One type of packaging film with thickness ‘‘l'' has an immobile sacrificial reagent atinitial concentration c20 within the wall of the package. A solute at concentrationc10 outside of the film, like water, oxygen, or radioactive cesium, diffuses into thefilm, reacting irreversibly with the sacrificial reagent as it goes. The product may bemobile or immobile; since the reaction is irreversible, it does not matter. Thisreaction shows the solute's penetration across the film.

(a) Write mass balancesfor the solute and the immobile reagent.

(b) Write possible initial and boundaryconditions for these equations.

(c) If the reaction were infinitely fast, how wouldyour equations change?