Chemical Engineering Fundamentals: Material and Energy Balances and Thermodynamics
What the exam tests
Steady and unsteady material balances, reactive balances with recycle and purge, and the thermodynamic property framework - equations of state, fugacity, activity coefficients, vapour–liquid equilibrium and energy balances around reactors and separators.
Core rules
- Choose a basis (100 mol/s, 1 h) and a system boundary before writing anything; count unknowns against independent equations.
- In reacting systems, use extent of reaction ξ or atomic balances; atomic balances are safer when the reaction network is uncertain.
- Recycle with purge: inerts accumulate until the purge flow equals the inert feed, so purge size fixes the steady state.
- Phase equilibrium requires equality of fugacity, not partial pressure. Raoult's law is the ideal limit; modified Raoult (γᵢPᵢˢᵃᵗ) covers non-ideality; Henry's law covers dilute solutes.
- Energy balance: Q − W = Σn_out h_out − Σn_in h_in. Correct heats of reaction to the actual temperature with Kirchhoff's law.
Worked example
Fresh feed is 100 mol/s of A. Per-pass conversion is 50% and overall conversion is 90%. Find the recycle R. A leaving the system = 10 mol/s. Reactor feed = 100 + R, so reactor outlet A = 0.5(100 + R). Of that, R is recycled and 10 leaves: 0.5(100 + R) − R = 10, giving 50 − 0.5R = 10, so R = 80 mol/s and the recycle ratio is 0.8 per unit fresh feed.
Traps
- Mixing mass and mole fractions inside a mole balance.
- Forgetting that inerts build up, so the purge sets the steady state.
- Using ΔH°f at 298 K for a reactor at 600 K with no Cp correction.
- Treating a high-pressure vapour as ideal when the fugacity coefficient is far from 1.