Q$16.$ The following feed at $60C,2070k\frac{N}{m^2}$ abs$,$ is to be fractionated at that pressure so that the vapour distillate product contains $0\mathrm{.}913\%$ of the isopentane and the bottoms $0\mathrm{.}284\%$ of the isobutene: $C{H}_4=0\mathrm{.}50$;$C_3{H}_8=0\mathrm{.}03$;$i-C_4{H}_{10}=0\mathrm{.}10$;$n-C_4{H}_{10}=0\mathrm{.}15$;$i-C_5{H}_{12}=0\mathrm{.}07$;$n-C_5{H}_{12}=0\mathrm{.}05$; and $n-C_6{H}_{14}=0\mathrm{.}10.$ Compute the $($i$)$ minimum reflux ratio; and $($ii$)$ minimum number of trays. At a reflux ratio$=2\mathrm{.}0,$ estimate the $($iii$)$ product analyses; and $($iv$)$ number of theoretical trays by the correlations of Gilliland, Erbar and Maddox.