One thousand kilograms per hour of a mixture containing equal parts by mass of ethanol and water is distilled. Product streams leave the top and the bottom of the distillation column. The flowrate of the bottom stream is measured and found to be 673 kg/h, and the overhead stream is analyzed and found to contain 96 wt% ethanol. Find the flowrates of all components in all streams.

We can find the flowrates of water and ethanol in the overhead stream from the information given in the problem statement. Generally,

Foverhead,water = Foverhead,total * xoverhead,water = 327*0.04 = 13.08

Foverhead,ethanol = Foverhead,total * xoverhead,ethanol = 327*0.96 = 313.92

Let's fill that information into the table:

Streams\mass flow rate Total Ethanol Water
Feed 1000 500 500
Overhead 327 313.92 13.08
Bottoms 673 Fbottoms,ethanol Fbottoms,water

Now we're down to the point where we can write two mass balances to solve the rest of the problem. Which mass balances do you think are the ones we can use from the list below to fill in the rest of the table?

Ffeed,total = Foverhead,total + Fbottoms,total
Ffeed,ethanol = Foverhead,ethanol + Fbottoms,ethanol
Ffeed,water = Foverhead,water + Fbottoms,water
Ffeed,total = Foverhead,water + Fbottoms,ethanol
Ffeed,total = Ffeed,water + Ffeed,ethanol

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