1. Write the balanced chemical equation:

The reaction of sodium azide (NaN₃) produces sodium metal (Na) and nitrogen gas (N₂):

2 NaN₃(s) → 2 Na(s) + 3 N₂(g)

2. Determine the mole ratio:

The balanced equation shows that 2 moles of NaN₃ produce 3 moles of N₂.

3. Calculate the moles of N₂ produced:

* We are given 0.500 moles of NaN₃.

* Using the mole ratio from the balanced equation: (3 moles N₂ / 2 moles NaN₃)

* Multiply the moles of NaN₃ by the mole ratio: 0.500 moles NaN₃ * (3 moles N₂ / 2 moles NaN₃) = 0.750 moles N₂

Therefore, 0.750 moles of nitrogen gas are produced when 0.500 moles of sodium azide react.