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 $\mathrm{H}_{2} \mathrm{SO}_{4} ?$

Step by step solution

01

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 \(130 kJ/mol\))

02

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 = \(130 kJ/mol\)

03

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: \(\frac{2,000,000 g}{98.08 g/mol} = 20,404.86 mol\)

04

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 \(2,652,631.8 kJ\).

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