Govt. Exams
Entrance Exams
In a CSTR, conversion depends on residence time (τ = V/Q). When volumetric flow rate Q doubles while V remains constant, residence time τ decreases by half. Since conversion X_A = kτ/(1+kτ) for first-order reaction, decreased τ leads to decreased conversion. This is a fundamental principle in reactor design for 2024-25 competitive exams.
Pressure increase increases concentration proportionally; for 2nd order rate = kC_A², quadrupling concentration increases rate 16-fold; doubling pressure quadruples rate.
Recycle reduces required volume by factor (1+R)/R compared to PFR for same conversion and residence time.
Using Arrhenius: ln(k₂/k₁) = (E_a/R)(T₂-T₁)/(T₁T₂) ≈ 1.96, so k₂/k₁ ≈ 2.0
Conversion X = (C_A0 - C_A)/C_A0 = (2 - 0.5)/2 = 0.75 or 75%.
Thiele modulus φ = √(k·ρ_cat·a_s/D_eff) represents ratio of internal diffusion to surface reaction rate.
For second-order: ∫dC_A/C_A² = -k∫dt gives 1/C_A - 1/C_A0 = kt.
When [S] >> K_s, μ ≈ μ_max, making growth zero-order in substrate (Monod equation simplification).
Space-time τ = V/v₀ = 100/10 = 10 min.
For parallel reactions, instantaneous selectivity S_B/C = k₁/k₂, independent of time at low conversions.