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

Step by step solution

01

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

Given that the third process produces \(130\, \mathrm{kJ/mol}\) of heat, we will use that to find the total heat produced in preparing one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). Heat produced in 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) = 130 kJ/mol.

02

Convert the mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from pounds to grams

We have to calculate the heat produced in preparing 5,000 pounds of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). First, we need to convert the mass from pounds to grams. 1 pound = 453.592 grams 5000 pounds = 5000 × 453.592 5000 pounds = 2267960 grams

03

Calculate the number of moles of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in 5000 pounds

Now, we need to find the number of moles in 2267960 grams of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). The molar mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is \(2\times1+32+64=98\,\mathrm{g/mol}\). Number of moles = (mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\))/(molar mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)) Number of moles = 2267960 g / 98 g/mol Number of moles = 23142 moles

04

Calculate the heat produced in preparing 5000 pounds of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

We know that 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) produces 130 kJ of heat. So, to find the heat produced in preparing 23142 moles of \(\mathrm{H}_{2} \mathrm{SO}_{4}\), we multiply the heat produced per mole by the total number of moles. Heat produced = (heat produced per mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)) × (number of moles) Heat produced = (130 kJ/mol) × (23142 moles) Heat produced = 3008460 kJ. Therefore, the heat produced in preparing one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from a mole of S is 130 kJ/mol, and the heat produced in preparing 5,000 pounds of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is 3,008,460 kJ.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!