$21-14$ Using the equation for $K_p$ given in problem $21-10$ for the oxidation of $S{O}_2,$ determine the outlet conversion from the third stage of a three$-$stage FBCR$,$ given that, for each stage, the outlet temperature is $20K$ from the $f_{eq}(T)$ curve. The inlet temperature to the first stage is $700K.$ Between stages $1$ and $2,$ the temperature is reduced by $120K,$ and between stages $2$ and $3,$ the temperature is reduced by $85K.$ The feed contains $19\mathrm{.}7$mol$\%S{O}_2(A),23\mathrm{.}8$mol$\%O_2,56\mathrm{.}5$mol$\%N_2,$ and a trace $($say $0\mathrm{.}0001$mol$\%)$ of $S{O}_3.$

Data: $F_{Ao}=220mol{s}^{-1}$;$m^{}=40\mathrm{.}3kg{s}^{-1}$;$H_{RA}=-100kJmo{l}^{-1}$;$c_P=0\mathrm{.}94J{g}^{-1}{K}^{-1}$;$P_0=101$kPa.