
- ▸Arrhenius: k = A·e^(−Ea/RT); a rule of thumb — rate doubles per ~10 °C rise near ambient (Ea ≈ 50 kJ/mol).
- ▸Order n: zero order → concentration falls linearly with time; first → exponential decay (t½ independent of C0); second → 1/C linear in time.
- ▸Method to find order: plot ln(C0/C) vs t (first-order straight?), 1/C vs t (second-order?), integrate/differentiate data; half-life method: t½ ∝ C0^(1−n).
- ▸Batch: well-mixed, no flow, concentration changes with time — good for small-scale, slow reactions, Pharma batch logic.
- ▸PFR: no radial variation, concentration falls along length; best conversion per volume for positive-order reactions (always ≥ CSTR for n > 0).
- ▸CSTR: perfectly mixed, exit = reactor concentration, runs at the (low) exit rate everywhere; needs larger volume for high conversion but easy temperature control — exothermic runaway protection.
- ▸Multiple CSTRs in series approach PFR behaviour; recycle reactors sit between. Selectivity: use PFR for A→R→S series reactions with moderate T and short τ.
Batch vs PFR vs CSTR
| Aspect | Batch | PFR | CSTR |
|---|---|---|---|
| Mixing | Well-mixed, unsteady state | No axial mixing, steady | Perfectly mixed, steady |
| Concentration profile | Uniform, falls with time | Falls along length | Uniform at exit value |
| Conversion per volume (n>0) | Good | Best | Worst of the three |
| Temperature control | Moderate | Difficult (hot spots) | Easiest (jacket, isothermal) |
| Typical use | Pharma, fine chemicals | Large-scale homogeneous kinetics | Exothermic large-scale, polymerisation |
Top 4 campus interview questions
MCQ mastery quiz
1. In Arrhenius form, raising temperature increases the rate constant because…
2. For a first-order reaction, the half-life is…
3. For the same conversion of a positive-order reaction, the smallest reactor volume is…
4. A CSTR is preferred for a strongly exothermic reaction mainly because…
5. If 1/C plotted against time is a straight line, the reaction is…