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ANSWER
The number of moles of water produced is 4.54 moles
EXPLANATION
Given that:
[tex]\text{ CH}_4\text{ }+2O_2\text{ }\rightarrow\text{ CO}_2\text{ }+\text{ 2H}_2O[/tex]The mass of carbon dioxide is 100g
To find the moles of water, follow the steps below
Step 1: Calculate the moles of carbon dioxide using the formula below
[tex]\text{ Mole }=\text{ }\frac{\text{ mass}}{molar\text{ mass}}[/tex]Recall, that the molar mass of CO2 is 44.01 g/ mol
Step 2: Substitute the given data into the formula in step 1
[tex]\begin{gathered} \text{ mole }=\text{ }\frac{100}{44.01} \\ \text{ mole }=2.272\text{ moles} \end{gathered}[/tex]Step 3: Find the moles of water produced using a stoichiometry ratio
In the reaction above, 1 mole of CO2 is equivalent to 2 moles of H2O
Let x represent the number of moles of water
[tex]\begin{gathered} \text{ 1 mole CO}_2\text{ }\rightarrow\text{ 2 moles H}_2O \\ \text{ 2.272 moles CO}_2\text{ }\rightarrow\text{ x moles H}_2O \\ \text{ Cross multiply} \\ \text{ 1 mole CO}_2\text{ }\times\text{ x moles H}_2O\text{ }=\text{ 2 moles H}_2O\times2.272\text{ moles CO}_2 \\ \text{ Isolate x} \\ \text{ x }=\frac{2\text{ moles H}_2O\times2.272\cancel{molesCO_2}}{1\cancel{moleCO_2}} \\ \text{ x }=\text{ 2 }\times\text{ 2.272} \\ \text{ x }=\text{ 4.54 moles} \end{gathered}[/tex]Therefore, the number of moles of water produced is 4.54 moles
