Question

In the "contact process" for making sulfuric acid, sulfur is first burned to \(\mathrm{SO}_{2}\). Environmental restrictions allow no more than \(0.30 \%\) of this \(\mathrm{SO}_{2}\) to be vented to the atmosphere. (a) If enough sulfur is burned in a plant to produce \(1.80 \times 10^{6} \mathrm{kg}\) of pure, anhydrous \(\mathrm{H}_{2} \mathrm{SO}_{4}\) per day, what is the maximum amount of \(\mathrm{SO}_{2}\) that is allowed to be exhausted to the atmosphere? (b) One way to prevent any \(\mathrm{SO}_{2}\) from reaching the atmosphere is to "scrub" the exhaust gases with slaked lime, \(\mathrm{Ca}(\mathrm{OH})_{2}\) \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{SO}_{2}(\mathrm{g}) \rightarrow \mathrm{CaSO}_{3}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell)\) $$ 2 \mathrm{CaSO}_{3}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CaSO}_{4}(\mathrm{s}) $$ What mass of \(\mathrm{Ca}(\mathrm{OH})_{2}\) (in kilograms) is needed to remove the \(\mathrm{SO}_{2}\) calculated in part (a)?

Short answer

Maximum vented \(\mathrm{SO}_2\) is 3.528 kg; \(\mathrm{Ca(OH)_2}\) required is 4.079 kg.

Step-by-step solution

Determine Molar Mass of Sulfuric Acid

Calculate the molar mass of \( \mathrm{H}_2\mathrm{SO}_4 \) by adding the atomic masses of its elements: \(2 \times 1.01 \) for H, \(32.07 \) for S, and \(4 \times 16.00 \) for O. \[ \mathrm{Molar\ Mass\ of\ H_2SO_4} = 2(1.01) + 32.07 + 4(16.00) = 98.09 \text{ g/mol} \]

Calculate Moles of H₂SO₄ Produced

Convert the mass of \( \mathrm{H}_2\mathrm{SO}_4 \) produced per day to moles by using its molar mass.\[ \text{Moles of } \mathrm{H}_2\mathrm{SO}_4 = \frac{1.80 \times 10^6 \text{ kg}}{98.09 \text{ g/mol}} \times \frac{10^3 \text{ g}}{1 \text{ kg}} = 1.835 \times 10^4 \text{ mol} \]

Calculate Moles of SO₂ Required

In the contact process, each \( \mathrm{H}_2\mathrm{SO}_4 \) requires \(1\) mole of \( \mathrm{SO}_2 \). Therefore, the moles of \( \mathrm{SO}_2 \) required are the same as that of \( \mathrm{H}_2\mathrm{SO}_4 \).\[ \text{Moles of } \mathrm{SO}_2 = 1.835 \times 10^4 \text{ mol} \]

Calculate Mass of SO₂ Produced

Convert the moles of \( \mathrm{SO}_2 \) to mass. The molar mass of \( \mathrm{SO}_2 \) is \(64.07 \text{ g/mol}\).\[ \text{Mass of } \mathrm{SO}_2 = 1.835 \times 10^4 \text{ mol} \times 64.07 \text{ g/mol} = 1.176 \times 10^6 \text{ g} = 1176 \text{ kg} \]

Determine Allowed SO₂ Venting

Calculate the maximum mass of \( \mathrm{SO}_2 \) allowed to be vented based on the \(0.30\%\) restriction.\[ \text{Allowed venting} = 0.30\% \times 1176 \text{ kg} = \frac{0.30}{100} \times 1176 \text{ kg} = 3.528 \text{ kg} \]

Stoichiometry for SO₂ Scrubbing

Use the balanced equation to find the moles of \( \mathrm{Ca(OH)_2} \) needed. From reaction stoichiometry, \(1\) mole of \( \mathrm{Ca(OH)_2} \) reacts with \(1\) mole of \( \mathrm{SO}_2 \).\[ \text{Moles of } \mathrm{Ca(OH)_2} = 3.528 \text{ kg of } \mathrm{SO_2} \times \frac{1000 \text{ g/kg}}{64.07 \text{ g/mol}} \approx 55.06 \text{ mol} \]

Calculate Mass of Ca(OH)₂ Required

Convert the moles of \( \mathrm{Ca(OH)_2} \) to mass. The molar mass of \( \mathrm{Ca(OH)_2} \) is \(74.09 \text{ g/mol}\).\[ \text{Mass of } \mathrm{Ca(OH)_2} = 55.06 \text{ mol} \times 74.09 \text{ g/mol} = 4079 \text{ g} = 4.079 \text{ kg} \]

Key concepts

Contact Process in Sulfuric Acid Production

The Contact Process is a key industrial method for producing sulfuric acid \(\mathrm{H}_2\mathrm{SO}_4\), which is widely used in various industries. It begins with the burning of sulfur to form sulfur dioxide \(\mathrm{SO}_2\). This \(\mathrm{SO}_2\) is then oxidized to sulfur trioxide \(\mathrm{SO}_3\) using a vanadium oxide catalyst in a series of reactor stages.
The final step involves absorbing the \(\mathrm{SO}_3\) into concentrated sulfuric acid to form oleum, which, when mixed with water, produces more sulfuric acid. This process is designed to maximize efficiency and minimize emissions.

Environmental Regulations

Environmental regulations play a critical role in controlling emissions from industrial processes, including the Contact Process. Regulations often mandate strict limits on pollutant emissions to protect air quality and public health.
In the case of sulfur dioxide emissions, such as those from sulfuric acid production, regulations can limit atmospheric venting to very low percentages, often much less than one percent of the total industrial output. These limitations compel industries to adopt practices like scrubbing exhaust gases to reduce pollutants before they are released into the atmosphere.
Such regulations are not only essential for maintaining environmental standards but also for ensuring sustainable industrial practices.

Stoichiometry in Sulfuric Acid Production

Stoichiometry is a fundamental concept that is frequently applied in chemical processes like sulfuric acid production. It involves calculating the quantities of reactants and products involved in chemical reactions.
In this context, stoichiometry helps determine the amount of sulfur \(\mathrm{S}\) needed to produce a specific amount of \(\mathrm{H}_2\mathrm{SO}_4\), and subsequently, the corresponding amount of \(\mathrm{SO}_2\) produced. Understanding stoichiometry ensures that all industrial processes are both efficient and compliant with regulatory limits.
The detailed calculations of mole ratios and masses are invaluable for optimizing production while minimizing waste and emissions.

Sulfur Dioxide Emissions Control

Controlling sulfur dioxide emissions is crucial due to its environmental and health impacts. One effective method to manage these emissions is through 'scrubbing.' This involves passing exhaust gases through materials that react with \(\mathrm{SO}_2\), like slaked lime \(\mathrm{Ca(OH)_2}\).
The chemical reaction between \(\mathrm{SO}_2\) and \(\mathrm{Ca(OH)_2}\) forms solid calcium sulfite, which can be further processed or disposed of safely. By employing such technologies, industries can keep within legal emission limits and reduce the potential for acid rain and respiratory problems in humans.
Effective sulfur dioxide management is essential not only for regulatory compliance but also for the overall health of ecosystems.