The feed to a rectifying column is $32\mathrm{.}0$mol$\%n-$butane, $56\mathrm{.}0$mol$\%n-$pentane, and $12\mathrm{.}0$mol$\%n-$hexane. Feed rate is $100\mathrm{.}0\frac{\text{k}\text{m}\text{o}\text{l}}{h}$ and at a pressure of $3\mathrm{.}0$ bar $.$ The feed is either a saturated vapour or a saturated liquid. The column operates at $3\mathrm{.}0$ bar, has a total condenser with a saturated liquid reflux, and CMO can be assumed valid. The distillate product is $99\mathrm{.}6$mol$\%n-$butane and $D=20\mathrm{.}0\frac{\text{k}\text{m}\text{o}\text{l}}{h}.$ List your assumptions, if any

a$.$ Find bottoms flowrate, and mole fractions of distillate and bottoms.

b$.$ Use your knowledge of distillation to determine whether the feed is a saturated vapour or a liquid.