To determine how many moles of water ([tex]\( H_2O \)[/tex]) are used in a reaction given 528 grams of carbon dioxide ([tex]\( CO_2 \)[/tex]), we need to follow a detailed step-by-step approach. Here's the process:
1. Determine the Molar Masses:
- The molar mass of carbon dioxide ([tex]\( CO_2 \)[/tex]) is given as [tex]\( 44.01 \, \text{g/mol} \)[/tex].
- The molar mass of water ([tex]\( H_2O \)[/tex]) is given as [tex]\( 18.02 \, \text{g/mol} \)[/tex].
2. Calculate the Moles of [tex]\( CO_2 \)[/tex] Used:
- We start with 528 grams of [tex]\( CO_2 \)[/tex].
- The number of moles of [tex]\( CO_2 \)[/tex] can be calculated by dividing the mass of [tex]\( CO_2 \)[/tex] by its molar mass:
[tex]\[
\text{Moles of } CO_2 = \frac{\text{mass of } CO_2}{\text{molar mass of } CO_2}
\][/tex]
Substituting the given values:
[tex]\[
\text{Moles of } CO_2 = \frac{528 \, \text{g}}{44.01 \, \text{g/mol}} \approx 11.997 \, \text{moles}
\][/tex]
3. Relate Moles of [tex]\( CO_2 \)[/tex] to Moles of [tex]\( H_2O \)[/tex]:
- According to the reaction and the given context, the moles of [tex]\( H_2O \)[/tex] used are the same as the moles of [tex]\( CO_2 \)[/tex] used in the reaction.
- Therefore, the moles of [tex]\( H_2O \)[/tex] are also [tex]\( \approx 11.997 \, \text{moles} \)[/tex].
4. Choose the Closest Answer:
- Among the given options:
[tex]\[
12.0 \, \text{moles}, \, 72.0 \, \text{moles}, \, 216 \, \text{moles}, \, 528 \, \text{moles}
\][/tex]
- The calculated value [tex]\( \approx 11.997 \, \text{moles} \)[/tex] is closest to [tex]\( 12.0 \, \text{moles} \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{12.0 \, \text{moles}}
\][/tex]
