Calculation $2$: A mixture of $28\%($mole fraction$)S{O}_2$ and $72\%($mole fraction$)$ air is charged to a flow reactor in which $S{O}_2$ is oxidized. This reaction conducts at $P_0=1485$kPa and $T_0=500K.$ Assume air only consists of $N_2$ and $O_2.$

$2S{O}_2+O_2$longrightarrow$2S{O}_3$

First, set up a stoichiometric table using only the symbols using $S{O}_2$ as the basis of calculation. The symbols used to construct this table are ${}_j,F_j,$ and $x.$ is the conversion of $S{O}_2$; Construct this table using initial molar flow rate of $S{O}_2).$

Second, express the concentration of $S{O}_2,O_2,$ and $S{O}_3$ as a function of conversion. Assume no pressure drop and this reaction is an isothermal reaction.

Evaluate the parameters $,$ and $($:${}_{\text{I}}\}$ and re$-$express concentration of $S{O}_2,O_2,$ and $S{O}_3$ as a function of conversion. $($Assumption: ideal gas law is valid here$).$