Let's break down the problem step-by-step:
1. Identify the mole ratio from the balanced chemical equation:
- The balanced equation is \( 4 Na + O_2 \rightarrow 2 Na_2O \).
- From this, we can determine the ratio of moles of \( Na \) to moles of \( Na_2O \).
- For every 4 moles of \( Na \), 2 moles of \( Na_2O \) are produced.
- Therefore, the ratio is \( 4:2 \), which simplifies to \( 2:1 \). This means 2 moles of \( Na \) produce 1 mole of \( Na_2O \).
2. Given the moles of \( Na \):
- We are given that 2.90 moles of \( Na \) react completely.
3. Use the mole ratio to find the moles of \( Na_2O \) produced:
- Since the ratio is 2 moles of \( Na \) to 1 mole of \( Na_2O \), we use this ratio to determine the number of moles of \( Na_2O \) produced from 2.90 moles of \( Na \).
- Mathematically, it translates to \( (2.90 \text{ moles of } Na) \times \left(\frac{1 \text{ mole of } Na_2O}{2 \text{ moles of } Na}\right) \).
4. Perform the calculation:
- \( \frac{2.90}{2} = 1.45 \) moles of \( Na_2O \).
Therefore, if 2.90 moles of [tex]\( Na \)[/tex] react completely, there will be 1.45 moles of [tex]\( Na_2O \)[/tex] produced. This value is expressed to three significant figures.
