To determine how many moles of [tex]\( \text{Na}_2 \text{O} \)[/tex] will be produced from 2.90 moles of [tex]\( \text{Na} \)[/tex], we should follow these steps:
1. Understand the balanced chemical equation:
[tex]\[ 4 \text{Na} + \text{O}_2 \rightarrow 2 \text{Na}_2 \text{O} \][/tex]
This equation tells us that 4 moles of sodium (Na) produce 2 moles of sodium oxide (Na_2O).
2. Identify the moles of reactants provided:
If we have 2.90 moles of [tex]\( \text{Na} \)[/tex], we need to determine how many moles of [tex]\( \text{Na}_2 \text{O} \)[/tex] will be formed.
3. Use stoichiometry to find the relationship:
The equation indicates that 4 moles of [tex]\( \text{Na} \)[/tex] produce 2 moles of [tex]\( \text{Na}_2 \text{O} \)[/tex].
4. Set up the stoichiometric ratio:
If 4 moles of [tex]\( \text{Na} \)[/tex] produce 2 moles of [tex]\( \text{Na}_2 \text{O} \)[/tex], then the moles of [tex]\( \text{Na}_2 \text{O} \)[/tex] produced by 2.90 moles of [tex]\( \text{Na} \)[/tex] can be calculated as:
[tex]\[ \frac{2.90 \text{ moles of Na} \times 2 \text{ moles of } \text{Na}_2 \text{O}}{4 \text{ moles of Na}} \][/tex]
5. Perform the calculation:
[tex]\[ \frac{2.90 \times 2}{4} = \frac{5.80}{4} = 1.45 \][/tex]
6. Round the answer to three significant figures:
The result is already in three significant figures: 1.45.
Therefore, there will be [tex]\( \boxed{1.45} \)[/tex] moles of [tex]\( \text{Na}_2 \text{O} \)[/tex].
