A slurry reactor has been operating to carry out a hydrogenation reaction. After one year of operation, a reduction in the reaction rate is observed and the problem is being investigated. Two possible caused are: A) agglomeration of catalyst pellets or B) a partially blocked sparger, which would limit the gas absorption rate in the slurry. The following information is available from plant data before and after the problem developed, where m is the catalyst loading [g/dm], CA is the solubility of gas in the liquid phase [mol/dm] and RA is the overall reaction rate [mol/dm min]. Prior to malfunction m [dm/g] CAi [mol/dm] 100 50 33.3 0.3 0.3 0.3 RA [mol/dm min 0.071 0.040 0.028 After malfunction m [dm/g] 100 50 33.3 CAi [mol/dm] 0.3 0.3 0.3 RA [mol/dm min] 0.050 0.032 0.023 a) Derive expression relating the overall reaction rate to the sum of the three resistances to the overall reaction rate: gas absorption, Rb, external diffusion, Re, and reaction/internal diffusion, Rr. assume that the reaction is first order with respect to hydrogen. b) Assuming that the external diffusion from bulk liquid to catalyst pellet surface is fast, determine whether the sparger or catalyst agglomeration is causing the problem. Justify your answer with a graph. c) At a catalyst loading of 80 g/dm, by how much does the relative contribution of each of the resistance (as a percentage) change after the malfunction?