What does the Damköhler number (Da) represent in reactor design?
Answer: B
Da = reaction rate/flow rate, determining whether reaction or flow dominates; Da >> 1 means reaction-limited.
Q.382Easy
For a reversible reaction at equilibrium, which statement is true?
Answer: B
At equilibrium, the net rate is zero because forward and reverse reaction rates are equal.
Q.383Medium
In a reactor with catalyst deactivation following first-order decay, what is the effect on reactant conversion over time?
Answer: B
Catalyst activity decays as a = exp(-k_d·t), causing effective rate constant to decrease, reducing conversion over time.
Q.384Easy
Which of the following statements about adiabatic reactors is correct?
Answer: C
In adiabatic reactors, Q = 0, so ΔT depends on heat of reaction (ΔH_r) and heat capacity of reactants.
Q.385Medium
For competitive-consecutive reactions: A → B (k₁), A → C (k₂), B → D (k₃), selectivity of B over C is defined as S_B/C = ?
Answer: A
For parallel reactions, instantaneous selectivity S_B/C = k₁/k₂, independent of time at low conversions.
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Q.386Easy
What is the space-time (τ) in a PFR if reactor volume is 100 L and volumetric feed rate is 10 L/min?
Answer: C
Space-time τ = V/v₀ = 10100 = 10 min.
Q.387Medium
In microbial fermentation kinetics, the Monod equation models specific growth rate. What happens when substrate concentration >> K_s?
Answer: A
When [S] >> K_s, μ ≈ μ_max, making growth zero-order in substrate (Monod equation simplification).
Q.388Medium
For isothermal batch reactor with r = -dC_A/dt = kC_A^n, what is the integrated rate law for n=2?
Answer: A
For second-order: ∫dC_A/C_A² = -k∫dt gives 1/C_A - 1/C_A0 = kt.
Q.389Hard
Thiele modulus (φ) represents the ratio of which two parameters in heterogeneous catalysis?
Answer: B
Thiele modulus φ = √(k·ρ_cat·a_s/D_eff) represents ratio of internal diffusion to surface reaction rate.
Q.390Easy
In CSTR, if inlet concentration C_A0 = 2 M, outlet concentration C_A = 0.5 M, what is fractional conversion?
Answer: C
Conversion X = (C_A0 - C_A)/C_A0 = (2 - 0.5)/2 = 0.75 or 75%.
Q.391Medium
For a reaction with activation energy E_a = 50 kJ/mol, by what factor does rate constant increase if temperature increases from 300K to 310K? (R = 8.314 J/mol·K)
Answer: B
Using Arrhenius: ln(k₂/k₁) = (E_a/R)(T₂-T₁)/(T₁T₂) ≈ 1.96, so k₂/k₁ ≈ 2.0
Q.392Hard
In a recycle reactor with recycle ratio R, what is the volume reduction factor compared to PFR for equivalent conversion?
Answer: A
Recycle reduces required volume by factor (1+R)/R compared to PFR for same conversion and residence time.
Q.393Hard
For homogeneous gas-phase reaction in batch reactor, if pressure increases at constant volume, what happens to reaction rate for 2A → Products?
Answer: C
Pressure increase increases concentration proportionally; for 2nd order rate = kC_A², quadrupling concentration increases rate 16-fold; doubling pressure quadruples rate.
Q.394Medium
In a CSTR operating at steady state with a first-order irreversible reaction A → B, if the volumetric flow rate is doubled while keeping reactor volume constant, how does the conversion of reactant A change?
Answer: B
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.
Q.395Easy
Which of the following is NOT an extensive property?
Answer: B
Temperature is an intensive property as it does not depend on the quantity of substance. Volume, mass, and internal energy are extensive properties that depend on the amount of material.
Q.396Easy
According to the first law of thermodynamics, ΔU = Q - W. In this equation, W represents:
Answer: B
In the convention ΔU = Q - W, W is work done by the system. This is the IUPAC recommended convention used in most thermodynamics calculations.
Q.397Medium
Which thermodynamic potential is most useful for constant temperature and pressure processes?
Answer: C
Gibbs Free Energy (G = H - TS) is the appropriate thermodynamic potential for processes at constant T and P. ΔG = 0 at equilibrium and ΔG < 0 for spontaneous processes.
Q.398Easy
A system absorbs 500 J of heat and does 200 J of work. The change in internal energy is:
Answer: A
Using ΔU = Q - W, where Q = +500 J (absorbed) and W = +200 J (work done by system). Therefore, ΔU = 500 - 200 = 300 J.
Q.399Medium
For an ideal gas undergoing isothermal expansion, the work done is given by:
Answer: A
For isothermal process of ideal gas, W = nRTln(V₂/V₁) = nRTln(P₁/P₂). This is derived from the first law with ΔU = 0 for isothermal ideal gas process.
Q.400Easy
The compressibility factor Z for an ideal gas is:
Answer: B
For ideal gas, Z = PV/nRT = 1 always. For real gases, Z ≠ 1 due to intermolecular forces and molecular volume.
