Consider the cylindrical shaped absorbent material designed to selectively remove solute A from solution. The uptake of solute A through the homogeneous absorbent material is limited by the molecular diffusion. Furthermore, the absorbent has a higher affinity for solute A relative to the surrounding solution that is described by the linear equilibrium relationship c_A = K · C'_A, where c_A is the molar concentration of A in the absorbent, C'_A is the molar concentration of A in the surrounding fluid, and K is a partition coefficient for solute A between the fluid and the absorbent material. The surrounding solution is very well mixed and has a constant concentration of C'_A∞ = 2.00 gmol/m³. The diffusion coefficient of A in the homogeneous absorbent material is 4 × 10^-7 cm²/s, and the partition coefficient K = 1.5 cm³ fluid/cm³ absorbent. The cylindrical absorbent pellet is 1.0 cm in diameter and 5.0 cm in length. Initially, no solute A is absorbed into the absorbent material.

a. Assume edge effects associated with the ends of the cylinder can be neglected. Under this assumption, how long will it take (in hours) for the solute A concentration to reach 2.94 gmol/m³ at a depth of 0.40 cm from the surface of the cylinder?
b. Repeat part (a) calculation for the case where “end effects” are not neglected—i.e., for two-dimensional diffusion. The radial position is 0.4 cm from the cylindrical surface, and the axial position is 1.0 cm from the end of the rod.