Question

Sulfur dioxide can be removed from the smokestack emissions of power plants by reacting it with hydrogen sulfide, producing sulfur and water. What volume of hydrogen sulfide at \(27^{\circ} \mathrm{C}\) and \(755 \mathrm{~mm} \mathrm{Hg}\) is required to remove the sulfur dioxide produced by a power plant that burns one metric ton of coal containing \(5.0 \%\) sulfur by mass? How many grams of sulfur are produced by the reaction of \(\mathrm{H}_{2} \mathrm{~S}\) with \(\mathrm{SO}_{2} ?\)

Short answer

The volume of hydrogen sulfide required to remove the sulfur dioxide produced by the power plant is 19681.76 L, and the mass of sulfur produced by the reaction of H₂S with SO₂ is 37503.5 g.

Step-by-step solution

Calculate moles of sulfur in coal

We are given that 1 metric ton of coal contains 5.0% sulfur by mass. A metric ton is equal to 1000 kg, so we can find the mass of sulfur in the coal as follows: Mass of sulfur = \(1000\,\mathrm{kg} \times 5.0\% = 50\,\mathrm{kg}\) Now, we will convert this mass into moles using the molar mass of sulfur, which is 32.06 g/mol. Moles of sulfur = \(\frac{50\,\mathrm{kg}}{32.06\,\mathrm{g/mol}} \times 1000\,\mathrm{g/kg} = 1559.65\,\mathrm{moles}\)

Convert moles of sulfur to moles of \(\mathrm{SO}_2\)

When the sulfur in coal reacts with oxygen, it forms sulfur dioxide according to the following equation: S + O\(_2 \rightarrow \mathrm{SO}_2\) The stoichiometry of the reaction implies that one mole of sulfur will form one mole of sulfur dioxide. Moles of \(\mathrm{SO}_2\) = Moles of sulfur = 1559.65 moles

Use stoichiometry to find moles of \(\mathrm{H}_2\mathrm{S}\)

The reaction between hydrogen sulfide and sulfur dioxide can be represented as: 2 H\(_2\)S + SO\(_2 \rightarrow 3\, S + 2\, H\)_2$O From the stoichiometry of the reaction, we can calculate the moles of \(\mathrm{H}_2\mathrm{S}\) required for the reaction: Moles of \(\mathrm{H}_2\mathrm{S}\) = \(\frac{1}{2} \times\) Moles of \(\mathrm{SO}_2\) = \(\frac{1}{2} \times 1559.65\,\mathrm{moles} = 779.825\,\mathrm{moles}\)

Convert moles of \(\mathrm{H}_2\mathrm{S}\) to volume

Using the Ideal Gas Law, we can calculate the volume of hydrogen sulfide at the given temperature and pressure: \(PV = nRT\) where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (using 62.364 \({\mathrm{L}}\, {\mathrm{mm}}\, {\mathrm{Hg}} \mathrm{/}\, {\mathrm{mol}}\, {\mathrm{K}}\)) and T is the temperature in Kelvin. We are given the pressure (P) as 755 mm Hg and the temperature (T) as \(27^{\circ} \mathrm{C}\). Convert the temperature to Kelvin: T = \(27 + 273.15 = 300.15\,\mathrm{K}\) Now, we can calculate the volume of \(\mathrm{H}_2\mathrm{S}\) as follows: V = \(\frac{nRT}{P} = \frac{779.825\,\mathrm{moles} \times 62.364\, {\mathrm{L}}\, {\mathrm{mm}}\, {\mathrm{Hg}} \mathrm{/}\, {\mathrm{mol}}\, {\mathrm{K}} \times 300.15\,\mathrm{K}}{755\,\mathrm{mm}\,\mathrm{Hg}} = 19681.76\,\mathrm{L}\)

Calculate mass of sulfur produced

From the stoichiometry of the reaction between hydrogen sulfide and sulfur dioxide, we can determine the moles of sulfur produced: Moles of Sulfur = \(\frac{3}{2} \times\) Moles of \(\mathrm{H}_2\mathrm{S}\) = \(\frac{3}{2} \times 779.825\,\mathrm{moles} = 1169.7375\,\mathrm{moles}\) Now, we will convert the moles of sulfur to mass using the molar mass of sulfur: Mass of sulfur = \(1169.7375\,\mathrm{moles} \times 32.06\,\mathrm{g/mol} = 37503.5\,\mathrm{g}\) In conclusion, the volume of hydrogen sulfide required to remove the sulfur dioxide produced by the power plant is 19681.76 L, and the mass of sulfur produced by the reaction of \(\mathrm{H}_{2} \mathrm{~S}\) with \(\mathrm{SO}_{2}\) is 37503.5 g.

Key concepts

Sulfur Dioxide Emissions

Sulfur dioxide (SO₂) emissions are a significant environmental concern, primarily resulting from the burning of fossil fuels like coal and oil in power plants and other industrial processes. Upon release into the atmosphere, SO₂ can lead to acid rain, respiratory problems, and other environmental issues.

To mitigate these effects, techniques such as flue-gas desulfurization are employed, where SO₂ is reacted with compounds like hydrogen sulfide (H₂S) to produce less harmful substances. Understanding the chemical and stoichiometric principles behind these processes is essential for environmental engineers and scientists in designing effective emission control strategies.

Stoichiometry Calculations

Stoichiometry calculations enable chemists and engineers to predict the outcomes of chemical reactions, quantifying the relationships between reactants and products. With a known percent of sulfur in coal, the stoichiometry helps in determining how much SO₂ will form and how much H₂S is required to remove it.

Example of Stoichiometry in Action

During the conversion of sulfur in coal to SO₂, a 1:1 mole ratio is maintained. However, when SO₂ reacts with H₂S, the ratio is not 1:1. In such complex chemical equations, stoichiometry serves as a crucial tool to balance the reaction and calculate the precise amount of each substance needed for the reaction to proceed.

Ideal Gas Law

The Ideal Gas Law, represented by the equation PV = nRT, describes the behavior of an ideal gas in terms of pressure (P), volume (V), temperature (T), and the number of moles (n). The gas constant (R) serves as a bridge between these units. This law is pivotal when converting between the amount of gas in moles and its volume, especially under varying conditions of temperature and pressure.

Application in Calculations

For example, to determine the volume of H₂S needed at specific conditions, we rearrange the Ideal Gas Law to solve for V (volume). This allows us to relate the amount of gas that will be used to purify emissions from a power plant, providing a practical insight into the scale of pollution control required.

Molar Mass

Molar mass is the weight of one mole of a substance, commonly expressed in grams per mole (g/mol). This fundamental concept in chemistry helps convert between mass and moles, enabling us to grasp the scale of chemicals involved in reactions.

Critical to stoichiometry, the molar mass of sulfur (32.06 g/mol) is used to convert the mass of sulfur in coal to moles, which can then be used to predict the amount of SO₂ released and the mass of sulfur produced after treatment. Molar mass calculations serve as a cornerstone for understanding the conversion of reactants to products, both quantitatively and qualitatively.