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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 5000 pounds of \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\)

Step by step solution

01

Calculate heat produced for 1 mole of Hâ‚‚SOâ‚„

Initially, we are given the heat produced during the third process of synthesizing Hâ‚‚SOâ‚„, which is 130 kJ/mol. We can use this information to determine the total heat produced in preparing a mole of Hâ‚‚SOâ‚„. For one mole of Hâ‚‚SOâ‚„: Heat produced (Q) = 130 kJ/mol

02

Convert the weight of Hâ‚‚SOâ‚„ to moles

Now that we know the heat produced per mole of Hâ‚‚SOâ‚„, we can find the heat produced in preparing 5000 pounds of Hâ‚‚SOâ‚„. First, we need to convert the weight of Hâ‚‚SOâ‚„ from pounds to moles. To do this: - Convert from pounds to grams. - Find the molecular weight of Hâ‚‚SOâ‚„ and then convert from grams to moles. Molecular weight of Hâ‚‚SOâ‚„ = 2H (1.008 g/mol) + 1S (32.07 g/mol) + 4O (16.00 g/mol) = 98.086 g/mol 5000 pounds of Hâ‚‚SOâ‚„ = 5000 * 454 grams (1 pound = 454 grams) = 2,270,000 grams Next, convert the weight to moles using the molecular weight: Moles of Hâ‚‚SOâ‚„ = \(\frac{2,270,000\,\text{grams}}{98.086\,\text{g/mol}}\) = 23,142.62 moles

03

Calculate heat produced for 5000 pounds of Hâ‚‚SOâ‚„

Now that we know the number of moles of Hâ‚‚SOâ‚„ (23,142.62 mol), we can calculate the heat produced in kJ during the synthesis of 5000 pounds of Hâ‚‚SOâ‚„ using the heat produced per mole (Q) from step 1. Heat produced for 23,142.62 moles = 23,142.62 mol * 130 kJ/mol = 3,008,541 kJ

04

Final answer

So, the heat produced in preparing 1 mole of Hâ‚‚SOâ‚„ from 1 mole of S is 130 kJ, and the heat produced in preparing 5000 pounds of Hâ‚‚SOâ‚„ is 3,008,541 kJ.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermochemistry

Thermochemistry is the study of energy changes during chemical reactions. It helps us understand how heat is absorbed or released in processes like the production of sulfuric acid (\(\text{H}_2\text{SO}_4\)).
In any reaction, bonds are broken and new ones are formed, which involves changes in energy. In the context of sulfuric acid production:

• The oxidation of sulfur to sulfur dioxide (\(\text{SO}_2\)) and further to sulfur trioxide (\(\text{SO}_3\)) involves energy changes.
• When sulfur trioxide dissolves in sulfuric acid and reacts with water, it releases heat.

By understanding these energy changes, industries can efficiently harness the thermal energy produced during the creation of sulfuric acid to generate electricity, reducing operational costs. This is a pivotal aspect of industrial chemical processes.

Chemical Processes

Chemical processes play a vital role in the synthesis of compounds like sulfuric acid. The creation of \(\text{H}_2\text{SO}_4\) involves a series of structured reactions:

• Oxidation of sulfur (\(\text{S}\)) to sulfur dioxide (\(\text{SO}_2\)).
• Oxidation of sulfur dioxide to sulfur trioxide (\(\text{SO}_3\)).
• Dissolving of sulfur trioxide in existing sulfuric acid and then reacting it with water to yield more \(\text{H}_2\text{SO}_4\).

Each step involves careful control of conditions to maximize production efficiency. This chain of chemical transformations ensures a comprehensive approach to achieving the desired product with minimal energy wastage. Understanding these processes helps optimize and control industrial methods used worldwide.

Molar Heat Calculation

Molar heat calculation is an essential concept in thermochemistry, allowing us to determine the energy change per mole of substance produced or consumed. In the context of sulfuric acid production:

• We know the third step in the \(\text{H}_2\text{SO}_4\) synthesis produces 130 kJ per mole.
• To find the total heat for large-scale production, such as 5000 pounds of sulfuric acid, we convert pounds to moles using molar mass.
• This involves converting pounds to grams, and dividing by the molar mass of sulfuric acid, which is approximately 98.086 g/mol.
• The final step is multiplying the number of moles by the energy per mole to find the total heat produced.

This method helps industries compute energy requirements accurately for large-volume productions, enabling more effective energy management and cost savings.