Chemical Engineering - MCQ Practice Questions

In laminar flow, k ∝ D^($\frac{1}{2}$). Therefore, if D doubles, k increases by √2 times (approximately 1.414 times).

All three equations represent valid forms of mass transfer rate equations. Option A uses liquid phase coefficient, Option B is Fick's law, Option C uses gas phase coefficient, and all are interconnected through film theory.

For gas absorption with equilibrium relation y = Hx, the overall liquid phase coefficient is 1/K_L = 1/k_L + H/k_G, where H is Henry's law constant.

For laminar flow over a flat plate, the Chilton-Colburn analogy gives Sh = 0.664 Re^0.5 Sc^($\frac{1}{3}$), analogous to the Nusselt number in heat transfer.

A larger gap between the operating line and equilibrium line indicates greater concentration difference, which increases the driving force (ΔC) for mass transfer, leading to higher transfer rates.

Penetration theory (Higbie) assumes that fluid elements reach the interface, remain for a contact time θ, and then leave, with transient diffusion occurring during exposure.

Permeance has units of mol/(m²·s·Pa) when flux is in mol/(m²·s) and driving force (pressure difference) is in Pa. It represents the ease of species permeation through the membrane.

According to kinetic theory, D_AB depends on T, P, and molecular properties (mass, size, collision diameter) but NOT directly on composition in ideal systems (though real systems may show weak composition dependence).

Counter-current flow provides greater concentration differences throughout the tower (larger average driving force), requiring less height and contact time compared to cocurrent operation for equivalent separation.

The Ranz-Marshall correlation for laminar flow over a flat plate is Sh = 0.664 Re^($\frac{1}{2}$) Sc^($\frac{1}{3}$), derived from boundary layer theory.

Both Gnielinski correlation (modified form) and Chilton-Colburn analogy (j_D = j_H = j_f/2) are applicable for turbulent pipe flow mass transfer.

Raoult's Law applies to ideal solutions (high concentration), while Henry's Law applies to dilute solutions. The choice depends on the system behavior.

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.

For CO₂-air-water system, CO₂ has low solubility in water, making the liquid phase the controlling resistance in mass transfer.

The Ranz-Marshall correlation for a sphere is Sh = 2 + 0.6 Re^($\frac{1}{2}$) Sc^($\frac{1}{3}$). Froude number (related to gravity effects) is not part of this correlation.

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.

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.

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.

For gas-phase controlling resistance: 1/KG = 1/kG + (m/kL), where m is Henry's Law constant and accounts for equilibrium relationship.

Sh = kL·L/D is analogous to Nu = h·L/k. Both represent dimensionless transfer coefficients for mass and heat respectively.