Question

One method proposed for removing SO \(_{2}\) from the flue gases of power plants involves reaction with aqueous \(\mathrm{H}_{2} \mathrm{S}\) . Elemental sulfur is the product. (a) Write a balanced chemical equation for the reaction. (b) What volume of \(\mathrm{H}_{2} \mathrm{S}\) at \(27^{\circ} \mathrm{C}\) and 760 torr would be required to remove the \(\mathrm{SO}_{2}\) formed by burning 2.0 tons of coal containing 3.5\(\% \mathrm{S}\) by mass? (\mathbf{c} ) What mass o f elemental sulfur is produced? Assume that all reactions are 100\(\%\) efficient.

Short answer

The balanced chemical equation for the reaction between aqueous H2S and SO2 to produce elemental sulfur is: \[2H_2S (aq) + SO2 (g) \rightarrow 3S (s) + 2H_2O (l)\] The calculated volume of H2S required to remove the SO2 formed by burning 2.0 tons of coal containing 3.5% S by mass, under given temperature and pressure conditions is about 107271.76 L. Finally, assuming 100% efficiency, the mass of elemental sulfur produced from this reaction is approximately 209,835.21 g (or about 209.84 kg).

Step-by-step solution

Write the balanced chemical equation

The unbalanced chemical reaction between hydrogen sulfide (H2S) and sulfur dioxide (SO2) is: \[H_2S + SO_2 \rightarrow S + H_2O\] Let's balance the equation by adjusting the coefficients: \[2H_2S + SO_2 \rightarrow 3S + 2H_2O\] The balanced chemical equation for the reaction is: \[2H_2S (aq) + SO_2 (g) \rightarrow 3S (s) + 2H_2O (l)\]

Calculate the moles of sulfur in the coal

We are given that there are 2.0 tons of coal and it contains 3.5% S by mass. Let's first convert tons to grams and then find the mass of sulfur in the coal: Mass of coal = 2.0 tons × (1000 kg/ton) × (1000 g/kg) = 2,000,000 g Mass of sulfur = (2,000,000 g × 0.035) = 70,000 g Now, let's find the moles of sulfur (S) using its molar mass (32.06 g/mol): Moles of S = (70,000 g)/(32.06 g/mol) = 2181.91 mol

Use stoichiometry to find the moles of H2S required

From the balanced chemical equation, it is clear that 2 moles of H2S react with 1 mole of SO2. Since SO2 is formed by burning S, we already have the moles of S: Moles of SO2 = 2181.91 mol Now, we can use stoichiometry to find the moles of H2S needed: Moles of H2S = 2 × Moles of SO2 = 2 × 2181.91 mol = 4363.82 mol

Use the ideal gas law to find the volume of H2S

We are given that the H2S gas is at 27°C and 760 torr. First, let's convert the temperature and pressure into Kelvin and atmospheres, respectively: Temperature = 27°C + 273.15 = 300.15 K Pressure = 760 torr × (1 atm/760 torr) = 1 atm Now, let's use the ideal gas law (PV = nRT) to calculate the volume of H2S (V): \(V = \dfrac{nRT}{P}\) where n = moles of H2S, R = gas constant (0.08206 L atm/mol K), T = temperature in K, and P = pressure in atm. V = (4363.82 mol × 0.08206 L atm/mol K × 300.15 K) / 1 atm = 107271.76 L

Calculate the mass of elemental sulfur produced

From the balanced chemical equation, we know that 3 moles of elemental sulfur (S) are produced for every 2 moles of H2S reacted: Moles of elemental sulfur produced = (3/2) × Moles of H2S = (3/2) × 4363.82 mol = 6545.73 mol Now we can calculate the mass of elemental sulfur produced: Mass of elemental sulfur = Moles of elemental sulfur × Molar mass of S = 6545.73 mol × 32.06 g/mol = 209,835.21 g The mass of elemental sulfur produced is 209,835.21 g.

Key concepts

Understanding Stoichiometry in Chemical Equations

Stoichiometry is at the heart of chemical reactions. It's a section of chemistry that focuses on the quantitative relationships between the reactants and products in a chemical equation. Simply put, stoichiometry allows us to predict the amounts of substances consumed and produced during a reaction.

When we balance a chemical equation like \[2H_2S (aq) + SO_2 (g) \rightarrow 3S (s) + 2H_2O (l)\]

stoichiometry tells us what amount of each substance is needed to ensure that the reaction goes to completion without leaving any excess reactants. For instance, in our exercise, the stoichiometry indicated that two moles of hydrogen sulfide react with one mole of sulfur dioxide, to produce three moles of sulfur and two moles of water. This proportion is vital when trying to figure out how much reagent is required to remove a specific amount of sulfur dioxide, a common polluting gas emanating from coal combustion in power plants.

Let's improve the explanation by using bullet points to summarize key stoichiometry concepts:

• Mole Ratio: The coefficients in a balanced equation tell us the mole ratio of reactants to products.
• Mass Conservation: Stoichiometry is based on the law of conservation of mass where the total mass of reactants equals the total mass of products.
• Calculations: To perform stoichiometric calculations, one usually starts by identifying the mole ratio, then uses the given quantities to find unknown values such as mass, volume, or number of moles.

Grasping stoichiometry is not only crucial for homework exercises but also for practical applications in industrial processes and environmental science.

Applying the Ideal Gas Law to Real-World Problems

The ideal gas law is a fundamental equation in the study of gases that describes the relationship between pressure (P), volume (V), number of moles (n), and temperature (T). It’s given by the equation \[PV = nRT\]

where R is the gas constant. This law lets us predict how a gas will behave under different conditions, and it's especially useful in chemical engineering scenarios, such as the removal of sulfur dioxide from emissions.

In our exercise, after determining the amount of hydrogen sulfide gas required using stoichiometry, we use the ideal gas law to calculate the volume of this gas. Given the number of moles, temperature in Kelvin, and pressure in atmospheres, we can solve for volume, which tells us how much gas is required at specific atmospheric conditions.

Additional important points on the ideal gas law include:

• Standard Conditions: The values for temperature and pressure need to be converted to absolute temperature (Kelvin) and atmospheres, respectively, to use the gas constant in L atm/mol K.
• Real Gases: The law assumes the gas behaves ideally, which is a good approximation under many conditions but may deviate at high pressures or low temperatures.
• Universal Application: This law can be applied to any ideal gas, regardless of its chemical identity.

Mastering the ideal gas law can be incredibly beneficial for understanding phenomena in not just chemistry but also meteorology, respiration physiology, and many other fields where gas behavior is relevant.

The Environmental Impact of Sulfur Dioxide Removal

Sulfur dioxide (SO2) removal is a vital environmental process, particularly in industries like power generation, where the burning of fossil fuels can release significant amounts of SO2 into the atmosphere. This chemical compound is a contributor to acid rain, which can damage ecosystems, architecture, and human health.

To curb the harmful effects of SO2, one proposed method, as shown in our exercise, involves a reaction with hydrogen sulfide to produce elemental sulfur and water:\[2H_2S (aq) + SO_2 (g) \rightarrow 3S (s) + 2H_2O (l)\]

This reaction is a practical example of how a harmful substance can be converted into less harmful products—elemental sulfur can be reused or safely disposed of, unlike sulfur dioxide. The process also illustrates how industrial chemistry can play a role in environmental protection.

Let's highlight the critical aspects of sulfur dioxide removal:

• Air Quality Improvement: Removing SO2 from emissions is essential to reduce air pollution and improve air quality.
• Industrial Responsibility: Power plants and other industries are increasingly held accountable for their environmental impact; methods like this are part of their response to regulatory demands.
• Chemical Conversion: The process involves converting one pollutant into a less harmful substance through chemical reactions, showcasing the importance of chemistry in environmental management.

Understanding the chemistry and techniques for sulfur dioxide removal not only helps with academic exercises but also provides insight into the real-world applications that work towards a cleaner environment.