To determine how many moles of [tex]\( O_2 \)[/tex] are required to produce 10 moles of [tex]\( H_2O \)[/tex], we need to refer to the balanced chemical equation given:
[tex]\[ C_3H_8 + 5 O_2 \rightarrow 3 CO_2 + 4 H_2O \][/tex]
From this equation, it is clear that:
- 5 moles of [tex]\( O_2 \)[/tex] produce 4 moles of [tex]\( H_2O \)[/tex].
We need to find how many moles of [tex]\( O_2 \)[/tex] are needed to produce 10 moles of [tex]\( H_2O \)[/tex]. We can set up a proportion to solve for the unknown number of moles of [tex]\( O_2 \)[/tex]:
[tex]\[
\frac{5 \text{ moles of } O_2}{4 \text{ moles of } H_2O} = \frac{x \text{ moles of } O_2}{10 \text{ moles of } H_2O}
\][/tex]
Cross-multiplying to solve for [tex]\( x \)[/tex]:
[tex]\[
4x = 5 \times 10
\][/tex]
So,
[tex]\[
4x = 50
\][/tex]
Dividing both sides by 4:
[tex]\[
x = \frac{50}{4} = 12.5
\][/tex]
Therefore, 12.5 moles of [tex]\( O_2 \)[/tex] are required to produce 10 moles of [tex]\( H_2O \)[/tex].
The correct answer is:
[tex]\[
\boxed{12.5}
\][/tex]
