We are separating a mixture of propylene, propane, and isobutane in a distillation column with a partial condenser and a partial reboiler at a pressure of 15.0 bar. We desire a 0.999 fractional recovery of propylene in the distillate, at least a 0.950 fractional recovery of propane in the bottoms, and at least a 0.9999 fractional recovery of isobutane in the bottoms. How many stages are required at total reflux? Data: At \(34^{\circ} \mathrm{C}, \mathrm{K}\) Propylene \(=1.00, \mathrm{~K}\) propane \(=0.89, \mathrm{~K}\) isobutane \(=\) 0.42 .

At \(40^{\circ} \mathrm{C}, \mathrm{K}\) propylene \(=1.13, \mathrm{~K}\) propane \(=1.000\), and \(\mathrm{K}\) isobutane \(=\) 0.46 .