In a membrane reactor for an equilibrium-limited reaction, what is the primary advantage?
Answer: B
By selectively removing product through the membrane, the equilibrium constant expression is displaced, allowing conversion beyond the thermodynamic limit.
Q.182Medium
The mean residence time in a reactor can be calculated from RTD data using:
Answer: D
Both equations are valid: the integral formulation and the volumetric flow definition give the same mean residence time.
Q.183Medium
In a tubular reactor with axial dispersion, increasing the Peclet number (Pe) results in:
Answer: A
Peclet number Pe = uL/D. High Pe means low diffusion relative to convection, approaching ideal PFR behavior with narrow RTD.
Q.184Medium
In a heterogeneous catalytic reaction, the overall rate is limited by which step if the external mass transfer coefficient is very small?
Answer: C
A very small external mass transfer coefficient creates a large resistance to diffusion from bulk to particle surface, making external mass transfer the rate-limiting step.
Q.185Medium
In a plug flow reactor (PFR), what is the relationship between conversion and reactor volume for a first-order reaction?
Answer: B
For a first-order reaction in PFR, X = 1 - exp(-kτ), showing exponential relationship with residence time and thus volume.
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Q.186Medium
Which reactor configuration provides the highest conversion for an endothermic reaction at equilibrium?
Answer: D
Membrane reactors shift equilibrium by removing products, overcoming equilibrium limitations in endothermic reactions.
Q.187Medium
In a CSTR operating at steady state, if volumetric flow rate increases while keeping concentration constant, what happens to conversion?
Answer: B
Increased flow rate reduces residence time τ = V/F. For CSTR, X = kτ/(1+kτ), so increased τ means decreased conversion.
Q.188Medium
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.189Medium
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.190Medium
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.
Q.191Medium
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.192Medium
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.193Medium
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.194Medium
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.195Medium
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.196Medium
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.197Medium
For a process where ΔG < 0 at all temperatures, the process must be:
Answer: B
From ΔG = ΔH - TΔS, for ΔG < 0 at all T: ΔH < 0 (exothermic) and ΔS > 0 (entropy increases). This is a spontaneous process at all temperatures.
Q.198Medium
The heat of vaporization of water is 40.66 kJ/mol at 373 K. The entropy of vaporization is approximately:
Answer: C
ΔS_vap = ΔH_vap/T = 40660 J/mol / 373 K ≈ 109 J/mol·K. This follows Trouton's rule (~85-105 J/mol·K for most liquids).
Q.199Medium
For a reversible process, the Clausius inequality states:
Answer: B
For reversible processes, ΔS = Q_rev/T. For irreversible processes, ΔS > Q_irrev/T. This is the Clausius inequality: dS ≥ dQ/T.
Q.200Medium
A cyclic heat engine operates between hot reservoir at 500 K and cold reservoir at 300 K. Maximum theoretical efficiency is:
Answer: B
Maximum efficiency is Carnot efficiency: η_max = 1 - T_cold/T_hot = 1 - 500300 = 0.40 = 40%. No heat engine can exceed this efficiency.
