To determine how many moles of Na₂O will be produced from 2.90 moles of Na, we can use the stoichiometric relationship given in the balanced chemical equation:
[tex]\[
4 \, \text{Na} + \text{O}_2 \rightarrow 2 \, \text{Na}_2\text{O}
\][/tex]
From this equation, we observe that 4 moles of Na react to produce 2 moles of Na₂O.
Step-by-step solution:
1. Begin with the given amount of Na: 2.90 moles.
2. Determine the stoichiometric relationship from the balanced equation:
- 4 moles of Na produce 2 moles of Na₂O.
3. Set up the conversion factor using this relationship:
[tex]\[
\text{Moles of } \text{Na}_2\text{O} = \left( \frac{2 \, \text{moles of Na}_2\text{O}}{4 \, \text{moles of Na}} \right) \times 2.90 \, \text{moles of Na}
\][/tex]
4. Simplify the conversion factor:
[tex]\[
\text{Moles of } \text{Na}_2\text{O} = \left( \frac{2}{4} \right) \times 2.90 = \left( 0.5 \right) \times 2.90 = 1.45 \, \text{moles}
\][/tex]
Thus, the number of moles of Na₂O produced when 2.90 moles of Na react completely is 1.45 moles, expressed to three significant figures.
So, the answer is:
There will be [tex]\(\boxed{1.45}\)[/tex] moles of [tex]\(\text{Na}_2\text{O}\)[/tex].
