To solve this problem, we need to determine how many moles of hexane ([tex]\(C_6H_{14}\)[/tex]) are required to produce 18.4 moles of carbon dioxide ([tex]\(CO_2\)[/tex]), using the balanced chemical equation:
[tex]\[
2 C_6H_{14} + 19 O_2 \rightarrow 12 CO_2 + 14 H_2O
\][/tex]
### Step-by-Step Solution
1. Identify the stoichiometric coefficients: From the balanced equation, we see that 2 moles of [tex]\(C_6H_{14}\)[/tex] produce 12 moles of [tex]\(CO_2\)[/tex].
2. Set up the ratio from the balanced equation:
[tex]\[
\frac{2 \text{ moles of } C_6H_{14}}{12 \text{ moles of } CO_2}
\][/tex]
3. Determine the number of moles of [tex]\(C_6H_{14}\)[/tex] required for 18.4 moles of [tex]\(CO_2\)[/tex]:
We need to find how many moles of [tex]\(C_6H_{14}\)[/tex] ([tex]\(x\)[/tex]) correspond to 18.4 moles of [tex]\(CO_2\)[/tex]. Set up the proportion:
[tex]\[
\frac{2 \text{ moles of } C_6H_{14}}{12 \text{ moles of } CO_2} = \frac{x \text{ moles of } C_6H_{14}}{18.4 \text{ moles of } CO_2}
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \left(\frac{2}{12}\right) \times 18.4
\][/tex]
Simplify the fraction:
[tex]\[
x = \left(\frac{1}{6}\right) \times 18.4
\][/tex]
Multiply:
[tex]\[
x = 3.0666666666666664
\][/tex]
So, the number of moles of [tex]\(C_6H_{14}\)[/tex] required to produce 18.4 moles of [tex]\(CO_2\)[/tex] is approximately 3.07 moles.
### Conclusion
The correct answer from the multiple choices provided is:
3.07 mol
