5. In controlled release systems, pills are designed to release to the patient a constant molar rate of a specific drug (A). A typical controlled release pill is a hollow sphere filled with a saturated solution of the drug in water, which contains small crystals of the solid drug (figure). The purpose of the crystals is to keep the solution inside the pill saturated at all times. The drug diffuses through a solid membrane (B), and is carried away by the fluid flowing around the pill. To study this process in the laboratory, a pill was suspended in a constant flow of water (drug concentration can be assumed to be zero) intended to simulate the external mass transfer process that takes place inside the patient. The following information is available: the concentration of the drug in the membrane that is at equilibrium with a solution with concentration ca is given by Cam KCA, where K = 0.25. The diffusivity of A in the membrane is DAB = 2.50x10 cm/s. Convection around the pill is characterized by a mass transfer coefficient keco. A is dilute in water and within the membrane. The inner and outer radii of the membrane are R = 3 mm and R2 = 4.2 mm, respectively. The solubility of the drug in water is 1.5x10 mol/cm. Determine: a) The steady-state concentration profile of A in the membrane. The solution must not contain ke. b) The rate of release of A from the pill into the flowing water (moles of A released per unit time). Pure water R saturated solution Membrane (B) crystals of pure A