As a design engineer, you are designing a process to convert some excess butene $(C_4{H}_8)$ to ethylene $(C_2{H}_4)$ using the reaction $C_4{H}_{8}2C_2{H}_4.$ Your process will include reaction and separation, and two streams will exit the process: an ethylene$-$ rich stream and a butene$-$rich stream. The following are requirements for the process:

Feed $($input$)$ stream: Flow rate: $765lb\frac{m}{h}r$; Composition: Pure butene Ethylene$-$rich output stream: Flow rate: $25\mathrm{.}5lbm\frac{o}{h}r$; Composition: $89$mole$\%$ ethylene $($the rest is butene$)$

Butene$-$rich output stream: Flow rate: $240f\frac{t^3}{h}r$ Composition: ethylene and butene Of the incoming butene, $79\%$ is converted to ethylene. What will be the concentrations of ethylene and butene $($in units of $($:$l\frac{b_{\text{m}\text{o}\text{l}}}{f}{t}^3\}$ in the butene$-$rich outlet stream? $(10$ pts$)$