A gas mixture of constant composition 5.0 mole% CO₂ and 95 mole% air flows around a porous, spherical particle of diameter 3.0 cm that initially only contains only air (no CO₂) within the gas space of the pores of the particle. At the process conditions of interest (30 C, 1.0 atm), the binary diffusion coefficient of CO² in air (DAB) is 0.159 cm²/s, and the effective diffusion coefficient (D_Ae) ofCO₂ inside the porous particle (e 0.3) is 0.0143 cm²/s.

a. What is the mole fraction of CO₂ in the center of the spherical particle after 30 s?
b. How long will it take for the center of the spherical particle to have a composition of 4.8 mole% CO₂, assuming that the bulk gas CO₂ composition equals the CO₂ composition at the outer surface of the particle?
c. If the particle diameter is doubled to 6.0 cm, what is the new time required to achieve a composition of 4.8 mole% CO₂ in the center of particle?