I need this question answered ASAP please. Please show ALL working in detail. Please use the necessary nomographs for any of the required calculations. Thank you very much!!

Question:

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$=0\mathrm{.}05$

propane$=0\mathrm{.}38$

i$-$butane$=0\mathrm{.}27$

n$-$butane$=0\mathrm{.}30$

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 $1.$

b$)$ Determine the percentage of the stream, $L_N$ that vapourises in the reboiler $($operating at $20C$ and $4$atm $)$ and the compositions of the vapour and liquid streams, $V_{N+1}$ and $W$ respectively. Derive the equation from first principles.

c$)$ If the provision of steam to the reboiler is upset causing the temperature of the reboiler to fall by $5C,$ comment on the effect this would have on the fraction of $L_N$ that is vapourised, the composition of the bottoms product and the operation of the distillation column.