Consider the case of diffusion and reaction inside a slab. Initially the concentration of solute in the slab is \(c_{a o}\). The slab is made of a material that when heated catalyzes the reaction of \(a\) so that \(a\) decomposes with first-order kinetics and a reaction rate constant, \(k^{\prime \prime}\). A heating fluid bathes the slab so that at the outer surfaces, the concentration of \(a\) is always 0 . Determine the concentration profile within the slab as a function of time so that we will know when the reaction is essentially complete and we can remove the slab from the heating fluid (Figure P6.26).

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FIGURE P6.26 C ao =k"ca Cao D as X