Vanadium Pentaoxide can be used as a catalyst for the following reaction

$S{O}_2+\frac{1}{2}{O}_{2}longrightarrowS{O}_3$

It was determined that the rate expression for this reaction is as follows:

$r=\frac{k{P}_{SO2}{P}_{O2}^{\frac{1}{2}}}{(1+K_1{P}_{SO2}{)}^2}$

where:

$k=0\mathrm{.}184\frac{lb*mol}{h*at{m}^{\frac{3}{2}}*l{b}_{\text{c}\text{a}\text{t}}}$

and

$K_1=0\mathrm{.}996at{m}^{-1}$

If $S{O}_2$ and $O_2$ are fed into the reactor at $100\frac{lb*mol}{h}$ each, how many pounds of catalysts

are need to reach $20\%$ conversion if the reactor operates isothermally at $649F$ and

under constant pressure of $1$ atm?