Final answer:
At equilibrium, 25% of O₂ is reacted which means 1 mole of O₂ is used, consuming 2 moles of SO₂ to produce 2 moles of SO₃. The total number of moles of gases at equilibrium is 7 moles.
Step-by-step explanation:
The student's question concerns the chemical reaction between sulfur dioxide (SO₂) and oxygen (O₂) to form sulfur trioxide (SO₃), which is represented by the balanced equation:
2 SO₂(g) + O₂(g) ⇒ 2 SO₃(g)
Initially, there are 4 moles of SO₂ and 4 moles of O₂. At equilibrium, it is given that 25% of O₂ is used up. To calculate the total number of moles of gases at equilibrium, we need to consider the stoichiometry of the reaction. Since only 25% of O₂ is reacted, this means 1 mole of O₂ (which is 25% of 4 moles) and due to the stoichiometry, 2 moles of SO₂ will react to form 2 moles of SO₃. The remaining unreacted gases will be 4 moles - 2 moles = 2 moles of SO₂ and 4 moles - 1 mole = 3 moles of O₂. Therefore, the total number of moles of all gases at equilibrium is 2 moles of SO₂ + 3 moles of O₂ + 2 moles of SO₃ = 7 moles.