1. Balanced Chemical Equation:

First, we need the balanced chemical equation for the reaction of nitrogen gas (N₂) with hydrogen gas (H₂) to produce ammonia (NH₃):

N₂ + 3H₂ → 2NH₃

2. Mole Ratio:

The balanced equation tells us that 1 mole of N₂ reacts to produce 2 moles of NH₃. This is the mole ratio we'll use.

3. Calculation:

We know that 0.50 moles of NH₃ are produced. To find the moles of N₂ that reacted, we can set up a proportion:

(1 mol N₂) / (2 mol NH₃) = (x mol N₂) / (0.50 mol NH₃)

Solving for x:

x mol N₂ = (1 mol N₂) * (0.50 mol NH₃) / (2 mol NH₃)

x mol N₂ = 0.25 mol N₂

Answer:

Therefore, 0.25 moles of N₂ reacted to produce 0.50 moles of NH₃.