"Published in Newark, California, USA"
The waste acid from a nitrating process contains 30% H2SO4, 35% HNO3, and 35% H2O by weight. The acid is to be concentrated to contain 39% H2SO4 and 42% HNO3 by addition of 10% oleum and concentrated nitric acid containing 72% HNO3 by weight. Calculate the amount of waste acid, oleum, and concentrated nitric acid to be mixed to get 1000 kg of desired mixed acid.
Solution:
The given word problem is about the mixing of acids and oleum 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 Nitric Acid
z = be the amount of Oleum
Overall Material Balance of Mixer:
Material Balance of HNO3:
Oleum is a chemical substance which consist of the mixture of sulfuric acid and sulfur trioxide. If you have 100 kg of 10% oleum, then you have 10 kg of SO3 and 90 kg of H2SO4.
We can express SO3 in terms of H2SO4 by gravimetric analysis as follows
From the chemical equation above, if 1 kmol SO3 = 1 kmol H2SO4, then it follows that their molecular weight will be equal to 80 kg SO3 = 98 kg H2SO4.
The weight of H2SO4 in SO3 can be calculated as follows
The total weight of H2SO4 in oleum is
Hence, the % of H2SO4 in solution is
Oleum is a highly concentrated H2SO4 than the regular concentrated H2SO4 because the % H2SO4 is more than 100%.
Material Balance of H2SO4:
Substitute the values 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 = 159.93 kg
Amount of Concentrated HNO3 = 505.57 kg
Amount of 10% Oleum = 334.50 kg