Diffusion in small pores – definition and dependence of Knudsen diffusivity When catalyst pore diameter is much smaller than the mean free path of gas molecules, wall collisions dominate. The effective diffusivity under this regime (Knudsen diffusivity) is affected primarily by which variable(s)?

Introduction / Context:
In porous catalysts, mass transfer may occur in different regimes. When the pore diameter is small relative to the gas mean free path, molecule–wall collisions dominate over molecule–molecule collisions. This is the Knudsen regime, critical in interpreting effectiveness factors and internal diffusion limitations.

Given Data / Assumptions:

• Mean free path ≫ pore diameter → Knudsen regime.
• Gas diffusion inside cylindrical pores.
• Ideal-gas behavior at process pressures.

Concept / Approach:
Knudsen diffusivity D_K for species i is proportional to the pore radius and to the square root of absolute temperature, and is independent of total pressure: D_K ≈ (2/3) * r_pore * sqrt(8 R T / (π M_i)). Thus, temperature increases D_K via √T, while pressure does not appear explicitly (unlike molecular diffusion D_ij ∝ T^(3/2)/P).

Step-by-Step Solution:

Verification / Alternative check:
Dimension and units check confirm D_K has dimensions of area/time and the lack of pressure dependence aligns with kinetic theory for molecule–wall collision dominance.

Why Other Options Are Wrong:

• Pressure: Does not enter D_K; pressure mainly affects molecular (bulk) diffusion, not Knudsen.
• Both (a) and (b) / Neither: Only temperature applies here.

Common Pitfalls:
Using gas-phase binary diffusivity correlations inside tiny pores; in Knudsen regime, use D_K, not D_ij, for the controlling mechanism.

Final Answer:
Temperature