Question

One method proposed for removing \(\mathrm{SO}_{2}\) 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 740 torr would be required to remove the \(\mathrm{SO}_{2}\) formed by burning \(1.0\) ton of coal containing \(3.5 \%\) S by mass? (c) What mass of elemental sulfur is produced? Assume that all reactions are \(100 \%\) efficient.

Short answer

The balanced chemical equation for the reaction is \(SO_{2} + 2H_{2}S \rightarrow 3S + 2H_{2}O\). To remove the \(SO_{2}\) formed by burning 1.0 ton of coal containing 3.5% S by mass, 52150.6 liters of \(H_{2}S\) at 27°C and 740 torr would be required. The mass of elemental sulfur produced is 105 kg.

Step-by-step solution

Write a balanced chemical equation

To get a balanced chemical equation for the reaction between sulfur dioxide (SO₂) and hydrogen sulfide (H₂S), we can follow these steps: 1. Write down the unbalanced equation: SO₂ + H₂S -> S (Elemental Sulfur) + H₂O 2. Balance the equation: To balance oxygen and hydrogen atoms, we need two H₂O molecules: SO₂ + H₂S -> S + 2H₂O Now we have 2 Oxygens and 4 Hydrogens on the right side, but only 2 Oxygens and 2 Hydrogens on the left side. To balance the equation, we will need two H₂S molecules as follows: SO₂ + 2H₂S -> 3S + 2H₂O Now, both sides have balanced atoms: 1 sulfur atom from SO₂ and 2 sulfur atoms from 2H₂S on the left, and 3 sulfur atoms on the right; 2 oxygen atoms from SO₂ and 2 hydrogen atoms from 2H₂S on the left, and 2 oxygen atoms and 4 hydrogen atoms on the right. The balanced chemical equation is: SO₂ + 2H₂S -> 3S + 2H₂O.

Determine the moles of SO₂ formed

To calculate the moles of SO₂ formed by burning 1.0 ton of coal, we need to use the information given: 3.5% of the coal mass is sulfur (S). 1 ton of coal = 1000 kg The mass of sulfur in the coal = 3.5% * 1000 kg = 35 kg As the complete combustion of the coal produces SO₂ from sulfur, we will use the molar mass of S and SO₂ to find the moles of SO₂ formed: Molar mass of S = 32 g/mol Molar mass of SO₂ = 32 g/mol + 16 g/mol*2 = 64 g/mol Using the mass and molar mass of sulfur, we can find the moles of sulfur: moles of S = mass of S / molar mass of S = (35 kg * 1000 g/kg) / 32 g/mol = 1093.75 mol Since each mole of sulfur forms one mole of SO₂, moles of SO₂ = 1093.75 mol

Calculate the volume of H₂S required

To calculate the volume of H₂S required to remove the SO₂ formed, we will use the stoichiometry given by the balanced chemical equation: 1 mol SO₂ requires 2 mol H₂S. moles of H₂S = 2 * moles of SO₂ = 2 * 1093.75 mol = 2187.5 mol Next, we use the ideal gas law (PV=nRT) to find the volume of H₂S. We are given the temperature T = 27°C = 300 K and the pressure P = 740 torr. We need to convert the pressure into atmospheres: 1 atm = 760 torr P = 740 torr * (1 atm/760 torr) = 0.9737 atm Now, solving for the volume V, we have: R (gas constant) = 0.0821 L⋅atm/(K⋅mol) V = nRT/P = (2187.5 mol * 0.0821 L⋅atm/(K⋅mol) * 300 K) / 0.9737 atm = 52150.6 L Hence, the volume of H₂S required is 52150.6 liters.

Calculate the mass of elemental sulfur produced

To find the mass of elemental sulfur (S) produced, we use the stoichiometry given by the balanced chemical equation: 1 mol SO₂ produces 3 mol S. moles of S produced = 3 * moles of SO₂ = 3 * 1093.75 mol = 3281.25 mol Now, using the molar mass of sulfur (S = 32 g/mol), we find the mass of elemental sulfur produced: mass of S = moles of S * molar mass of S = 3281.25 mol * 32 g/mol = 104997.5 g = 105 kg (rounded to three significant figures) The mass of elemental sulfur produced is 105 kg.

Key concepts

Balancing Chemical Equations

Balancing chemical equations is an essential step in understanding how a chemical reaction occurs. A balanced equation means that the number of each type of atom on the left side (reactants) is equal to the number on the right side (products). This adherence to the Law of Conservation of Mass ensures that atoms are neither created nor destroyed in the reaction.

In the case of reacting sulfur dioxide (SO₂) with hydrogen sulfide (H₂S) to form elemental sulfur (S) and water (H₂O), we initially write the unbalanced equation:

• SO₂ + H₂S → S + H₂O

To achieve balance:

• Make sure the number of sulfur, oxygen, and hydrogen atoms is the same on both sides of the equation.
• Adjust the coefficients in front of each compound.

The final balanced equation for this reaction is:

• SO₂ + 2H₂S → 3S + 2H₂O

This process ensures that every atom is accounted for, allowing for accurate stoichiometric calculations later. Balancing equations can sometimes involve trial and error, but it fundamentally relies on arithmetic and logical adjustments of the coefficients.

Stoichiometry

Stoichiometry deals with the quantitative relationships between reactants and products in a chemical reaction. It uses the balanced chemical equation to perform calculations, such as finding how much of a reactant is needed to completely react with another reactant, or how much product is formed.

In our problem, once the equation (SO₂ + 2H₂S → 3S + 2H₂O) is balanced, stoichiometry allows us to calculate the required moles of H₂S given the moles of SO₂ we have. Using the equation:

• 1 mole of SO₂ needs 2 moles of H₂S

Knowing the moles of SO₂ formed from burning coal allows us to then calculate moles of H₂S:

• If we have 1093.75 moles of SO₂, we need 2 × 1093.75 = 2187.5 moles of H₂S

This calculation demonstrates the stoichiometric concept of mole-to-mole relationships in a reaction, pivotal for determining the amount of each reactant or product needed or produced in a chemical reaction.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that describes the behavior of ideal gases. It relates the pressure, volume, temperature, and number of moles of a gas via the equation: \( PV = nRT \).

• \( P \) is pressure in atm
• \( V \) is volume in liters
• \( n \) is the number of moles
• \( R \) is the ideal gas constant, \( 0.0821 \text{ L} \cdot \text{atm}/(\text{K} \cdot \text{mol}) \)
• \( T \) is temperature in Kelvin

In our exercise, we used the Ideal Gas Law to find the volume of H₂S needed, given the moles calculated from stoichiometry. Given \( P = 0.9737 \text{ atm} \), \( T = 300 \text{ K} \), and \( n = 2187.5 \text{ mol} \), we solved for \( V \):\[V = \frac{nRT}{P} = \frac{2187.5 \times 0.0821 \times 300}{0.9737} \approx 52150.6 \text{ liters}\]This approach highlights how various parameters of a gas can be interconnected, allowing for comprehensive problem-solving concerning gases.

Mass Calculations

Mass calculations in chemistry often involve converting between moles and grams, using the molar mass as a conversion factor. This step is crucial to connect the calculated moles from stoichiometry to tangible, measurable quantities like grams or kilograms.

In the chemical reaction of SO₂ and H₂S, mass calculations help us find the mass of elemental sulfur (S) produced. Knowing each mole of SO₂ yields 3 moles of sulfur, and each mole of sulfur has a molar mass of 32 g/mol, allows us to calculate:

• Moles of sulfur = 3 × Moles of SO₂ = 3 × 1093.75 = 3281.25 moles
• Total mass of sulfur = 3281.25 moles × 32 g/mol = 104997.5 g = 105 kg

By applying these mass calculations, we can relate the balanced equation you started with directly to real-world quantities, completing the cycle from theory to practice.