Consider cylindrical-shaped absorbent material designed to selectively remove solute A from a solution. The uptake of solute A through the homogeneous material is limited by molecular diffusion....

Consider cylindrical-shaped absorbent material designed to selectively remove solute A from a solution. The uptake of solute A through the homogeneous material is limited by molecular diffusion. Furthermore, the absorbent has a higher affinity for solute A relative to the surrounding solution as described by the linear equilibrium relationship

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. Assume that (1) the surrounding fluid is very well mixed and has a constant concentration of c’_A
 2.00 g mol/m³; (2) the diffusion coefficient of A in the homogeneous absorbent material is
 and K
 1.5 cm³
fluid/cm³
absorbent; (3) the cylindrical absorbent pellet is 1.0 cm in diameter and 5.0 cm long; and (4) there is no solute A initially in the absorbent material.

If the ‘‘edge effects’’ associated with the ends of the cylinder can be neglected, how long will take for the solute A concentration to reach 2.94 g mol/m³
at a depth of 0.4 cm from the surface of the cylinder?