"Published in Suisun City, California, USA"
The waste acid from a nitrating process containing 20% HNO3, 55% H2SO4, and 25% H20 by weight is to be concentrated by addition of concentrated sulfuric acid containing 95% H2SO4 and concentrated nitric acid containing 90% HNO3 to get desired mixed acid containing 26% HNO3 and 60% H2SO4. Calculate the quantities of waste and concentrated acids required for 1000 kg of desired mixed acid.
Solution:
The given word problem is about the mixing of different acids 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. Since all incoming substances are acids, then there's no chemical reactions involved in the mixture. 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: 1000 kg of Desired Mixed Acid
Let x = be the amount of waste acid
y = be the amount of concentrated sulfuric acid
z = be the amount of concentrated nitric acid
Overall Material Balance around the Mixer:
Material Balance of Sulfuric Acid:
Material Balance for Nitric Acid:
Substitute the value of y and z to the first equation, we have
Substitute the value of x to the second equation, we have
Substitute the value of x to the third equation, we have
Therefore,
Amount of Waste Acid = 401.6 kg
Amount of Concentrated Sulfuric Acid = 398.65 kg
Amount of Concentrated Nitric Acid = 199.75 kg