To solve this problem, we need to analyze the chemical reaction step by step.
The given chemical equation is:
[tex]\[ \text{Na}_2\text{O}_2 + \text{CO}_2 \rightarrow \text{Na}_2\text{CO}_3 + \text{O}_2 \][/tex]
1. Identify the molar ratio:
In the balanced chemical equation provided, each molecule of [tex]\(\text{CO}_2\)[/tex] reacts with [tex]\(\text{Na}_2\text{O}_2\)[/tex] to produce [tex]\(\text{Na}_2\text{CO}_3\)[/tex] and [tex]\(\text{O}_2\)[/tex] with a 1:1 molar ratio. This means one mole of [tex]\(\text{CO}_2\)[/tex] will produce one mole of [tex]\(\text{O}_2\)[/tex].
2. Understand the volume relationship:
At Standard Temperature and Pressure (STP), gases have a direct relationship between volume and moles. That is, the volume of gases is proportional to the number of moles.
3. Apply the volume ratio:
Given the 1:1 molar ratio in the reaction, the volume of [tex]\(\text{CO}_2\)[/tex] used will be equal to the volume of [tex]\(\text{O}_2\)[/tex] produced.
4. Given information:
We are given that 2.80 liters of [tex]\(\text{CO}_2\)[/tex] are used in the reaction.
5. Calculate the volume of [tex]\(\text{O}_2\)[/tex]:
Because the molar and volume ratio is 1:1, the volume of [tex]\(\text{O}_2\)[/tex] produced will be the same as the volume of [tex]\(\text{CO}_2\)[/tex] used.
Therefore, the volume of [tex]\(\text{O}_2\)[/tex] produced is:
[tex]\[ 2.80 \text{ liters} \][/tex]
So the correct answer is:
[tex]\[ \boxed{2.80 \text{ liters}} \][/tex]
