Reconsider the first example in the text a final time. However, in this instance let's assume we have a first-order chemical reaction \(a \xrightarrow{k_{a}^{\prime \prime}} b\) occurring in the liquid. Species \(a\) diffuses through the liquid and at the catalytic surface species \(a\) undergoes an instantaneous reaction that destroys it.

a. Develop the differential equation that describe the concentration profile of \(a\).

b. What are the boundary conditions for this problem?

c. Solve the problem to determine the concentration profiles of \(a\).