Problem 80 - Chemistry: An Atoms-Focused Approach

Question

One reaction in the production of sulfuric acid involves the conversion of sulfur dioxide to sulfur trioxide. In the presence of excess \(\mathrm{O}_{2}, 88 \mathrm{kg} \mathrm{SO}_{2}\) produces \(106 \mathrm{kg} \mathrm{SO}_{3}\) What is the percent yield?

Step-by-Step Solution

Answer

Answer: The percent yield of the reaction is 96.36%.

Step 1: Write the balanced chemical equation

The balanced chemical equation for the conversion of sulfur dioxide to sulfur trioxide in the presence of excess oxygen is: 2 SO₂ (g) + O₂ (g) → 2 SO₃ (g)

Step 2: Calculate the moles of SO₂ reacted

Use the molar mass of SO₂ to convert the mass of SO₂ to moles. The molar mass of S = 32.07 g/mol and O = 16.00 g/mol. Therefore, the molar mass of SO₂ = 1(32.07) + 2(16.00) = 64.07 g/mol. The mass of SO₂ given = 88,000 g (converted from 88 kg) Number of moles of SO₂ = mass of SO₂ / molar mass of SO₂ = 88000/64.07 = 1373.67 moles

Step 3: Calculate the theoretical yield of SO₃ based on stoichiometry

From the balanced chemical equation, the stoichiometric ratio of SO₂ to SO₃ is 1:1. Therefore, the moles of SO₃ that should be produced theoretically are the same as the moles of SO₂ reacted. Number of moles of SO₃ = 1373.67 moles (theoretical yield) To find the mass of this theoretical yield, use the molar mass of SO₃: The molar mass of SO₃ = 1(32.07) + 3(16.00) = 80.07 g/mol. Theoretical mass of SO₃ = moles of SO₃ * molar mass of SO₃ = 1373.67 * 80.07 = 110,000 g (110 kg)

Step 4: Calculate the percent yield

Percent yield = (actual yield / theoretical yield) * 100 Actual yield = 106,000 g (106 kg) Percent yield = (106000/110000) * 100 = 96.36% The percent yield of the reaction is 96.36%.

Key Concepts

Balanced Chemical Equation

In chemical reactions, a balanced equation is essential as it represents the precise nature of the transformation. Each element must maintain the same number of atoms on both sides of the equation. This equality ensures the reaction abides by the law of conservation of mass. Let's take a look at the reaction involved in sulfuric acid production:

• Initial substances: Sulfur dioxide (SO₂) and oxygen (O₂) are reactants.
• Result: Sulfur trioxide (SO₃) is produced.

Thus, the balanced equation is: 2 SO₂ (g) + O₂ (g) → 2 SO₃ (g). Here, two molecules of sulfur dioxide react with one molecule of oxygen to form two molecules of sulfur trioxide. By balancing the equation, we can then accurately calculate reactant and product quantities. This is the foundation for further calculations in stoichiometry.

Stoichiometry

Stoichiometry involves calculating the relationships between reactants and products in chemical reactions. For this Sulfur Dioxide to Sulfur Trioxide conversion, the stoichiometry plays a crucial role:

• The balanced equation 2 SO₂ + O₂ → 2 SO₃ provides a 1:1 molar relationship between SO₂ and SO₃.
• This means one mole of SO₂ will yield one mole of SO₃, under ideal conditions.
• Accurate stoichiometry allows us to predict the amount of product formed from a given amount of a reactant, assuming complete efficiency.

Understanding stoichiometry is key to calculating theoretical yields, which are needed to determine actual reaction efficiency, known as percent yield. With stoichiometry, students can master the quantitative aspects of chemical reactions, crucial for both laboratory and industrial applications.

Molar Mass Calculation

To perform stoichiometric calculations, it's essential to determine the molar masses of reactants and products. Molar mass is the mass of one mole of a substance, expressed in grams per mole.

• Sulfur dioxide (SO₂) has a molar mass calculated by summing the atomic masses: S (32.07 g/mol) + Oₓ₂ (2 × 16.00 g/mol) = 64.07 g/mol.
• Sulfur trioxide (SO₃) is similarly calculated: S (32.07 g/mol) + Oₓ₃ (3 × 16.00 g/mol) = 80.07 g/mol.

Knowing these values is critical:

• Allows conversion between mass and moles, providing a consistent and comparable measure of quantity.
• Facilitates the calculation of reactants needed or products formed.
• Essential for calculating percent yield, as it links theoretical and actual yields.

Grasping molar mass calculations is fundamental to conducting any quantitative chemical analysis.

Sulfuric Acid Production

Sulfuric acid is a vital industrial chemical, produced through several steps, with the reaction between sulfur dioxide and oxygen being a key stage. Here's why this step is crucial:

• The conversion of SO₂ to SO₃ is a critical part of the Contact Process, a primary method for producing sulfuric acid.
• The balanced reaction: 2 SO₂ + O₂ → 2 SO₃ demonstrates the progression toward the acid.
• Sulfur trioxide (SO₃) can be further reacted with water to form sulfuric acid (H₂SO₄).

The process's efficiency is often measured by the percent yield. High yields are essential for economic viability and environmental sustainability. Sulfuric acid is utilized in:

• Fertilizer manufacturing
• Petroleum refining
• Wastewater processing

Hence, this reaction is not just academically interesting but also of great industrial significance.