When is a non-key distributing, and when is it nondistributing? For almost all chemicals, five 9 s purity \{concentrations of impurity below \(10.0 \mathrm{ppm}\), mass (mass fraction \(<1.0 \times 10^{-5}\) ) or [approximately mole fraction \(\left.\left.<\left(1.0 \times 10^{-5}\right)\right]\right\}\) would be low enough that the chemical can be accepted in the product and could be considered to be nondistributing (this is a very tight definition of nondistributing). A less strict concentration limit (four 9s purity) would use \(100.0 \mathrm{ppm}\). Another possible definition of nondistributing that is less strict is a concentration that causes less than a \(0.1 \%\) or \(0.01 \%\) change in calculations of other variables (e.g., concentrations of other components, flow rates, equilibrium behavior, and so forth). Return to Example \(7-1\) and use the Fenske equation to explore under what conditions the NK benzene can be considered nondistributing.

Example 7-1

A distillation column with a partial reboiler and a total condenser is separating a saturated vapor feed that is 40.0 mol% benzene (B), 30.0 mol% toluene (T), and 30.0 mol% cumene (C). Recovery of toluene in the distillate is 95%, and recovery of cumene in the bottoms is 98%. Reflux is a saturated liquid, and constant molal overflow (CMO) is valid. Pressure is at 1.0 atm. Relative volatilities are constant. Choosing toluene as the reference component, α_B-T = 2.25 and α_C-T = 0.21. Find the number of equilibrium stages required at total reflux, the recovery fraction of benzene in the distillate and in the bottoms, and the mole fractions in the distillate and bottoms.

a. Redo the calculations in Example \(7-1\) by assuming benzene is nondistributing, and determine new flow rates of \(\mathrm{D}\) and \(\mathrm{B}\) and new mole fractions in distillate and bottoms. Are the percentage changes in flow rates of \(\mathrm{B}\) and \(\mathrm{D}\) and percentage change in mole fractions of toluene and cumene small enough that benzene could be considered nondistributing by either the \(0.1 \%\) or the \(0.01 \%\) criteria?

b. Redo the calculations in Example 7-1 with \(\mathrm{FR}_{\text {tol,dist }}=\mathrm{FR}_{\text {cum,bot }}\). Find the value of \(\mathrm{FR}_{\text {tol,dist }}=\mathrm{FR}_{\text {cum,bot }}\) and the corresponding value of \(\mathrm{N}_{\text {min }}\) at which benzene first meets the \(10.0 \mathrm{ppm}\) criterion for nondistributing.

c. Redo the calculations in Example 7-1 with \(\mathrm{FR}_{\text {tol,dist }}=\mathrm{FR}_{\text {cum,bot }}\). Find the value of \(\mathrm{FR}_{\text {tol,dist }}=\mathrm{FR}_{\text {cum,bot }}\) and the corresponding value of \(\mathrm{N}_{\min }\) at which benzene first meets the change of less than \(0.01 \%\) in toluene and cumene distillate and bottoms concentrations criterion for nondistributing.

d. Find the value of \(\mathrm{FR}_{\text {tol,dist }}=\mathrm{FR}_{\text {cum,bot }}\) and the corresponding value of \(\mathrm{N}_{\min }\) at which benzene first meets the change of less than \(0.1 \%\) in toluene and cumene distillate and bottoms concentrations criterion for nondistributing.