$x=\frac{\frac{k{C}_{A0}W}{v_0}(1-\frac{W}{2})}{1+\frac{k{C}_{A0}W}{v_0}(1-\frac{W}{2})}a$A second$-$order reaction is taking place in a packed bed reactor. $40$kg catalyst is loaded in the reactor. For a volumetric flow rate of $4$m$^3/$h and entering concentration of $0\mathrm{.}1$kmol$/$m$^3,$ find the conversion for $=0\mathrm{.}045$ kg$^-1.($k$=10$ m$^6/($kmol$*$kgcat$*$h$)).$

$X=$

bThe company decided to change the catalyst in the reactor. The new catalyst particle diameter is $2$ times bigger than the previous one. And also they doubled the entering pressure. If we are in the laminar flow regime, Calculate the new conversion. $($ The reactor is operated at isothermal conditions$).$ For the laminar flow regime $\backslash$alpha parameter changes according to the equation below;$$

$2=1($ A c$1/$ A c$2)^2($ D p$1/$ D p$2)^2($P $01/$ P $02)^2*($T $02/$ T $01)$

Note: image $is$ formula $ofX=....$