A distillation column is used to remove natural gas liquids from an unstabilised natural gas stream. The column is designed with kettle reboiler as shown in Figure $1.$ The liquid leaving the bottom tray of the distillation tower, $L_N,$ has the following composition given in mole fractions:

ethane:

Figure $1-$ Bottoms Section of a Distillation Tower & Reboiler

a$)$ If the pressure at the bottom of the column is $5\mathrm{.}0$atm, estimate the temperature of the stream $L_N$ using the $k$ values provided in Table $1$ below.

$[6]$

Table $1-$ Distribution Coefficient, K Values for Light Hydrocarbons

$\backslash$table$[[,$Ki values at $5$atm,Ki values at $4$atm$],[$Component$,5C,10C,15C,20C,20C$