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 H₂SO₄

Initially, we are given the heat produced during the third process of synthesizing H₂SO₄, which is 130 kJ/mol. We can use this information to determine the total heat produced in preparing a mole of H₂SO₄. For one mole of H₂SO₄: Heat produced (Q) = 130 kJ/mol

02

Convert the weight of H₂SO₄ to moles

Now that we know the heat produced per mole of H₂SO₄, we can find the heat produced in preparing 5000 pounds of H₂SO₄. First, we need to convert the weight of H₂SO₄ from pounds to moles. To do this: - Convert from pounds to grams. - Find the molecular weight of H₂SO₄ and then convert from grams to moles. Molecular weight of H₂SO₄ = 2H (1.008 g/mol) + 1S (32.07 g/mol) + 4O (16.00 g/mol) = 98.086 g/mol 5000 pounds of H₂SO₄ = 5000 * 454 grams (1 pound = 454 grams) = 2,270,000 grams Next, convert the weight to moles using the molecular weight: Moles of H₂SO₄ = \(\frac{2,270,000\,\text{grams}}{98.086\,\text{g/mol}}\) = 23,142.62 moles

03

Calculate heat produced for 5000 pounds of H₂SO₄

Now that we know the number of moles of H₂SO₄ (23,142.62 mol), we can calculate the heat produced in kJ during the synthesis of 5000 pounds of H₂SO₄ 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 H₂SO₄ from 1 mole of S is 130 kJ, and the heat produced in preparing 5000 pounds of H₂SO₄ is 3,008,541 kJ.

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