Final answer:
To produce 12.5 mol of H₂O from the given reaction, 8.33 moles of NH₃ are needed based on the 2:3 mole ratio from the balanced chemical equation.
Step-by-step explanation:
To determine how many moles of NH₃ are needed to produce 12.5 mol of H₂O, we must use the balanced chemical equation provided:
4NH₃(g) + 7O₂(g) → 4NO₂(g) + 6H₂O(g)
From the equation, we can see that 4 moles of NH₃ produce 6 moles of H₂O. This means there is a mole ratio of NH₃ to H₂O of 4:6 or simply a 2:3 ratio. To calculate the moles of NH₃ needed for 12.5 moles of H₂O, we set up a proportion:
(4 mol NH₃ / 6 mol H₂O) = (x mol NH₃ / 12.5 mol H₂O)
By cross-multiplying and solving for x, we get:
x = (4 mol NH₃ * 12.5 mol H₂O) / 6 mol H₂O = 8.33 mol NH₃
Therefore, 8.33 moles of NH₃ are needed to produce 12.5 mol of H₂O.