Problem $3$

Estimate the volume of a plug$-$flow reactor $($in $m3)$ required for production of ethylene from ethane $($A$)$ based on the following data and assumptions:

$(1)$ The feed is pure ethane at $1k\frac{g}{s},1000K$ and $\frac{2}{b}ar.$

$(2)$ The reaction is first$-$order and irreversible at low conversion, with rate constant $k_A=0\mathrm{.}254\frac{1}{s}$ at $1000K.$

$(3)$ The reactor is operated isothermally and isobarically.

$(4)$ Conversion of ethane is $20\%$ at the outlet.