A countercurrent extraction cascade equipped with a perfect solvent separator to ped de extract reflux is used to separate methyl cyclopentane $(A)$ and $n-$hexane $(C)$ into a final gtract and raffinate containing $95wt\%$ and $5wt\%$A respectively, on a solvent$-$free basis, using aniline the solvent. The feed rate is $1,000k\frac{g}{h}$ with $55wt\%A,$ and the mass ratio of solvent to feed is $1\mathrm{.}0.$ Tontains no aniline and the fresh solvent is pure. Recycle solvent is equally assumed te bapyte. The equilibrium data for the methyl cyclopentane$-$aniline$-$n$-$hexane system are tabulated thuk:

$($a$)$ Calculate the weight fraction of n$-$l exan in the extract liquids on a solvent$-$free basis when the weight fraction of aniline on a solvent$-$free basio is $2\mathrm{.}75.$

$($b$)$ Determine the $($i$)$ minimum famber of theoretical stages required for the specified solvent$-$free extract and raffinate compositions. minimum extract reflux ratio for the specified feed and product compositions, $($iii$)$ operating rflux atio and number of ideal stages on both sides of the feed required to produce the same end prodyct $0m$ the same feed and $($iv$)$ important flow quantities of the various streams per $1000k\frac{g}{h}$ of feepratton a solvent$-$free basis.