Assume a monolithic catalyst that contains cylindrical pores is used for a first order irreversible reaction (A+B). The reaction rate constant is k and the diffusivity of A through the catalyst pore is DA. If a fraction of a of the pore length (L) of the cylindrical pore has been deactivated by poison, this means that the cylindrical region of length of (a L) near the pore mouth will have no catalytic activity, whereas the rest of catalyst pore remains catalytically active. Assume the reaction is run under isothermal steady state condition, and there is no external mass transport limitation. (1) What is the concentration profile expression in this cylindrical catalyst pore? (2) What is the rate of reaction in the catalyst pore? (3) What is the effectiveness factor of the reaction in this pore mouth poisoned catalyst? (Assume the reaction only happens on the wall surface of the cylindrical pore. The pore radius is r.) . x=0 x=aL x=L