In a production process, reactor exit flow is a mixture of methyl ethyl keton $($MEK$),$ secbutanol and n$-$butanol. The mixture has $0\mathrm{.}5\%$ MEK, $69\mathrm{.}2\%$ sec$-$butanol, and $30\mathrm{.}3\%n$ butanol: The sec$-$butanol is wanted to produce with $99\mathrm{.}2\%$ purity. Therefore, exit flow of reactor is cooled and sent to the seperation units. The exit flow rate of the reactor is $100$ kmo$\frac{l}{h}$ and it is at $115C$ and $\frac{1\mathrm{.}2}{b}ar.$ The feed is sent to the distillation column as a vaporliquid mixture $)=(0\mathrm{.}75.$ The distillate flowrate is $70$kmo$\frac{l}{h}$ and all methyl ethyl keton $($MEK$)$ is obtained from top of the column in distillate stream. Also, sec$-$butanol mole fraction is $0\mathrm{.}005$ in the bottom product stream. Reflux ratio is given as $R_D=1\mathrm{.}3R_{\text{D}\text{m}\text{i}\text{n}}$ for this column. Hint: MEK concentration in the feed stream is quite low. Hence, the feed stream can be accepted as binary mixture. Determine the related parameters of colums that are:

a$)$ at given conditions $R_D=1\mathrm{.}3R_{\text{D}\text{m}\text{i}\text{n}}$

i$.$ Molar flowrates of enriching and stripping sections in the colum with McCabe Thiele method,

ii$.$ Top and bottom temperature of column

iii. Calculate the heat loads of total conders and partial reboiler in $kW,$

iv$.$ Number of theoretical stages $($number of trays$)$

Note: ${}_{\text{M}\text{E}\text{K}}=431\mathrm{.}12k\frac{J}{k}g,{}_{s-\text{b}\text{u}\text{t}}=584\mathrm{.}97k\frac{J}{k}g,{}_{n-\text{b}\text{u}\text{t}}=598\mathrm{.}1k\frac{J}{k}g$