Stoichiometry Problem - Material Balance, 9

Category: Chemical Engineering Math, Algebra

"Published in Newark, California, USA"

10,000 kg/hr of solution containing 20% methanol is continuously fed to a distillation column. Distillate (product) is found to contain 98% methanol and waste solution from the column carries 1% methanol. All percentages are by weight. Calculate

(a) the mass flow rates of distillate and bottom product, and
(b) the percent loss of methanol.

Solution:

The given word problem is about the distillation of methanol solution which involves the principles of Stoichiometry. Distillation is a method of separating mixtures based on differences in volatility of components in a boiling liquid mixture. Distillation is a unit operation, or a physical separation process, and not a chemical reaction.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: 10,000 kg/hr of Feed

Let x = be the mass flow rate of Distillate
      y = be the mass flow rate of Waste Solution

Overall Material Balance of Distillation Column:

Material Balance of Methanol:

Substitute the value of y to the first equation, we have

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

Therefore,

Mass Flow Rate of Distillate =  1,958.763 kg/hr
Mass Flow Rate of Waste Solution = 8,041.237 kg/hr

Next, we can calculate the percent loss for methanol as follows

Stoichiometry Problem - Material Balance, 8

Category: Chemical Engineering Math, Algebra

"Published in Newark, California, USA"

It is desired to have a mixed acid containing 10% HNO₃, 43% H₂SO₄, and 17% H₂O by weight. Sulfuric acid of 98% by weight is readily available. Calculate

(a) the strength of nitric acid, and
(b) the weight ratio of sulfuric acid to nitric acid.

Solution:

The given word problem is about the mixing of nitric acid and sulfuric acid which involves the principles of Stoichiometry. The strength or concentration of nitric acid is unknown and we need to solve it as well as the weight ratio of nitric acid and sulfuric acid. 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 weight of concentrated sulfuric acid, concentrated nitric acid, and mixed acid 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 Acid

Let x = be the amount of concentrated sulfuric acid
      y = be the amount of concentrated nitric acid

Overall Material Balance of Mixer:

Material Balance of H₂SO₄:

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

The value of y which is the amount of the concentrated nitric acid is not a pure nitric acid. We need first to get the amount of pure nitric acid in order to get the strength or concentration of concentrated nitric acid.

Material Balance of HNO₃:

Therefore, the strength or concentration of concentrated nitric acid is
 

The weight ratio of conc. H₂SO₄ to conc. HNO₃ is

Stoichiometry Problem - Material Balance, 7

Category: Chemical Engineering Math, Algebra

"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

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