Stoichiometry Problem - Material Balance, 15

Category: Chemical Engineering Math, Algebra

"Published in Suisun City, California, USA"

A waste acid from a nitrating process contains 23% HNO₃, 57% H₂SO₄, and 20% water by weight. This acid is to be concentrated to contain 27% HNO₃, 60% H₂SO₄ by the addition of concentrated H₂SO₄ containing 93% H₂SO₄ and concentrated HNO₃ containing 90% HNO₃. Calculate the amounts in kg of waste and concentrated acids that must be combined to obtain 1,000 kg of desired mixture.

Solution:

The given word problem is about the mixing of waste and concentrated 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

Photo by Math Principles in Everyday Life

Basis: 1,000 kg of Desired Mixture

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 of Mixer:

Material Balance of H₂SO₄:

Material Balance of HNO₃:

 

    

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 = 418.618 kg
Amount of Conc. Sulfuric Acid = 388.548 kg
Amount of Conc. Nitric Acid = 192.834 kg  

Stoichiometry Problem - Material Balance, 14

Category: Chemical Engineering Math, Algebra

"Published in Suisun City, California, USA"

In order to carry out nitration reaction, it is desired to have a mixed acid containing 39% HNO₃, 42% H₂SO₄, and 19% H₂O by weight. Nitric acid of 68.3% by weight is readily available. Calculate the

(a) required strength of sulfuric acid in order to obtain the above mixed acid and
(b) the weight ratio of nitric acid to sulfuric acid to be mixed.

Solution:

The given word problem is about the mixing of different acids which involves the principles of Stoichiometry. The concentration or strength of concentrated sulfuric acid is unknown and we need to solve it. 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

Photo by Math Principles in Everyday Life

Since the amount of concentrated nitric acid, concentrated sulfuric acid, and mixed acids are not given in the problem, let's assign a basis of 100 kg of mixed acid in the problem.

Basis: 100 kg of Mixed Acids

Let x = be the amount of Concentrated Nitric Acid
      y = be the amount of Concentrated Sulfuric Acid

Overall Material Balance of Mixer:

Material Balance of Nitric Acid:

 

Substitute the value of x to the above equation, we have

Material Balance of Sulfuric Acid:

 

 

Therefore, the concentration or strength of Concentrated H₂SO₄ is

The weight ratio of Concentrated HNO₃ to Concentrated H₂SO₄ is

Stoichiometry Problem - Material Balance, 13

Category: Chemical Engineering Math, Algebra

"Published in Suisun City, California, USA"

A gas mixture containing 15% mole A and 85% mole inerts is fed to an absorption tower where it is contacted with liquid solvent B which absorbs A. The mole ratio of solvent to gas entering tower is 2:1. The gas leaving the absorber contains 2.5% mole A, 1.5% mole B, and the rest inerts. Find

(a) the percentage recovery of solute A, and
(b) the fraction of the solvent B fed to a column lost in gas leaving the tower.

Note that during the process, some solvent evaporates and gets added in the gas leaving the tower.

Solution:

The given word problem is about gas absorption of solute A with solvent B 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

Photo by Math Principles in Everyday Life

Basis: 100 kmole of Gas Entering in absorption tower

Let x = be the amount of Gas Leaving from absorption tower
      y = be the amount of Solute A - Solvent B leaving from absorption tower

If the mole ratio of solvent to gas entering is 2:1, then it follows that

Overall Material Balance of Absorption Tower:

Material Balance of Inerts:

Material Balance of Solute A:

Therefore, the percentage recovery of Solute A is

The amount of loss for Solvent B during the absorption is 

Therefore, the fraction of loss for Solvent B is