To determine how many moles of hexane (C₆H₁₄) must burn to form 18.4 moles of carbon dioxide (CO₂), we need to analyze 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]
The balanced chemical equation tells us that:
- 2 moles of hexane (C₆H₁₄) produce 12 moles of carbon dioxide (CO₂).
First, we determine the molar ratio between hexane and carbon dioxide:
[tex]\[ \frac{\text{moles of CO}_2}{\text{moles of C}_6\text{H}_{14}} = \frac{12}{2} = 6 \][/tex]
This means that 1 mole of hexane (C₆H₁₄) produces 6 moles of carbon dioxide (CO₂).
Next, we need to find out how many moles of hexane are required to produce 18.4 moles of carbon dioxide. We set up the following ratio:
[tex]\[ \frac{\text{moles of C}_6\text{H}_{14}}{\text{moles of CO}_2} = \frac{1}{6} \][/tex]
Now, let's use this ratio to calculate the moles of hexane needed to produce 18.4 moles of carbon dioxide:
[tex]\[ \text{moles of C}_6\text{H}_{14} = \frac{18.4 \text{ moles of CO}_2}{6} \][/tex]
[tex]\[ \text{moles of C}_6\text{H}_{14} = 3.0666666666666664 \][/tex]
Rounding to two significant figures, we get:
[tex]\[ \text{moles of C}_6\text{H}_{14} \approx 3.07 \][/tex]
Thus, the number of moles of hexane required to form 18.4 moles of carbon dioxide is approximately [tex]\( 3.07 \, \text{mol} \)[/tex].
The correct answer is: [tex]\( 3.07 \, \text{mol} \)[/tex].
