Question

Consider the flowsheet shown in the figure for manufacturing C via the reaction A + B → C in an isothermal CSTR. Pure A and pure B are fed, along with a recycle stream of R kmol/h. The split in the separator is perfect so that the recycle stream contains only A and B (no C) and the product stream is pure C. Let $x_{i}$ denote the mole fraction of species i (i = A, B, C) in the CSTR, which is operated in excess B with $x_{B}/x_{A} = 4.$ The reaction is first-order in A with the reaction rate $(−r_{A}) = k_{x}\cdot x_{A},$ where $k_{x} = 5.0 kmol/(m³\cdot h).$ The reactor volume V in $m³$ is to be optimized to minimize the cost objective J = V + 0.25R, where R is the recycle rate in kmol/h. For a product rate P = 100 kmol/h, the optimum value of V is ____ $m³$ (rounded off to the nearest integer). Given: d/dz[z/(1−z)] $= 1/(1−z)².$

Official answer: 150