The elementary gas$-$phase reaction AlongrightarrowB$+2C$ is camied out isothermally in a packed bed reactor. Pure A enters the reactor at $10$atm and $127C$ and a molar flow rate of $2\mathrm{.}5mo\frac{l}{m}in$ The rate constant is $0\mathrm{.}44\frac{L}{m}in*kg.$

a$)$ Calculate the catalyst weight necessary to achieve $90\%$ conversion without pressure drop.

b$)$ Calculate the catalyst weight necessary to achieve $90\%$ conversion? Take $=0\mathrm{.}001k{g}^{-1}.$

c$)$ Plot $x$ and $y$ down the length of the reactor using Polymath