"Published in Newark, California, USA"
A mixture of phenol and water forms two separate liquid phases, one rich in phenol and other rich in water, composition of layers is 70% and 9% (by weight) phenol respectively. If 500 kg of phenol and 700 kg of water are mixed and layers allowed to separate, what will be the weights of two layers?
Solution:
The given word problem is about liquid-liquid extraction of phenol-water mixture which involves the principles of Stoichiometry. Liquid–liquid extraction also known as solvent extraction and partitioning, is a method to separate compounds based on their relative solubility in two different immiscible liquids, usually water and an organic solvent. It is an extraction of a substance from one liquid into another liquid phase. Liquid–liquid extraction is a basic technique in chemical laboratories, where it is performed using a separatory funnel.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: 500 kg of Phenol and 700 kg of Water
Let x = be the amount of Phenol Rich Layer
y = be the amount of Water Rich Layer
Overall Material Balance of Liquid-liquid Extractor:
Material Balance of Phenol:
Substitute the value of y to the first equation, we have
Substitute the value of x to the first equation, we have
Therefore,
Amount of Phenol Rich Layer = 642.419 kg
Amount of Water Rich Layer = 557.581 kg