Final answer:
The mass of H₂ that must have reacted is approximately 0.10209 grams.
Step-by-step explanation:
The balanced equation for the Haber process is:
N₂(g) + 3H₂(g) → 2NH₃(g)
This equation shows that for every 3 moles of H₂, 2 moles of NH₃ are formed. To find the mass of H₂ that reacted, we can use the molar mass of NH₃. The molar mass of NH₃ is 17.03 g/mol, so we can set up a proportion:
(0.575 g NH₃) / (17.03 g/mol NH₃) = (x g H₂) / (2.0158 g/mol H₂)
Solving for x gives us x ≈ 0.10209 g H₂. Therefore, the mass of H₂ that must have reacted is approximately 0.10209 grams.