Q$.6$ A $1000kg$ of pyridine $-$water solution containing $59\%$ pyridine is to be extracted with equal amount of pure chlorobenzene. The raffinate from the first extraction is to be extracted with a weight of solvent equal to raffinate weight and so on $(S2=R1,S3=R2).$

$($a$)$What is the exit concentration and percentage recovery of pyridine after three stages?

$($b$)$ if all the solvent is used in single stage what is the percentage recovery and exit concentration.

The equilibrium data and tie line data is as given below.

$\backslash$table$[[$Chlorobenzene Layer$($C$.$B$.),$Water Layer$],[$Pyridine$,$C$.$B$,$Water,Pyridine,C$.$B$.,$Water,,,$],[0\mathrm{.}0,99\mathrm{.}95,0\mathrm{.}05,0,0\mathrm{.}08,99\mathrm{.}92,,,],[11\mathrm{.}05,88\mathrm{.}28,0\mathrm{.}67,5\mathrm{.}02,0\mathrm{.}16,94\mathrm{.}82,,,],[18\mathrm{.}95,79\mathrm{.}90,1\mathrm{.}15,11\mathrm{.}05,0\mathrm{.}24,88\mathrm{.}71,,,],[24\mathrm{.}10,74\mathrm{.}28,1\mathrm{.}62,18\mathrm{.}90,0\mathrm{.}38,80\mathrm{.}72,,,],[28\mathrm{.}60,69\mathrm{.}15,2\mathrm{.}25,25\mathrm{.}50,0\mathrm{.}58,73\mathrm{.}92,,,],[31\mathrm{.}55,65\mathrm{.}58,2\mathrm{.}87,36\mathrm{.}10,1\mathrm{.}85,62\mathrm{.}05,,,],[35\mathrm{.}05,61\mathrm{.}00,3\mathrm{.}95,44\mathrm{.}95,4\mathrm{.}18,50\mathrm{.}81,,,],[40\mathrm{.}60,53\mathrm{.}00,6\mathrm{.}40,53\mathrm{.}20,8\mathrm{.}50,37\mathrm{.}90,,,],[49\mathrm{.}00,37\mathrm{.}8,13\mathrm{.}2,49\mathrm{.}00,37\mathrm{.}8,13\mathrm{.}20,,,]]$