$[1]$ The irreversible gas$-$phase reaction of $S{O}_2$ to $S{O}_3$ is carried out in a PFR working at a total pressure of

$10$atm. The inlet feed includes a $100-$fold stoichiometric excess of $O_2($i$.$e$.,\frac{F_{O2}}{F_{SO2}}=50)$ to assure

complete conversion of $S{O}_2,$ indicating negligible changes in volumetric flow rate and total pressure

along the PFR$.$ Also, the inlet feed has a volumetric flow rate of $50\frac{m^3}{m}in$ at $800K$ and $10$atm.

$S{O}_2+\frac{1}{2}{O}_{2}S{O}_3$

Though the reaction rate is $-r_{SO2}=k{P}_{SO2}^{}{P}_{O2}^{},$ it can be simplified into $-r_{SO2}$~~$k^{\text{'}}{P}_{SO2}^{}$ when $P_{O2}$ is in

large excess. From experiments, the partial pressure of $S{O}_3(p_{S{O}_3})$ was recorded along the length of the

reactor $(z),$ as shown below. How would you obtain the reaction order of $S{O}_2()$ from the plot of $p_{S{O}_3}$

vs$.z?$ Use the linearized form of the equation obtained from the information of this plot. $[4$ pts$]$