1. In chemical engineering, plug flow reactors are often used to convert reactants into products. It has been determined that the efficiency of the conversion can be improved by recycling a portion of the product stream so that it returns to the entrance for an additional pass through the reactor as shown in Figure 1. Feed. A PFR Recycle Figure 1: Plug flow reactor The recycle rate is defined as: R- Product, B volume of fluid returned to entrance volume leaving the system Chemical A is process to generate a product B. For the case where A forms B according to an autocatalytic reaction (that is, in which one of the products acts as a catalyst or stimulus for the reaction), it can be shown that an optimal recycle rate must satisfy In 1+R(1-XA). R(1-XAD) R+1 R[1+R(1-XA)] where Xar the fraction of reactant A that is converted to product B. The optimal recycle rate corresponds to the minimum-sized reactor needed to attain the desired level of conversion. Use a numerical method bisection to determine the recycle ratios needed to minimize reactor size for a fractional conversion of XAr = 0.96.