A catalytic dehydrogenation process shown in Figure SAT$5\mathrm{.}3$P$4$ produces $1,2$butadiene $(C_4{H}_6)$ from pure normal butane $(C_4{H}_{10}).$ The product stream contains $75mo\frac{l}{h}r$ of $H_2$ and $13mo\frac{l}{h}r$ of $C_4{H}_{10}$ as well as $C_4{H}_6.$ The recycle stream is $30\%($mol$)C_4{H}_{10}$ and $70\%($mol$)C_4{H}_6,$ and the flow is $24mo\frac{l}{h}r.$

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Figure SAT$5\mathrm{.}3$P$4$

a$.$ What are the feed rate, $F,$ and the product flow rate of $C_4{H}_6$ leaving the process?

b$.$ What is the single$-$pass conversion of butane in the process?