Sure, let's go through the problem step-by-step to find out how many moles of hexane (C₆H₁₄) are required to form 18.4 moles of carbon dioxide (CO₂) based on the given chemical reaction:
[tex]\[
2 \text{ C}_6\text{H}_{14} + 19 \text{ O}_2 \rightarrow 12 \text{ CO}_2 + 14 \text{ H}_2\text{O}
\][/tex]
1. Identify the stoichiometric ratio:
The balanced chemical equation tells us that 2 moles of C₆H₁₄ produce 12 moles of CO₂.
2. Form the proportion:
We need to form a proportion to find the moles of C₆H₁₄ required to produce a given amount of CO₂. According to the equation:
[tex]\[
\frac{2 \text{ moles of C}_6\text{H}_{14}}{12 \text{ moles of CO}_2} = \frac{x \text{ moles of C}_6\text{H}_{14}}{18.4 \text{ moles of CO}_2}
\][/tex]
Here, \( x \) represents the moles of C₆H₁₄ we need to find.
3. Solve the proportion:
We can solve for \( x \) by cross-multiplying and then isolating \( x \):
[tex]\[
x = \frac{2 \text{ moles of C}_6\text{H}_{14} \times 18.4 \text{ moles of CO}_2}{12 \text{ moles of CO}_2}
\][/tex]
[tex]\[
x = \frac{36.8}{12}
\][/tex]
4. Calculate the result:
Divide 36.8 by 12:
[tex]\[
x \approx 3.07 \text{ moles of C}_6\text{H}_{14}
\][/tex]
Therefore, the number of moles of hexane (C₆H₁₄) required to form 18.4 moles of carbon dioxide (CO₂) is approximately [tex]\( \boxed{3.07} \text{ moles} \)[/tex].
