Final answer:
According to the stoichiometry of the balanced chemical equation and Avogadro's hypothesis, 70.0 mL of nitrogen reacts with the limiting 47.0 mL of oxygen to theoretically produce 31.3 mL of N₂O₃ at the same temperature and pressure.
Step-by-step explanation:
When considering the reaction of nitrogen gas (N₂) with oxygen gas (O₂) to form dinitrogen trioxide (N₂O₃), it is important to look at the stoichiometry of the balanced chemical equation:
N₂(g) + O₂(g) → N₂O₃(g)
According to Avogadro's hypothesis, equal volumes of gases at the same temperature and pressure contain the same number of particles. The reaction above is not balanced as written. To balance it, we need to make certain that there are equal numbers of each type of atom on both sides of the reaction. The balanced equation is:
2 N₂(g) + 3 O₂(g) → 2 N₂O₃(g)
This means that two volumes of nitrogen react with three volumes of oxygen to produce two volumes of dinitrogen trioxide, assuming all gases are at the same temperature and pressure. Given the volumes of the reactants, 70.0 mL of nitrogen and 47.0 mL of oxygen, we can see that oxygen is the limiting reactant because we would need 105 mL of oxygen to fully react with 70 mL of nitrogen (as per the stoichiometry of the balanced equation).
Since the stoichiometry shows that the volume ratio of N₂:O₂:N₂O₃ is 2:3:2 under the same conditions of temperature and pressure and since oxygen is the limiting reactant, then for every 3 volumes of oxygen, we get 2 volumes of N₂O₃. This means that 47 mL of oxygen would theoretically produce (47 mL × (2/3)) = 31.3 mL of N₂O₃.