A flash vessel is used to separate a mixture that consists of ethane, propane, $n-$

butane, $n-$pentane and $n-$hexane. Component flowrates and Antoine

coefficients are shown in Table Q$1.$ Antoine equation may be used to estimate

the vapour pressure of component $k(P_k)$ and is given in Equation $1.$

$log{P}_k=A_k-\frac{B_k}{+c_k}$

where $P_k^o$ is given in $mmHg$ and temperature $(T)$ in Kelvin. Determine the

following:

$($a$)$ Find the components molar flowrates and fractions in its overhead and

bottom streams if the vessel is operated at $368K$ and $8$atm $($note: $1$atm

$=760mmHg).$ Use $n-$butane as key component.

$(30$ marks$)$

$($b$)$ If recovery of $n-$pentane is to be reduced to $0\mathrm{.}7,$ with vessel operated at $8$

atm, determine the operating temperature that can achieve this

separation task.

$(20$ marks$)$

Table Q$1$: Component flowrates and Antoine coefficients for hydrocarbon mixture