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A multi-component distillation column to separate a mixture of five components: $A$ (Lightest), $B$, $C$, $D$, and $E$ (Heaviest). The feed composition is $30\\% \\, A$, $25\\% \\, B$, $20\\% \\, C$, $15\\% \\, D$, and $10\\% \\, E$ by mole, with a total feed flow rate of $1000 \\, \\text{kmol/hr}$. The feed enters the column as a saturated liquid at 1 atm.