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: (a) oxidation of \(S\) to \(\mathrm{SO}_{2}\), (b) oxidation of \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3},\) (c) the dissolving of \(\mathrm{SO}_{3}\) in \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and the subsequent 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 \(S\) ? How much heat is produced in preparing \(2000 \mathrm{~kg}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\)

Short answer

The heat produced in preparing a mole of H2SO4 from a mole of S is \(130 kJ/mol\), and the heat produced in preparing 2000 kg of H2SO4 is approximately \(2,652,631.8 kJ\).

Step-by-step solution

Understand the Synthesis Process

The synthesis of H2SO4 from sulfur involves three chemical processes: a) Oxidation of S to SO2 b) Oxidation of SO2 to SO3 c) Dissolving of SO3 in H2SO4 and subsequent reaction with water to form H2SO4 (produces \(130 kJ/mol\))

Calculate Heat Produced Per Mole of H2SO4

The heat produced during the third process will be the heat produced per mole of H2SO4 synthesized. Given that 130 kJ/mol of heat is produced during this process, we already have the answer to how much heat is produced in preparing a mole of H2SO4 from a mole of S: Heat produced per mole of H2SO4 = \(130 kJ/mol\)

Calculate the Moles of H2SO4 from 2000 kg

To find out how much heat is produced in preparing 2000 kg of H2SO4, first, we need to convert the mass (in kg) to moles using the molar mass of H2SO4. The molar mass of H2SO4 is \(98.08 g/mol\). 1. Convert the mass of H2SO4 to grams: \(2000 kg * 1000 g/kg = 2,000,000 g\) 2. Determine the moles of H2SO4: \(\frac{2,000,000 g}{98.08 g/mol} = 20,404.86 mol\)

Calculate Heat Produced in Preparing 2000 kg of H2SO4

Use the heat produced per mole of H2SO4 (from Step 2) and the number of moles of H2SO4 (from Step 3) to find the total heat produced: Total heat = Heat produced per mole of H2SO4 × Moles of H2SO4 Total heat = \(130 kJ/mol × 20,404.86 mol = 2,652,631.8 kJ\) So, the heat produced in preparing 2000 kg of H2SO4 is approximately \(2,652,631.8 kJ\).

Key concepts

Chemical Processes in Sulfuric Acid Synthesis

Sulfuric acid, or \(\text{H}_2\text{SO}_4\), is a crucial chemical in industrial processes. Its synthesis involves a set of chemical reactions, each playing a vital role in efficiently producing the compound. The journey begins with converting sulfur (\(S\)) into sulfur dioxide (\(\text{SO}_2\)), which is accomplished through a straightforward oxidation. Next comes the transformation of sulfur dioxide into sulfur trioxide (\(\text{SO}_3\))—another oxidation reaction. This step is pivotal because \(\text{SO}_3\) is more reactive and ready for further chemical transformations that lead to sulfuric acid.
The third step involves dissolving \(\text{SO}_3\) in existing sulfuric acid to form oleum, which is then reacted with water to form a higher concentration of \(\text{H}_2\text{SO}_4\). Understanding these processes helps us appreciate how sulfuric acid is efficiently synthesized in large quantities for various industrial uses. These reactions not only highlight the elegance of chemical engineering but also teach us how controlled processes can production scales without sacrificing quality.

Oxidation Reactions in Sulfuric Acid Production

At the heart of sulfuric acid manufacture are two critical oxidation reactions. The first converts elemental sulfur into sulfur dioxide (\(\text{SO}_2\)). This transformation is a simple oxidation where sulfur gains oxygen. Oxidation is a chemical reaction where a substance loses electrons, often combining with oxygen. In the context of sulfuric acid production, controlling this reaction is the first crucial step.
The next major oxidation happens when \(\text{SO}_2\) is further oxidized to form sulfur trioxide (\(\text{SO}_3\)). This reaction typically occurs in the presence of a catalyst, such as vanadium(V) oxide, to speed up the process. Catalysts are essential because they lower the energy barrier for the reaction to occur, making the process more efficient. The effectiveness of these oxidation reactions is key to the overall efficiency and environmental performance of a sulfuric acid plant, as they not only produce the necessary chemical intermediates but also determine the thermal energy available for recycling into electricity.

Heat Calculation in Sulfuric Acid Synthesis

Calculating the heat involved in sulfuric acid synthesis is pivotal for understanding energy management in the process. In the final step of turning sulfur trioxide \((\text{SO}_3)\) into sulfuric acid, a significant amount of heat is released—specifically \(130 \text{kJ/mol}\) of \(\text{H}_2\text{SO}_4\). This exothermic reaction is a result of the reaction where \(\text{SO}_3\) is absorbed into existing sulfuric acid and further reacted with water to increase the acid's concentration.
Understanding heat calculation involves knowing the molar masses of the compounds involved. With the molar mass of \(\text{H}_2\text{SO}_4\) being approximately \(98.08 \text{g/mol}\), one can calculate the total heat produced when synthesizing any quantity of \(\text{H}_2\text{SO}_4\). For instance, synthesizing \(2000 \text{kg}\) of sulfuric acid involves converting its mass to moles and then multiplying by the heat produced per mole. This calculation reveals how much energy can be potentially recycled into electricity, showcasing the importance of efficient energy use in industrial chemical reactions.