Consider the non$-$elementary reactio: A$+$B $->$ C$.$ Experiments have determined that the reaction is zero order in A and B$.$ a$)$ Derive the expression for the Damkohler number as a function of X for the reaction conducted in the liquid phase in an isothermal PFR$.$ Show your work. b$)$ The inlet concentration decreases by half due to a more dilute feedstock. How much does the conversion X change? Use the Damkohler number to justify your answer