A chromatographic column is packed with spherical particles of radius R that are coated withan immobilized enzyme, lactate dehydrogenase. The enzyme converts pyruvate (A) into lactate(B) at the particle surface in a reaction that has pseudo first-order kinetics (r = kCA, moles area-1t-1). Mass transfer takes place within a stagnant film of thickness δ. Assume that δ is much smaller than the particle diameter so that curvature can be neglected. The diffusivity of pyruvatein the liquid film can be represented as DAL and is not affected by the lactate.(a) Derive the concentration profile of pyruvate in the film.(b) Derive an expression for the flux of pyruvate and demonstrate that the flux isproportional to 1/(1+Da-1) where Da, the Damkohler number, is given by δk/DAL(c) Explain qualitatively what happens to the flux of pyruvate as the reaction rate becomesvery fast relative to the diffusion rate (as Da becomes large). Do increases in k have alarger effect on the flux at low or at high Da values? Give a physical explanation for your observation.