Chemical Engineering - MCQ Practice Questions

Mass transfer coefficient (k) is defined as the rate of mass transfer per unit interfacial area per unit concentration difference, with units of length/time.

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.

Schmidt number is Sc = kinematic viscosity/diffusivity = μ/(ρ × D_AB). It is a dimensionless number analogous to Prandtl number in heat transfer.

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.

Film theory assumes a linear concentration gradient across the stagnant boundary layer, making the analysis mathematically simple and suitable for engineering calculations.

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.

In the Stokes-Einstein equation, r is the molecular radius (or hydrodynamic radius) of the solute particle diffusing through the solvent.

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.

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.

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.

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).

In evaporative cooling towers, mass transfer is driven by the difference in water vapor concentration between the saturated air at the water surface and the bulk air stream (concentration gradient).

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.

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.

Eddy diffusivity (ε_D) accounts for the enhanced mass transfer due to turbulent mixing and eddy formation. Total diffusivity = D_AB + ε_D in turbulent regions.

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.

From Chapman-Enskog theory, D_AB ∝ T^($\frac{3}{2}$)/(P × σ²) × √(M_total), where D_AB is inversely related to molecular mass through the collision cross-section dependency.