Question 3 (22 marks)
The isothermal irreversible first-order gas phase reaction, A \rightarrow B, is carried out in a packed
plug-flow reactor. The pressure gradient along the length of the packed bed can be
approximated as constant, such that $\frac{dP}{dW} = -0.2$ atm/kg. For an entering pressure is 20 atm
and catalyst weight of 60 kg, 86.5% conversion is achieved. If the pressure-drop within the
PFR were given by the following equation, $\frac{dP}{dW} = -\frac{0.01}{2} (\frac{T}{T_0}) \left(\frac{P_0}{P/P_0}\right) (1 + \epsilon X)$, what will
the difference in conversion be compared to the constant pressure gradient case mentioned
above?