Problem 89 - Chemistry: The Central Science

Question

A sulfuric acid plant produces a considerable amount of heat. This heat is used to generate electricity, which helps reduce operating costs. The synthesis of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) consists of three main chemical processes: (1) oxidation of \(\mathrm{S}\) to \(\mathrm{SO}_{2},(2)\) oxidation of \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3},(3)\) the dissolving of \(\mathrm{SO}_{3}\) in \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and its reaction with water to form \(\mathrm{H}_{2} \mathrm{SO}_{4}\). If the third process produces \(130 \mathrm{~kJ} / \mathrm{mol}\), how much heat is produced in preparing a mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from a mole of \(\mathrm{S}\) ? How much heat is produced in preparing a ton of \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\)

Step-by-Step Solution

Answer

The heat produced in preparing a mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from a mole of \(\mathrm{S}\) is 130 kJ/mol, and the heat produced in preparing a ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is approximately 1,326,520 kJ.

Step 1: Calculate the heat produced per mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

The question states that the production of a mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from a mole of \(\mathrm{S}\) (sulfur) has a heat production of 130 kJ/mol. Therefore, the heat produced in preparing a mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is simply: Heat produced per mole = 130 kJ/mol

Step 2: Calculate the heat produced per ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

Now, we need to find out how much heat is produced in preparing a ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). First, we need to determine the number of moles in a ton and then use the heat produced per mole value obtained in step 1. The molecular weight of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is 98 g/mol. Since 1 ton = 1,000,000 g, we will convert 1 ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) to moles: Number of moles = (mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)/molecular weight of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)) Number of moles = (1,000,000 g / 98 g/mol) Number of moles ≈ 10,204 moles Now, we can use the heat produced per mole (130 kJ/mol) to calculate the heat produced per ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\): Heat produced = (Number of moles) x (Heat produced per mole) Heat produced ≈ (10,204 moles) x (130 kJ/mol) Heat produced ≈ 1,326,520 kJ

Step 3: Present the final answer

The heat produced in preparing a mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from a mole of \(\mathrm{S}\) is 130 kJ/mol, and the heat produced in preparing a ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is approximately 1,326,520 kJ.

Key Concepts

Heat Generation

In the production of sulfuric acid, heat is a byproduct of the chemical reactions involved. Particularly, the third process, involving the dissolving of sulfur trioxide (\( \text{SO}_3 \)) in sulfuric acid (\( \text{H}_2\text{SO}_4 \)) and its subsequent reaction with water, generates significant heat. This exothermic reaction produces approximately 130 kJ of heat per mole of sulfuric acid produced. Heat generation is a crucial component of sulfuric acid plants, not only because it helps in reducing operational costs by generating electricity, but also because controlling the heat is vital to ensure the reactions proceed safely and efficiently. By recovering the heat produced, plants can utilize it to power other processes, making sulfuric acid production more energy-efficient and economically viable.

Chemical Processes

The production of sulfuric acid includes a series of chemical processes, each playing a vital role in the overall reaction sequence.

• The first step is the oxidation of sulfur (\( \text{S} \)) to sulfur dioxide (\( \text{SO}_2 \)), which involves burning sulfur in the presence of oxygen.
• The second step further oxidizes sulfur dioxide to sulfur trioxide (\( \text{SO}_3 \)) using a vanadium(V) oxide catalyst.
• The final step incorporates dissolving sulfur trioxide in existing sulfuric acid, then reacting it with water to form even more sulfuric acid.

These processes are central to understanding how sulfuric acid is manufactured commercially. They serve as an excellent example of industrial chemical processes involving series reactions.

Energy Calculation

Calculating the energy or heat produced or consumed during reactions is an important task in chemical engineering. To find out how much heat is produced in making a ton of \( \text{H}_2\text{SO}_4 \), you must first determine how much is produced per mole. As earlier calculated, each mole of sulfuric acid releases 130 kJ of heat.
To find the total energy released for a ton of \( \text{H}_2\text{SO}_4 \), convert tons to grams, and then to moles: 1 ton equals 1,000,000 grams, and with the molar mass of sulfuric acid being 98 g/mol, we find\( \frac{1,000,000 \text{ g}}{98 \text{ g/mol}} \approx 10,204 \text{ moles} \).
Now, multiply the number of moles by the heat released per mole:\( 10,204 \text{ moles} \times 130 \text{ kJ/mol} = 1,326,520 \text{ kJ} \)
Understanding these calculations allows chemists and engineers to manage and exploit the thermal energy effectively.

Moles and Molar Mass

In chemistry, understanding moles and molar mass is fundamental to converting between mass and number of particles. A mole represents a specific number of particles, typically atoms or molecules, akin to a dozen but for microscopic entities.
The molar mass, expressed in grams per mole, indicates the mass of one mole of a substance and is numerically equal to its average atomic or molecular mass. For sulfuric acid (\( \text{H}_2\text{SO}_4 \)), the molar mass is calculated by summing the atomic masses of its constituent elements:

• Hydrogen (H), atomic mass ~1 g/mol, contributes ~2 g/mol for 2 atoms.
• Sulfur (S), with 32 g/mol, contributes 32 g/mol.
• Oxygen (O), with 16 g/mol, contributes ~64 g/mol for 4 atoms.

Together, these total 98 g/mol, the molar mass of \( \text{H}_2\text{SO}_4 \). Appreciating this concept is crucial for accurate chemical calculations.