"Published in Newark, California, USA"
An evaporator is fed with 15,000 kg/hr of a solution containing 10% NaCl, 15% NaOH, and the rest water. In the operation, water is evaporated and NaCl is precipitated as crystals. The thick liquor leaving the evaporator contains 45% NaOH, 2% NaCl, and the rest water. Calculate:
(a) kg/hr of water evaporated,
(b) kg/hr of salt precipitated, and
(c) kg/hr of thick liquor.
Solution:
The given word problem is about the evaporation of caustic liquid into water vapor, salt precipitate, and thick liquor 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 problem, it is better to draw the flow diagram as follows
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| Photo by Math Principles in Everyday Life |
Basis: 15,000 kg/hr of weak liquor
Let x = be the amount of water evaporated
y = be the amount of thick liquor
z = be the amount of salt precipitated
Overall Material Balance of Evaporator:
Material Balance of NaOH:
Material Balance of NaCl:
Substitute the values of y and z to the first equation which is the Overall Material Balance of Evaporator, we have
Therefore,
Amount of Water Evaporated = 8,600 kg/hr
Amount of Salt Precipitated = 1,400 kg/hr
Amount of Thick Liquor = 5,000 kg/hr