21. Balancing Chemical Equations Write the balanced chemical equation for the reaction in which methane, \( \mathrm{CH}_{4} \), reacts with oxygen gas to produce water and carbon dioxide.

To balance the chemical equation for the reaction where methane (\(\mathrm{CH_4}\)) reacts with oxygen gas (\(\mathrm{O_2}\)) to produce water (\(\mathrm{H_2O}\)) and carbon dioxide (\(\mathrm{CO_2}\)), follow these steps: 1. **Write the unbalanced equation:** \[ \mathrm{CH_4 + O_2 \rightarrow CO_2 + H_2O} \] 2. **Balance the carbon (C) atoms:** - There is 1 carbon atom in \(\mathrm{CH_4}\) and 1 carbon atom in \(\mathrm{CO_2}\). Carbon is already balanced. 3. **Balance the hydrogen (H) atoms:** - There are 4 hydrogen atoms in \(\mathrm{CH_4}\) and 2 hydrogen atoms in each \(\mathrm{H_2O}\) molecule. - To balance hydrogen, place a coefficient of 2 before \(\mathrm{H_2O}\): \[ \mathrm{CH_4 + O_2 \rightarrow CO_2 + 2\,H_2O} \] 4. **Balance the oxygen (O) atoms:** - On the right side, there are \(2\) oxygen atoms in \(\mathrm{CO_2}\) and \(2 \times 1 = 2\) oxygen atoms in \(2\,\mathrm{H_2O}\), totaling **4** oxygen atoms. - On the left side, each \(\mathrm{O_2}\) molecule has 2 oxygen atoms. To get 4 oxygen atoms, place a coefficient of 2 before \(\mathrm{O_2}\): \[ \mathrm{CH_4 + 2\,O_2 \rightarrow CO_2 + 2\,H_2O} \] 5. **Final Balanced Equation:** \[ \boxed{\mathrm{CH_4 + 2\,O_2 \rightarrow CO_2 + 2\,H_2O}} \] This equation ensures that the number of each type of atom is the same on both sides, adhering to the law of conservation of mass.