What volume, in liters, of sulfur dioxide gas at 455 K and 2.03 atm is needed to produce 89.6 g of sulfur trioxide, SO₃, according to the reaction: 2 SO₂(g) + O₂(g) → 2 SO₃(g)?

• A. 6.2 L
• B. 18.6 L
• C. 12.4 L
• D. 24.8 L

Answer: (C)

Verified step by step guidance

1. First, calculate the number of moles of sulfur trioxide (SO₃) produced using its molar mass. The molar mass of SO₃ is approximately 80.07 g/mol. Use the formula: \( \text{moles of SO₃} = \frac{\text{mass of SO₃}}{\text{molar mass of SO₃}} \).
2. Using the balanced chemical equation \( 2 \text{SO₂(g)} + \text{O₂(g)} \rightarrow 2 \text{SO₃(g)} \), determine the moles of sulfur dioxide (SO₂) needed. The stoichiometry of the reaction shows that 2 moles of SO₂ produce 2 moles of SO₃, so the moles of SO₂ required are equal to the moles of SO₃ produced.
3. Apply the ideal gas law to find the volume of SO₂ gas needed. The ideal gas law is given by \( PV = nRT \), where \( P \) is the pressure (2.03 atm), \( V \) is the volume in liters, \( n \) is the number of moles of SO₂, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin (455 K).
4. Rearrange the ideal gas law to solve for the volume \( V \): \( V = \frac{nRT}{P} \). Substitute the known values for \( n \), \( R \), \( T \), and \( P \) into the equation.
5. Calculate the volume \( V \) using the rearranged ideal gas law equation to find the volume of sulfur dioxide gas needed at the given conditions.