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A gas mixture containing 15% mole A and 85% mole inerts is fed to an absorption tower where it is contacted with liquid solvent B which absorbs A. The mole ratio of solvent to gas entering tower is 2:1. The gas leaving the absorber contains 2.5% mole A, 1.5% mole B, and the rest inerts. Find
(a) the percentage recovery of solute A, and
(b) the fraction of the solvent B fed to a column lost in gas leaving the tower.
Note that during the process, some solvent evaporates and gets added in the gas leaving the tower.
Solution:
The given word problem is about gas absorption of solute A with solvent B which involves the principles of Stoichiometry. 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: 100 kmole of Gas Entering in absorption tower
Let x = be the amount of Gas Leaving from absorption tower
y = be the amount of Solute A - Solvent B leaving from absorption tower
If the mole ratio of solvent to gas entering is 2:1, then it follows that
Overall Material Balance of Absorption Tower:
Material Balance of Inerts:
Material Balance of Solute A:
Therefore, the percentage recovery of Solute A is
The amount of loss for Solvent B during the absorption is
Therefore, the fraction of loss for Solvent B is
