To determine the number of moles of [tex]\( CO_2 \)[/tex] produced from the given moles of [tex]\( H_2O \)[/tex], we need to refer to the stoichiometry of the chemical reaction:
[tex]\[
CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O
\][/tex]
The stoichiometric coefficients from the balanced equation tell us that for every 1 mole of [tex]\( CO_2 \)[/tex] produced, 2 moles of [tex]\( H_2O \)[/tex] are produced. Therefore, the ratio of [tex]\( H_2O \)[/tex] to [tex]\( CO_2 \)[/tex] is 2:1.
If 10 moles of [tex]\( H_2O \)[/tex] are produced, we can set up the following proportion based on the stoichiometric ratio:
[tex]\[
\frac{H_2O}{CO_2} = \frac{2}{1}
\][/tex]
Since we have 10 moles of [tex]\( H_2O \)[/tex]:
[tex]\[
\frac{10}{CO_2} = \frac{2}{1}
\][/tex]
Solving for [tex]\( CO_2 \)[/tex]:
[tex]\[
CO_2 = \frac{10}{2} = 5 \, \text{moles}
\][/tex]
Thus, 5 moles of [tex]\( CO_2 \)[/tex] are produced when 10 moles of [tex]\( H_2O \)[/tex] are produced.
The correct answer is:
[tex]\[
5
\][/tex]
