The gas$-$phase reaction, A $+0\mathrm{.}5$ B $->3$P occurs in a packed bed reactor. The rate law is $$rA $=$ kCA$2$CB where k $=40$ L$3/($g$-$min$-$mol$2).$ The superficial gas velocity $($G$)$ is $1\mathrm{.}6$ kg$/$m$2-$s with a density of $1\mathrm{.}26$ kg$/$m$3$ and a viscosity of $2\mathrm{.}2$x$10-5$ kg$/$m$-$s$.$ The porosity, catalyst density, and particle diameter are, respectively, $0\mathrm{.}45,2\mathrm{.}3$ g$/$cm$3,$ and $4$ mm$.$ The cross sectional area of the reactor is $60$ cm$2.$ The inlet pressure and temperature are, respectively, $180$ kPa and $400$K$.$ The feed composition consists of $80$ mole $\%$ of A and $20$ mole$\%$ of B$.$ Calculate the conversion $($X$)$ of component A when the catalyst weight in the reactor is $10$ kg$.$ Assume that the system operates isothermally. Note that this problem requires a solver $($Matlab$,$ Polymath, etc$).$ Please express your answer to two decimal places. Be careful with the units.