Let's analyze the given chemical reaction:
[tex]\[ 2 \text{C} (s) + \text{O}_2 (g) \rightarrow 2 \text{CO}_2 (g) \][/tex]
This reaction shows that:
- 1 mole of [tex]\(\text{O}_2\)[/tex] reacts to produce 2 moles of [tex]\(\text{CO}_2\)[/tex].
Given that 0.25 moles of [tex]\(\text{O}_2\)[/tex] are reacting, we need to find the moles of [tex]\(\text{CO}_2\)[/tex] produced:
1. According to the stoichiometry of the reaction, 1 mole of [tex]\(\text{O}_2\)[/tex] produces 2 moles of [tex]\(\text{CO}_2\)[/tex].
2. Thus, the moles of [tex]\(\text{CO}_2\)[/tex] produced = (0.25 moles [tex]\(\text{O}_2\)[/tex]) * (2 moles [tex]\(\text{CO}_2\)[/tex] / 1 mole [tex]\(\text{O}_2\)[/tex]).
Using the stoichiometric ratio, we calculate:
[tex]\[ 0.25 \text{ moles } \text{O}_2 \times \frac{2 \text{ moles } \text{CO}_2}{1 \text{ mole } \text{O}_2} = 0.5 \text{ moles } \text{CO}_2 \][/tex]
So, the moles of [tex]\(\text{CO}_2\)[/tex] produced when 0.25 moles of [tex]\(\text{O}_2\)[/tex] reacts is:
[tex]\[ \boxed{0.5} \][/tex] moles.
