"Published in Newark, California, USA"
A spent lye sample obtained from a soap manufacturing unit is found to contain 9.6% glycerol and 10.3% salt (NaCl). It is concentrated at a rate of 4000 kg/hr in a double effect evaporator system until the final solution contains 80% glycerol and 6% salt. Assume that 5% glycerol is lost by entrainment. All percentages are by weight. Calculate the evaporation taking place in the system and the amount of salt that is crystallized in the salt box of the evaporator.
Solution:
The given word problem is about the evaporation of spent lye sample in a double effect evaporator 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: 4000 kg/hr of Spent Lye Sample
Let x = be the amount of Final Solution
y = be the amount of Crystallized Salt
z = be the amount of Evaporated Water
Overall Material Balance of Double Effect Evaporator:
Since the problem says that "5% glycerol is lost by entrainment", then the amount of glycerol at the Final Solution will be equal to
When glycerol becomes more concentrated, then it becomes more viscous. If it is more viscous, then it is hard to collect completely the concentrated glycerol from the container, mixer, or tank.
Material Balance of Glycerol:
Material Balance of Salt:
Substitute the values of x and y to the first equation, we have
Therefore,
Amount of Crystallized Salt = 384.5714 kg/hr
Amount of Evaporation = 3158.2857 kg/hr