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 \(\mathrm{H}_{2} \mathrm{SO}_{4}\) ?

Short answer

The heat produced in preparing one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from one mole of \(\mathrm{S}\) is \(130 \mathrm{~kJ/mol}\), and the heat produced in preparing one ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is \(\approx 1.33 \times 10^6 \mathrm{~kJ}\).

Step-by-step solution

Calculate the heat produced for one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

The problem states that the third process produces \(130 \mathrm{~kJ/mol}\). We will consider this as the heat produced in preparing one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from one mole of \(\mathrm{S}\). So, the heat produced for one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is: \(130 \mathrm{~kJ/mol}\)

Calculate the amount of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in one ton

To calculate the heat produced when preparing a ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\), we must first convert the mass to moles. 1 ton = 1000 kg The molar mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is: \(2 \times 1.01 \mathrm{~g/mol} (\mathrm{H}) + 32.07 \mathrm{~g/mol} (\mathrm{S}) + 4 \times 16.00 \mathrm{~g/mol} (\mathrm{O})\) = 98.08 g/mol To find the number of moles in one ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\): \(\frac{1000 \times 10^3 \mathrm{~g}}{98.08 \mathrm{~g/mol}}\)

Calculate the heat produced for one ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

Now that we have the number of moles in a ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\), we can calculate the total heat produced. Heat produced for one ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) = (number of moles in one ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)) x (heat produced per mole) \( \Rightarrow \frac{1000 \times 10^3 \mathrm{~g}}{98.08 \mathrm{~g/mol}} \times 130 \mathrm{~kJ/mol} \) Now, we can calculate the result.

Final Answer

The heat produced in preparing one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from one mole of \(\mathrm{S}\) is: \(130 \mathrm{~kJ/mol}\) The heat produced in preparing one ton of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is: \( \frac{1000 \times 10^3 \mathrm{~g}}{98.08 \mathrm{~g/mol}} \times 130 \mathrm{~kJ/mol} \) \( \approx 1.33 \times 10^6 \mathrm{~kJ}\)

Key concepts

Oxidation Reactions

The synthesis of sulfuric acid involves key oxidation reactions. In the first step, sulfur (\( \mathrm{S} \)) is oxidized to sulfur dioxide (\( \mathrm{SO}_2 \)). This reaction is crucial because it's the starting point for creating sulfuric acid. Oxidation is the loss of electrons, and in this reaction, sulfur gains oxygen from the air to form sulfur dioxide.

Following this, the second main reaction in sulfuric acid synthesis is the further oxidation of sulfur dioxide (\( \mathrm{SO}_2 \)) to sulfur trioxide (\( \mathrm{SO}_3 \)). This step is pivotal as sulfur trioxide later reacts with water and sulfuric acid to produce more sulfuric acid, completing the cycle.

• Oxidation reactions are characterized by the transfer of oxygen or loss of electrons.
• They are energy-releasing, making them exothermic, which correlates to heat production.
• In sulfuric acid production, these steps are tightly controlled to ensure efficiency and safety.

Understanding these oxidation reactions helps in controlling the efficiency and output of sulfuric acid production plants. They serve as a backbone for one of the most widely produced chemicals globally.

Thermochemical Calculations

Thermochemical calculations are essential in determining energy changes during chemical reactions. In the context of sulfuric acid synthesis, they allow us to compute how much heat is released when specific reactions occur.

In this exercise, the thermochemical calculation involves determining the heat produced when preparing sulfuric acid. It states that \( 130 \ \mathrm{kJ/mol} \) of energy is released during the third step of the process. This calculation assumes that every mole of reactant produces this specific amount of energy.

To perform thermochemical calculations, you need:

• Known quantities, such as molar mass and the energy change per mole of reaction (\( \mathrm{kJ/mol} \)).
• Conversion methods to calculate energy changes for larger quantities, such as from grams to kilograms.
• An understanding of the stoichiometry involved, or how different amounts of reactants are consumed and products are formed.

These calculations are not just academic; they have practical applications such as in designing energy-efficient industrial processes by identifying which reactions release or absorb significant amounts of heat.

Heat Production in Chemical Processes

Heat production is a critical aspect of chemical processes, especially in industrial applications like sulfuric acid synthesis. In chemical reactions, the difference in energy between reactants and products determines whether heat is absorbed or released.

During the oxidation of sulfur to sulfur dioxide and sulfur dioxide to sulfur trioxide, heat is released as the reactions are exothermic. This released heat is not wasted; in sulfuric acid plants, it is often used to generate electricity or to power other processes, improving cost efficiency.

• Exothermic reactions release heat, raising the temperature of their surroundings.
• Capturing and utilizing this heat can reduce energy costs, a significant factor in industrial operations.
• Heat management ensures safety, as uncontrolled heat can lead to hazardous situations.

In essence, understanding heat production and management in chemical processes enables the design of safer, more efficient, and environmentally friendly industrial systems. This knowledge is foundational to chemical engineering and industrial chemistry.