a) Write equations that define the Thiele modulus for irreversible first order reaction; A R. Explain all the symbols with the appropriate legend. (1 mark, K&U 3.2) b) Show how the effectiveness factor of spherical catalyst can be calculated from the Thiele modulus. (2 mark, K&U 3.2) c) A reaction A Ris to take place on a porous catalyst sphere (de, = 5 mm, De = 106 m/(m cat s)). Calculate how much the rate is slowed down by pore diffusional resistance if the concentration of reactant bathing the particle is 105 mol/m' and the diffusion-free kinetics are given by the following equation (4 marks, A&A 3.4) mol -r\" = 0.3 CA mcat d) Derive an appropriate equation to show how external mass transfer resistance affects the overall reaction rate for a first order irreversible reaction. (2 marks, K&U 3.2) e) The rate of the first order reaction A Rwas studied experimentally in a catalytic reactor. i. Use the provided data to determine if film resistance to mass transfer influences the rate mark, A&A 3.4) ii. Use the provided data to determine if internal resistance to mass transfer influences the rate (1 mark, A&A 3.4) iii. Use the provided data to determine if there are temperature variations within the pellet or across the gas film (1 mark, A&A 3.4) Data: For the spherical particle: . dp = 0.45 mm De = 17 x 105 m/(hr m cat) (effective mass conductivity) kefj= 1.8 kJ/(hr m cat K) (effective thermal conductivity) For the gas film surrounding the pellet (from correlations in the literature): h = 180 kJ/(hr m- cat K) (heat transfer coefficient) kg = 6 m/(hr mcat) (mass transfer coefficient) For the reaction . AH, =-10 kJ/mol A (exothermic) CAg = 30 mol/m (at 1 atm and 340C) -robs= 0.4 x 105 mol/(hr mi cat)