Graphical Solution of the CSTR Design Equation

The Monod equation, Eqn. (4-25), frequently provides a reasonable description of the growth rate of cells, such as yeast cells or the activated sludge that is formed during wastewater treatment 

In this equation, Ca is the mass concentration of the growth-limiting reactant (mass A/volume), Cc is the mass concentration of cells (mass C/volume), and k and K are constants. The stoichiometry of the reaction is such that T(C/A) is the mass of cells produced per mass of A consumed. Therefore, 

Since cells are produced by the reaction, the Monod equation predicts oMtocatalytic behavior, i.e., the higher the concentration of product C, the faster the reaction goes. The Monod equation also shows that the rate of cell production is zero when either Ca = OorCc = 0. 

Part A An ideal CSTR with a volume of Vis operating at steady state. The mass concentrations of A and C in the feed are Cao and Cco respectively. The volumetric flow rate of the feed to the reactor is v (volume/time). What is the mass concentrationof A in the reactor effluent, for the following values CaO = 10gfl,Cco = Og/1, V — l.Oliter, v — 0.51/h, y(C/A) = 0.50, k — 1.0h, As — 0.20 g/1. What is the mass concentration of cells in the reactor effluent for this condition The reaction takes place in the liquid phase. 

Nevertheless, materials such as coal and biomass are important in a practical sense, and scientists and engineers must deal with reactions involving these materials. In these cases, mass concentrations are used instead of molar concentrations. The use of mass concentrations in rate equations is less fundamental, perhaps, than the use of molar concentrations. This is because theories such as collision theory and transition-state thewy teach that reaction rates depend on molar concentrations. Nevertheless, the use of mass concentrations in problems involving complex materials has proven to be a practical approach is solving such problems. 

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