For the hydrogel tablet dissolution process described in Section $4\mathrm{.}2\mathrm{.}8,$

a$.$ Obtain the equations of change for the mass fractions.

b$.$ Derive the expression for the amount of drug release at any time.

$[$Key: Section $4\mathrm{.}2\mathrm{.}8$ Hydrogel Tablet

This example involves microscopic mass balance of drug, polymer and water in a watersoluble hydrogel tablet$\mathrm{.}5$ As shown in the attached Figure $4\mathrm{.}12,$ the tablet is a cylinder of radius R and height Z$.$ When ingested, water in the stomach diffuses into the tablet. The polymer begins to diffuse out from the tablet. From the surface, polymer and drug in the polymer matrix dissolve instantaneously into the bulk water. The water diffuses simultaneously into the tablet. During this process, the volume of the tablet changes with time. The tablet swells first but eventually dissolves in water. This is an example of a moving boundary problem without constant density assumption$]$