To determine the total number of liters of [tex]\(O_2(g)\)[/tex] at STP (Standard Temperature and Pressure) needed to produce [tex]\(6.0 \times 10^{23}\)[/tex] molecules of [tex]\(H_2O(\ell)\)[/tex], we can follow a step-by-step solution:
1. Determine the number of moles of [tex]\(H_2O\)[/tex] required:
- Avogadro's number states that 1 mole of any substance contains [tex]\(6.022 \times 10^{23}\)[/tex] molecules.
- We need [tex]\(6.0 \times 10^{23}\)[/tex] molecules of [tex]\(H_2O\)[/tex].
- To find the number of moles of [tex]\(H_2O\)[/tex], we use the formula:
[tex]\[
\text{Moles of } H_2O = \frac{6.0 \times 10^{23} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mole}}
\][/tex]
This gives us:
[tex]\[
\text{Moles of } H_2O \approx 0.996 \text{ moles}
\][/tex]
2. Determine the number of moles of [tex]\(O_2\)[/tex] required using stoichiometry:
- The balanced chemical equation is [tex]\(2 H_2(g) + O_2(g) \rightarrow 2 H_2O(l)\)[/tex].
- According to the equation, 1 mole of [tex]\(O_2\)[/tex] produces 2 moles of [tex]\(H_2O\)[/tex].
- Therefore, to produce 0.996 moles of [tex]\(H_2O\)[/tex], we need:
[tex]\[
\text{Moles of } O_2 = \frac{0.996 \text{ moles of } H_2O}{2}
\][/tex]
This gives us:
[tex]\[
\text{Moles of } O_2 \approx 0.498 \text{ moles}
\][/tex]
3. Calculate the volume of [tex]\(O_2(g)\)[/tex] needed at STP:
- At STP, 1 mole of any gas occupies 22.4 liters.
- To find the volume of [tex]\(O_2\)[/tex] required, we multiply the number of moles of [tex]\(O_2\)[/tex] by the molar volume:
[tex]\[
\text{Volume of } O_2 \approx 0.498 \text{ moles} \times 22.4 \text{ L/mole}
\][/tex]
This gives us:
[tex]\[
\text{Volume of } O_2 \approx 11.16 \text{ L}
\][/tex]
Therefore, the total number of liters of [tex]\(O_2(g)\)[/tex] at STP needed to produce [tex]\(6.0 \times 10^{23}\)[/tex] molecules of [tex]\(H_2O(\ell)\)[/tex] is closest to:
[tex]\[
\boxed{11.2 \text{ L}}
\][/tex]
Hence, the correct answer is:
[tex]\[ A. 11.2 \text{ L} \][/tex]
