Let's break down the question step-by-step.
The given chemical equation is:
[tex]\[ C_5H_{12} + 8 O_2 \rightarrow 5 CO_2 + 6 H_2O \][/tex]
We are provided with 3.50 moles of oxygen ([tex]\(O_2\)[/tex]) and we need to determine how many moles of pentane ([tex]\(C_5H_{12}\)[/tex]) can be formed from it.
1. Identify the mole ratio:
According to the balanced chemical equation, 1 mole of [tex]\(C_5H_{12}\)[/tex] reacts with 8 moles of [tex]\(O_2\)[/tex].
2. Determine the conversion factor:
To convert moles of [tex]\(O_2\)[/tex] to moles of [tex]\(C_5H_{12}\)[/tex], we use the mole ratio from the balanced equation:
[tex]\[ \frac{1 \text{ mole } C_5H_{12}}{8 \text{ moles } O_2} \][/tex]
3. Apply the conversion factor:
Multiply the given moles of [tex]\(O_2\)[/tex] by the conversion factor to get the moles of [tex]\(C_5H_{12}\)[/tex]:
[tex]\[
3.50 \text{ moles } O_2 \times \frac{1 \text{ mole } C_5H_{12}}{8 \text{ moles } O_2}
\][/tex]
4. Calculate:
[tex]\[
3.50 \text{ moles } O_2 \times \frac{1 \text{ mole } C_5H_{12}}{8 \text{ moles } O_2} = 0.4375 \text{ moles } C_5H_{12}
\][/tex]
Thus, from 3.50 moles of [tex]\(O_2\)[/tex], you can form 0.4375 moles of [tex]\(C_5H_{12}\)[/tex].
The correct option showing this conversion would be:
[tex]\[ 3.50 \text{ moles } O_2 \times \frac{1 \text{ mole } C_5H_{12}}{8 \text{ moles } O_2} \][/tex]
This option correctly uses the stoichiometric ratio from the balanced equation to find how many moles of [tex]\(C_5H_{12}\)[/tex] could be formed from the given moles of [tex]\(O_2\)[/tex].
