In the context of mass transfer, what does the Schmidt number (Sc) represent?
Answer: A
Schmidt number (Sc = ν/D_AB) represents the relative importance of momentum diffusion and mass diffusion in a fluid.
Q.22Medium
Which of the following equations is used to calculate the mass transfer coefficient in laminar flow over a flat plate?
Answer: A
The Ranz-Marshall correlation for laminar flow over a flat plate is Sh = 0.664 Re^(21) Sc^(31), derived from boundary layer theory.
Q.23Easy
In a gas absorption process using a packed tower, if the interfacial area 'a' increases, how does it affect the mass transfer rate?
Answer: B
Since mass transfer rate = k_G * a * ΔP, an increase in interfacial area directly increases the mass transfer rate (linear relationship).
Q.24Hard
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.25Easy
A gas absorption column operates at steady state. The overall mass transfer coefficient K_G is determined to be 2.5 kmol/(m²·s·atm). If the driving force is 0.8 atm, what is the mass flux?
Answer: B
Using N_A = K_G * ΔP = 2.5 × 0.8 = 2.0 kmol/(m²·s). This is a direct application of the mass transfer rate equation.
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Q.26Medium
Which correlation is commonly used for mass transfer in turbulent pipe flow?
Answer: D
Both Gnielinski correlation (modified form) and Chilton-Colburn analogy (j_D = j_H = j_f/2) are applicable for turbulent pipe flow mass transfer.
Q.27Medium
In a distillation column, the interface equilibrium at the liquid-vapor boundary can be described by:
Answer: C
Raoult's Law applies to ideal solutions (high concentration), while Henry's Law applies to dilute solutions. The choice depends on the system behavior.
Q.28Hard
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.29Easy
The mass transfer coefficient k_L in liquid phase absorption typically has units of:
Answer: A
The liquid phase mass transfer coefficient k_L has units of m/s or cm/s, representing the rate of mass transfer per unit concentration difference.
Q.30Medium
In a membrane separation process, the Sherwood number (Sh) for mass transfer at the membrane surface is defined as:
Answer: D
Sherwood number is defined differently for liquid (Sh = k_L * L / D_AB) and gas phases (Sh = k_G * R_g * T / (P * D_AB)), depending on the system.
Q.31Medium
A stripping operation is being designed to remove dissolved CO₂ from water using air. The mass transfer is primarily limited by:
Answer: B
For CO₂-air-water system, CO₂ has low solubility in water, making the liquid phase the controlling resistance in mass transfer.
Q.32Medium
The mass transfer rate from a solid sphere dissolving in a flowing liquid can be described using the Ranz-Marshall correlation. Which parameter is NOT included in this correlation?
Answer: C
The Ranz-Marshall correlation for a sphere is Sh = 2 + 0.6 Re^(21) Sc^(31). Froude number (related to gravity effects) is not part of this correlation.
Q.33Medium
In a wetted wall column for gas absorption, the liquid film thickness (δ) affects the mass transfer rate. Increasing δ will:
Answer: B
The liquid phase mass transfer coefficient k_L is inversely related to film thickness: k_L = D_AB/δ. Increasing δ decreases k_L and hence the mass transfer rate.
Q.34Hard
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.35Easy
In an adsorption process on activated carbon, the Langmuir isotherm is given by q = (q_m * K * C)/(1 + K*C). What does 'q_m' represent?
Answer: A
In Langmuir isotherm, q_m represents the maximum (monolayer) adsorption capacity when the adsorbent surface is completely saturated.
Q.36Hard
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.37Easy
In gas-liquid mass transfer, the Henry's Law constant (H) represents the:
Answer: A
Henry's Law constant (P = H*x) represents the equilibrium partial pressure of a gas over a solution, indicating gas solubility in the liquid.
Q.38Medium
A spray tower is used for absorption where droplets fall through a rising gas stream. The interfacial area in such a system primarily depends on:
Answer: A
Interfacial area 'a' in spray towers is directly proportional to the total surface area of droplets, which depends on droplet size (smaller droplets = larger area) and droplet density.
Q.39Hard
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.40Medium
In the design of a sieve tray distillation column, the mass transfer efficiency (Murphree efficiency) accounts for:
Answer: A
Murphree efficiency (E_M) reflects that equilibrium is not achieved on real trays due to limited contact time and finite mass transfer rates in the actual column.
