A distillation column will separate \(100.0 \mathrm{kmol} / \mathrm{h}\) of a saturated liquid feed at \(200 \mathrm{kPa}\) that is \(20.0 \mathrm{~mol} \%\) propane (Pro), \(35.0 \mathrm{~mol} \%\) n-pentane (Pen), and \(45.0 \mathrm{~mol} \% \mathrm{n}\)-hexane (Hex). The column has a total condenser and a partial reboiler. We want a fractional recovery of Hex in the bottoms \(=0.983\) and a fractional recovery of Pen in the distillate of 0.967 .

a. Make an appropriate assumption, and determine the flow rates of bottoms, B, and of distillate, \(\mathrm{D}\), in \(\mathrm{kmol} / \mathrm{h}\); and determine the mole fractions of bottoms and of distillate.

b. Determine the bubble-point temperature of the feed, and calculate relative volatilities at this temperature. Use Pen as your reference component. Report the bubble-point temperature, the \(\mathrm{K}\) values, and the values of relative volatilities. Use a DePriester chart or Eq. \((2-28)\). Show your work.

Equation (2-28)

c. Assume the relative volatilities found in part b are constant, and determine the minimum number of stages, \(\mathrm{N}_{\text {min }}\), required for this separation.

d. Do a calculation that justifies why the assumption made in part a is reasonable.

Transcribed Image Text:

In K = a/T+a/T + a + apl In p+ a2/p + a3/p