A liquid mixture contains 60.0 wt% ethanol (E), 5.0 wt% of a dissolved solute (S), and the balance water. A stream of this mixture is fed to a continuous distillation column operating at steady state.

a) The basis of calculation is 100 kg of the liquid mixture fed to the distillation column. The process flowchart is as follows: Liquid Mixture (100 kg) ? Distillation Column ? Top Product Stream: 50 kg, 90% Ethanol, 0% Solute Bottom Product Stream: 50 kg, X% Ethanol, Y% Solute The degree-of-freedom analysis is: Unknowns = 2 (mass fraction of ethanol in bottom product stream, mass fraction of solute in bottom product stream) Equations = 3 (mass balance for liquid mixture, mass balance for ethanol in top product stream, mass balance for solute) Since the number of unknowns is equal to or less than the number of equations, all unknown stream flows and compositions can be calculated. b) (i) The mass fraction of the solute (S) in the bottom stream can be calculated using mass balances: Mass of solute in feed = 5 kg Mass of ethanol in feed = 60 kg Mass of solute in top product stream = 0 kg Mass of ethanol in top product stream = 45 kg Therefore, mass of solute in bottom product stream = mass of solute in feed - mass of solute in top product stream = 5 kg - 0 kg = 5 kg Mass of bottom product stream = 50 kg Mass fraction of solute in bottom product stream = mass of solute in bottom product stream / mass of bottom product stream = 5 kg / 50 kg = 0.1 or 10% (ii) The fraction of ethanol in the feed that leaves in the bottom product stream can be calculated using mass balances: Mass of ethanol in bottom product stream = X * 50 kg Mass of ethanol in feed = 60 kg Mass of ethanol in top product stream = 0.9 * 45 kg = 40.5 kg Mass balance for ethanol: Mass of ethanol in feed = Mass of ethanol in top product stream + Mass of ethanol in bottom product stream 60 kg = 40.5 kg + X * 50 kg X = (60 kg - 40.5 kg) / 50 kg X = 0.39 or 39% Therefore, 39% of the ethanol in the feed leaves in the bottom product stream.