“Sour” natural gas is contaminated with hydrogen sulfide. The H₂S vapors are commonly treated removed by passing the gas through a packed bed of adsorbent particles. In the present process, natural gas with a bulk gas composition is 99 mole% methane (CH₄) and 1.0 mole% H₂S will be treated with a porous adsorbent material of void fraction of 0.50 and mean pore diameter of 20 nm at 30°C and 15.0 atm total system pressure. To design the adsorption bed, it is necessary to estimate the diffusion coefficient of H₂S within the porous adsorbent. The Lennard–Jones parameters for H₂S are σ = 3.623 Å and ε/k = 301.1 K.

a. What is molar concentration of H₂S in the gas mixture?

b. Estimate the binary gas-phase molecular diffusion coefficient of methane in H₂S by two methods, and compare the results.

c. Estimate the effective diffusion coefficient of H₂S within the porous material, assuming methane and hydrogen sulfide fill the gas void space within the porous material.