For gas reactions in PBRs$,$ the conversion is calculated by using the equation below.

$\frac{dx}{dW}=\frac{k{C}_{A0}^2}{F_{A0}}\frac{(1-x{)}^2}{(1+x{)}^2}(\frac{P}{P_0}{)}^2$

For gas reactions, Ergun equation is used to calculate the pressure drop through the PFR$.$

Explain why Ergun equation is necessary to calculate the conversion for gas reactions in PBRs$.$