Ethylene oxide $(C)$ can be produced by the vapor$-$phase catalytic oxidation of ethylene $(A)$ with

air $(B)$ :

$C_2{H}_4(A)+\frac{1}{2}{O}_2(B)C{H}_{2}OC{H}_2(C)$

$-r_A=k{P}_A^{\frac{1}{3}}{P}_B^{\frac{2}{3}}=k{P}_{A0}(\frac{1}{2}{)}^{\frac{2}{3}}(\frac{1-x}{1+x})y=k^{\text{'}}(\frac{1-x}{1+x})y$

Where $y=\frac{P}{P_0}$ pressure ratio.

The ratio of the volumetric flow rate, $f,$ is given by

$f=\frac{v}{v_0}=\frac{1+x}{y}$

Calculate the catalyst weight necessary to achieve $60\%$ conversion and plot $x,y,f,$ and the

reaction rate as a function of catalyst weight.

Data: $k=0\mathrm{.}00392mo\frac{l}{\text{a}\text{t}\text{m}*kgcat*sec},F_{A0}=0\mathrm{.}1362mo\frac{l}{sec,F_{B0}}=0\mathrm{.}068mo\frac{l}{sec,P_0}=10$

atm,$=0\mathrm{.}0367k{g}^{-1}.$

Hint: Use bisection method and the built$-$in ode solver in PYTHON.