"Published in Newark, California, USA"
10,000 kg/hr of solution containing 20% methanol is continuously fed to a distillation column. Distillate (product) is found to contain 98% methanol and waste solution from the column carries 1% methanol. All percentages are by weight. Calculate
(a) the mass flow rates of distillate and bottom product, and
(b) the percent loss of methanol.
Solution:
The given word problem is about the distillation of methanol solution which involves the principles of Stoichiometry. Distillation is a method of separating mixtures based on differences in volatility of components in a boiling liquid mixture. Distillation is a unit operation, or a physical separation process, and not a chemical reaction.The total amount of a substance in the reactants or incoming ingredients must be equal to the total amount of a substance in the final products. In short, the Law of Conservation of Mass must be followed all the time. To illustrate the given problem, it is better to draw the flow diagram as follows
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| Photo by Math Principles in Everyday Life |
Basis: 10,000 kg/hr of Feed
Let x = be the mass flow rate of Distillate
y = be the mass flow rate of Waste Solution
Overall Material Balance of Distillation Column:
Material Balance of Methanol:
Substitute the value of y to the first equation, we have
Substitute the value of x to the first equation, we have
Therefore,
Mass Flow Rate of Distillate = 1,958.763 kg/hr
Mass Flow Rate of Waste Solution = 8,041.237 kg/hr
Next, we can calculate the percent loss for methanol as follows
