<strong>Problem:</strong> A liquid mixture containing 40% (by weight) acetone and 60% (by weight) water is fed to a distillation column at a rate of 1000 kg/h. The distillate contains 95% acetone and the bottoms contain 5% acetone. Calculate the flow rates of distillate and bottoms.<br><strong>Given Data:</strong><br>Feed (F) = 1000 kg/h<br>xF (acetone in feed) = 0.4<br>xD (acetone in distillate) = 0.95<br>xB (acetone in bottoms) = 0.05<strong>Solution:</strong><br><strong>Step 1: Overall Material Balance</strong><br>F = D + B<br>1000 = D + B … (i)<br><strong>Step 2: Component Balance (Acetone)</strong><br>FxF = DxD + BxB<br>1000(0.4) = D(0.95) + B(0.05)<br>400 = 0.95D + 0.05B … (ii)<br><strong>Step 3: Solve Equations</strong><br>From (i), B = 1000 – D<br>Substitute in (ii):<br>400 = 0.95D + 0.05(1000 – D)<br>400 = 0.95D + 50 – 0.05D<br>350 = 0.9D<br>D = 388.89 kg/h<br><strong>Step 4: Calculate B</strong><br>B = 1000 – D = 1000 – 388.89 = 611.11 kg/h<br><strong>Results:</strong><br>Distillate (D) = 388.89 kg/h<br>Bottoms (B) = 611.11 kg/h<strong>Dive deeper:</strong><br><br><br><br><br>