A pharmaceutical company is designing an absorption tower for NH₃ removal from air using H₂SO₄ solution. The Henry's law constant for NH₃ at 25°C is very small. What does this indicate about the system?
Answer: A
A small Henry's law constant (H) for NH₃ indicates high solubility in the liquid phase. Since 1/K_L = 1/k_L + H/k_G, a small H means the gas phase resistance dominates.
Q.2Hard
For turbulent flow in a pipe, the Colburn analogy for mass transfer is: j_D = (Sh)/(Re × Sc^(31)). Which correlation best estimates j_D for smooth pipes?
Answer: A
For smooth pipes in turbulent flow, j_D ≈ 0.023 Re^(-0.2), which is analogous to the Dittus-Boelert correlation for heat transfer with the Colburn j-factor approach.
Q.3Hard
For simultaneous heat and mass transfer in a wet bulb thermometer, the Lewis number (Le) is defined as Le = Sc/Pr. If Le = 1, what can be inferred?
Answer: C
When Le = 1 (Sc/Pr = 1), both analogy relationships hold: α = D_AB and h/ρc_p = k_L, making heat and mass transfer coefficients proportionally equal.
Q.4Hard
A bioprocess company needs to calculate oxygen transfer rate in an aerated bioreactor. The volumetric mass transfer coefficient k_L·a depends on which parameters?
Answer: B
k_L·a in bioreactors depends on fluid mechanics (impeller speed, gas flow rate), liquid properties affecting k_L, and equipment design affecting interfacial area 'a'. Temperature indirectly affects through viscosity changes.
Q.5Hard
Which statement about the relationship between diffusivity and molar mass is correct according to kinetic theory?
Answer: A
From Chapman-Enskog theory, D_AB ∝ T^(23)/(P × σ²) × √(M_total), where D_AB is inversely related to molecular mass through the collision cross-section dependency.
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Q.6Hard
For a binary diffusion process, the flux equation according to Fick's law in terms of mole fractions is given by:
Answer: B
The molar flux equation in terms of mole fractions is N_A = cD_AB(dy_A/dz) + y_A(N_A + N_B), accounting for bulk flow effects.
Q.7Hard
For a countercurrent liquid-liquid extraction process, the Kremser equation is used. What is the minimum number of stages required if the separation factor is 2.0 and the extraction factor is 1.5?
Answer: D
The Kremser equation requires initial and final solute concentrations or minimum separation requirements, which are not provided in the question.
Q.8Hard
For a dilute binary gas mixture diffusing through a stagnant layer, the diffusion coefficient D_AB can be estimated using the Chapman-Enskog theory. Which statement is correct?
Answer: B
According to Chapman-Enskog theory, D_AB ∝ T^(23)/P for gases. Thus, D_AB is inversely proportional to pressure at constant temperature.
Q.9Hard
For simultaneous momentum and mass transfer in a boundary layer, the Chilton-Colburn analogy relates j_D to friction factor f_D by:
Answer: A
The Chilton-Colburn analogy states that j_D = j_H = f_D/2, assuming equivalent Pr and Sc values, relating mass transfer to friction factor.
Q.10Hard
For a hollow fiber membrane contactor used in gas-liquid mass transfer, the overall mass transfer coefficient K_OL is related to individual coefficients by:
Answer: B
For gas-liquid systems, 1/K_OL = 1/k_L + 1/(m*k_G), where m is the distribution coefficient. This accounts for both liquid and gas side resistances.
Q.11Hard
For a binary gas mixture, the Stefan flow correction factor accounts for:
Answer: A
When one component condenses/reacts, equal molar counter-diffusion assumption breaks down. Stefan factor (B_m) corrects for net molar flow.
Q.12Hard
In ion exchange resins, the mass transfer resistance primarily occurs in:
Answer: A
For ion exchange, intraparticle diffusion through pores is the rate-limiting step. External film resistance is negligible in comparison.
Q.13Hard
The Colburn analogy relates dimensionless groups for mass, heat, and momentum transfer as:
Answer: A
Colburn analogy: j_D = (Sh)/(Re·Sc^(31)) ≈ j_H ≈ f/2 for smooth surfaces. Useful for correlating data when only one phenomenon is studied.
Q.14Hard
For a pseudosteady-state diffusion with heterogeneous reaction, the effectiveness factor η accounts for:
Answer: A
η = (actual reaction rate)/(rate if all surface at bulk concentration). Important in catalytic reactors where diffusion and reaction compete.
Q.15Hard
The Thiele modulus (Φ) for a catalyst pellet determines whether the reaction is:
Answer: A
Φ = L√(k/D). When Φ >> 1, diffusion controls; when Φ << 1, kinetics controls. Critical for reactor design optimization.
Q.16Hard
For a reverse osmosis process, the concentration polarization effect results in:
Answer: A
Due to higher solute rejection, solutes accumulate near membrane surface, increasing local osmotic pressure and reducing driving force.
Q.17Hard
In coal gasification combustion analysis (2024-25 focus), the mass transfer of oxygen to solid particles is characterized by:
Answer: A
Shrinking core model applies: external diffusion, ash diffusion, and chemical reaction all contribute. Modern focus on clean energy requires optimized design.
Q.18Hard
In foam fractionation for protein separation, the enrichment factor depends on:
Answer: A
Foam fractionation enrichment factor depends on surface activity (interfacial tension), protein hydrophobicity, and preferential adsorption of proteins at gas-liquid interfaces.
Q.19Hard
For a non-isothermal diffusion process with coupled heat and mass transfer, the Lewis number Le is defined as:
Answer: A
Lewis number Le = α/D_AB, where α is thermal diffusivity. It indicates the relative importance of heat and mass transfer in coupled processes. Le ≈ Sc/Pr for most gases.
Q.20Hard
The asymptotic solutions for mass transfer in turbulent flow predict that the Sherwood number varies with Reynolds number as:
Answer: B
For turbulent flow, empirical correlations show Sh ∝ Re^0.8·Sc^0.33 (or 0.5 depending on flow regime), derived from boundary layer theory and mass transfer analogies.
