The largest chemical plant owned by your employer produces $10,000$kmo$\frac{l}{s}$ of a toxic gas which has a $N_{x}O$ content of $9\mathrm{.}5$mol$\%.$ It is desired to remove $83\%$ of its nitrous oxide content by contact with pure water and you have been tasked with the preliminary equipment design. According to your experienced supervisor, the design water flow rate should be $95\%$ higher than the minimum. The equilibrium data is also available $($see the provided plots $(x-y$ and $x-Y).$

$($a$)$ Calculate $Y_1,Y_2,Y_2,x_2,V_2$ and $V_s$

$($b$)$ Calculate $($graphically$)$ the minimum water flow rate

$($c$)$ Calculate the actual water flow rate $L_s$ and $L_2$

$($d$)$ Calculate the $N_{x}O$ concentration in the water leaving the absorber and $($:$x_1\}$ and $L_1.$

$($e$)$ Determine the $x-y$ operation line equation using the standard equation.

Hit: Remember that for a multi$-$stage process $x_0=x_2,Y_1=Y_2,x_N=x_1,Y_{N+1}=Y_1$

Calculate the values for $R$ and $C.$

$($f$)$ Draw the operation line $(x-y)$ on the corresponding plot using $6$ equidistant points

$($g$)$ Draw the pseudo$-$equilibrium line $($using $6$ equidistant points$)$ considering that the operation is carried out on a multi$-$stage absorber with an overall efficiency of $60\%.$

$($f$)$ Estimate $($graphically$)$ the required number of real stages.

$($g$)$ Determine the $N{O}_x$ compositions $(x,y)$ entering and leaving each stage. Use a schematic to show your answer