The Damköhler number (Da) for a chemical reaction is defined as the ratio of:
Answer: B
Da = (residence time)/(characteristic reaction time) = kτC^(n-1). When Da >> 1, reaction is fast; Da << 1, reaction is slow.
Q.362Medium
A series of 3 identical CSTRs in cascade is used to process a first-order reaction with overall conversion X = 90%. Which statement is true?
Answer: C
For equal volume CSTRs in series processing first-order reaction: C = C₀/(1+kτ)ⁿ, showing exponential decrease in concentration.
Q.363Medium
In a fixed-bed catalytic reactor, what is the primary cause of catalyst deactivation by sintering?
Answer: B
Sintering involves migration of metal atoms on the catalyst surface, leading to agglomeration and reduction of active surface area, particularly at high temperatures.
Q.364Hard
For a second-order reaction in a PFR, increasing the inlet concentration while maintaining constant volumetric flow rate will result in:
Answer: C
In a PFR, conversion (fractional) depends on space-time and reaction kinetics but is independent of inlet concentration for a given residence time.
Q.365Medium
Which reactor configuration would be best suited for a fast, highly exothermic reaction where precise temperature control is critical?
Answer: B
Semi-batch allows controlled feeding of reactants, limiting instantaneous heat generation while maintaining good mixing and temperature control.
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Q.366Hard
The Weisz-Prater criterion is used to determine:
Answer: A
Weisz-Prater number: CWP = (k''ρcRp²)/De. If CWP << 0.15, internal diffusion limitations are negligible.
Q.367Medium
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.368Medium
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.369Hard
For parallel reactions where A → B (desired) with rate constant k₁ and A → C (undesired) with rate constant k₂, the selectivity towards B is maximized by:
Answer: A
If Ea1 > Ea2, increasing temperature favors the desired reaction with higher activation energy, improving selectivity to B.
Q.370Easy
The conversion in a batch reactor at any time can be found by integrating the rate equation. For a first-order reaction, the half-life is:
Answer: D
For first-order: t₁/₂ = ln(2)/k = 0.693/k, which is independent of C₀ and inversely proportional to k.
Q.371Medium
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.372Easy
For the reaction 2A + B → Products, if the reaction is 2nd order in A and 1st order in B, the rate equation is:
Answer: A
Reaction order is determined by experimental data, not stoichiometry. The given orders are 2nd in A and 1st in B, so rate law is r = k[A]²[B].
Q.373Medium
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.374Hard
For a polymerization reaction in a batch reactor, the polydispersity index (PDI) and average molecular weight depend on:
Answer: B
PDI and molecular weight distribution in batch polymerization depend on the relative magnitudes of propagation and termination reactions and the degree of conversion achieved.
Q.375Medium
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.
Q.376Easy
What is the order of reaction if the half-life period is independent of initial concentration?
Answer: B
For first-order reactions, t₁/₂ = 0.693/k, which is independent of initial concentration C₀.
Q.377Hard
In consecutive reactions A → B → C (both first-order), maximum concentration of intermediate B occurs at which time?
Answer: B
Maximum [B] occurs when d[B]/dt = 0, giving t_max = ln(k₁/k₂)/(k₁-k₂) for k₁ ≠ k₂.
Q.378Medium
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.379Easy
For the reaction A + B → C, the rate law is r = kC_A²C_B. What is the overall order of reaction?
Answer: C
Overall order = sum of individual orders = 2 + 1 = 3.
Q.380Medium
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.
