A liquid feed that is \(48 \mathrm{wt} \% \mathrm{~m}\)-xylene and \(52 \mathrm{wt} \%\) o-xylene is separated in a fractional extractor (Figure \(13-5\) ) at \(25^{\circ} \mathrm{C}\) and \(101.3 \mathrm{kPa}\). Solvent 1 is \(\beta, \beta^{\prime}\)-thiodipropionitrile, and solvent 2 (diluent) is \(\mathrm{n}\) hexane. Equilibrium data are \(\mathrm{K}_{\mathrm{d}, \mathrm{m}-\mathrm{xy}}=0.050\) and \(\mathrm{K}_{\mathrm{d}, \mathrm{o}-\mathrm{xy}}=0.150\) where \(\mathrm{K}_{\mathrm{d}, \mathrm{A}}=\mathrm{y}_{\mathrm{A}}\) (in solvent) \(/ \mathrm{x}_{\mathrm{A}}\) (in diluent) (Perry and Green, 1984). For each kilogram of feed, \(200 \mathrm{~kg}\) of solvent 1 and \(20 \mathrm{~kg}\) of solvent 2 are used. Both solvents are pure when they enter the cascade. We desire a \(92 \%\) or better recovery of o-xylene in solvent 1 and a \(94 \%\) or better recovery of \(\mathrm{m}\)-xylene in \(\mathrm{n}\)-hexane. Use integer values of \(\mathrm{N}\) and \(\mathrm{N}_{\mathrm{F}}\). Find outlet recoveries, solvent-free compositions, \(\mathrm{N}\), and \(\mathrm{N}_{\mathrm{F}}\).

Figure 13-5

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Solvent 2 (R,X80 A+ Solvent I (E, YA,YB) Feed Xj Yjel NF (A+B+ Solvent 1 or 2) N B+ Solvent 2 Solvent I (R.XAN ) (EYAN!