In a binary diffusion process, the mass transfer coefficient 'k_c' has dimensions of:
Answer: A
The mass transfer coefficient k_c is defined as molar flux per unit concentration difference, having dimensions of velocity (Length/Time), commonly expressed in cm/s or m/s.
Q.62Easy
Which of the following best describes the Schmidt number (Sc) in mass transfer?
Answer: B
Schmidt number Sc = ν/D_AB where ν is kinematic viscosity and D_AB is mass diffusivity. It represents the relative importance of momentum and mass transport.
Q.63Easy
For a spherical particle undergoing mass transfer, the Sherwood number correlation for creeping flow (Re << 1) is approximately:
Answer: B
For a spherical particle in creeping flow with negligible convection, the Sherwood number approaches the purely diffusive limit of Sh = 2, independent of Reynolds and Schmidt numbers.
Q.64Easy
In liquid-liquid extraction, the distribution coefficient K_D is defined as the ratio of solute concentration in:
Answer: A
The distribution coefficient K_D = C_solvent/C_aqueous at equilibrium, determining the driving force for extraction and the selectivity of the separation process.
Q.65Medium
The Fick's first law of diffusion in binary mixtures states that the molar flux J_A is proportional to:
Answer: B
Fick's law: J_A = -D_AB(dC_A/dz) + C_A(J_A + J_B). The total flux includes both diffusive and convective contributions due to bulk flow.
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Q.66Medium
For equimolar counter-diffusion in a binary system, the molar fluxes satisfy:
Answer: D
In equimolar counter-diffusion, moles of A diffusing in one direction equal moles of B diffusing in the opposite direction, making J_A = -J_B and their sum zero.
Q.67Medium
The Stefan problem in mass transfer involves:
Answer: A
The Stefan problem deals with unsteady diffusion with a moving interface, commonly encountered in evaporation from droplets and sublimation processes where the interface position changes with time.
Q.68Medium
In a countercurrent absorption column, if the gas-phase mass transfer coefficient is k_G = 0.05 kmol/(m²·s·atm), the interfacial area 'a' = 200 m²/m³, and column cross-section = 5 m², the volumetric overall mass transfer coefficient is:
Answer: B
Overall volumetric mass transfer = k_G × a × Volume = 0.05 × 200 × (5 × height). For unit height, K_G·a·V = 0.05 × 200 × 5 = 50 kmol/(s·atm).
Q.69Medium
The penetration theory for mass transfer assumes that the contact time between fluid elements is:
Answer: B
Penetration theory assumes fluid elements contact the interface for a short time, then move away. Mass transfer is modeled using unsteady diffusion into a semi-infinite medium.
Q.70Medium
For absorption of a sparingly soluble gas in a liquid with fast reaction kinetics, the enhancement factor 'E' is determined by:
Answer: B
The enhancement factor E = k_L,with reaction/k_L,without reaction depends on the Hatta number (Ha = √(k·C_A0·D_A/k_L²)), which incorporates reaction kinetics and mass transfer parameters.
Q.71Medium
In membrane separation, the permeate flux in reverse osmosis is given by:
Answer: B
The reverse osmosis permeate flux follows: J = A(ΔP - Δπ), where A is membrane permeability, ΔP is applied pressure, and Δπ is osmotic pressure difference.
Q.72Medium
A gas A diffuses through a stagnant film of gas B. If the diffusivity D_AB = 0.1 cm²/s, film thickness δ = 0.01 cm, and concentration difference = 0.05 mol/cm³, the diffusive flux is:
Answer: B
Using Fick's law for stagnant diffusion: J = D_AB·ΔC/δ = 0.1 × 0.005.01 = 0.5 × 10⁻² = 5 × 10⁻³ mol/(cm²·s).
Q.73Medium
The height of a transfer unit (HTU) in a packed absorption column represents:
Answer: B
HTU = V·G/(k_G·a·A), where a smaller HTU indicates more efficient mass transfer. It represents the column height needed to achieve one logarithmic unit of concentration driving force reduction.
Q.74Hard
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.75Hard
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.76Hard
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.
Q.77Hard
In gas-solid adsorption, the Langmuir isotherm assumes:
Answer: B
The Langmuir model assumes monolayer adsorption on homogeneous surfaces with constant heat of adsorption, leading to saturation at high pressures.
Q.78Hard
For simultaneous diffusion and reaction (fast reaction regime) in a porous catalyst, the effectiveness factor η approaches:
Answer: B
In the fast reaction regime where diffusion limits the overall rate, η ≈ 1/Φ for spherical pellets, indicating severe internal diffusion limitations.
Q.79Hard
In hollow fiber membrane contactors for gas absorption, the advantage over conventional columns is:
Answer: A
Hollow fiber contactors provide 500-1500 m²/m³ interfacial area (vs 100-400 m²/m³ in packed columns), operate without flooding, and enable independent control of gas and liquid flows.
Q.80Hard
The correlation for mass transfer coefficient in agitated vessels (Harriott equation) is k_L·a ∝:
Answer: A
The Harriott correlation shows k_L·a ∝ (P/V)^0.4·D^0.5, indicating dependence on power input intensity and diffusivity, fundamental to oxygen transfer calculations in bioprocess engineering.
