To determine the mass of water formed by the complete combustion of 1 mole of methane (CH₄), we can follow these steps:
1. Determine the Balanced Chemical Equation:
The balanced equation for the complete combustion of methane is:
[tex]\[
\text{CH}_4 + 2 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O}
\][/tex]
This equation indicates that 1 mole of methane produces 2 moles of water.
2. Calculate the Molar Mass of Methane (CH₄):
The molar mass of methane is calculated using the atomic masses of carbon and hydrogen:
[tex]\[
\text{Carbon (C)}: 12.01 \text{ g/mol} \\
\text{Hydrogen (H)}: 1.01 \text{ g/mol} \times 4 = 4.04 \text{ g/mol}
\][/tex]
[tex]\[
\text{Molar Mass of CH}_4 = 12.01 \text{ g/mol} + 4.04 \text{ g/mol} = 16.05 \text{ g/mol}
\][/tex]
3. Calculate the Molar Mass of Water (H₂O):
The molar mass of water is calculated using the atomic masses of hydrogen and oxygen:
[tex]\[
\text{Hydrogen (H)}: 1.01 \text{ g/mol} \times 2 = 2.02 \text{ g/mol} \\
\text{Oxygen (O)}: 16 \text{ g/mol}
\][/tex]
[tex]\[
\text{Molar Mass of H}_2\text{O} = 2.02 \text{ g/mol} + 16 \text{ g/mol} = 18.02 \text{ g/mol}
\][/tex]
4. Determine the Mass of Water Produced:
According to the balanced chemical equation, 1 mole of CH₄ produces 2 moles of H₂O. Now, using the molar mass of water:
[tex]\[
\text{Mass of H}_2\text{O} \text{ produced} = 2 \times \text{Molar Mass of H}_2\text{O}
\][/tex]
[tex]\[
\text{Mass of H}_2\text{O} \text{ produced} = 2 \times 18.02 \text{ g} = 36.04 \text{ g}
\][/tex]
Given the options 36 g, 0.5 g, 22 g, and 18 g, the closest and most appropriate value to our result is 36 g.
Therefore, the mass of water formed by the combustion of 1 mole of methane is approximately:
[tex]\[
\boxed{36 \text{ g}}
\][/tex]
