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Step 1: Write the unbalanced half-reaction Nitrous acid (\(\mathrm{HNO_{2}}\)) is converted into nitrate ion (\(\mathrm{NO_{3}^{-}}\)). \[ \mathrm{HNO_{2}} \rightarrow \mathrm{NO_{3}^{-}} \] Step 2: Find the change of oxidation state The oxidation state for nitrogen in nitrous acid is +3, while it is +5 in nitrate ion. The nitrogen gains 2 electrons in the process (it's being oxidized). \[ \mathrm{HNO_{2}} \rightarrow \mathrm{NO_{3}^{-}} + 2e^{-} \] Step 3: Balance the other atoms by adding water and protons \(\mathrm{H^{+}}\) To balance the oxygen atoms, we can add one water molecule to the left side. \[ \mathrm{HNO_{2}} + \mathrm{H_{2}O} \rightarrow \mathrm{NO_{3}^{-}} + 2e^{-} \] Now, we balance the hydrogen atoms by adding 2 protons \(\mathrm{H^{+}}\) to the right side. \[ \mathrm{HNO_{2}} + \mathrm{H_{2}O} \rightarrow \mathrm{NO_{3}^{-}} + 2e^{-} + 2\mathrm{H^{+}} \] The balanced half-reaction for the oxidation of nitrous acid is: \[ \mathrm{HNO_{2}} + \mathrm{H_{2}O} \rightarrow \mathrm{NO_{3}^{-}} + 2e^{-} + 2\mathrm{H^{+}} \]

Step 1: Write the unbalanced half-reaction Dinitrogen (\(\mathrm{N_{2}}\)) is converted into nitrous oxide (\(\mathrm{N_{2}O}\)). \[ \mathrm{N_{2}} \rightarrow \mathrm{N_{2}O} \] Step 2: Find the change of oxidation state The oxidation state of nitrogen in dinitrogen is 0, while it is +1 in nitrous oxide. Each nitrogen gains 1 electron in this process (they're being oxidized). \[ \mathrm{N_{2}} \rightarrow \mathrm{N_{2}O} + 2e^{-} \] Step 3: Balance the other atoms by adding water and protons \(\mathrm{H^{+}}\) To balance the oxygen atom, we can add one water molecule to the left side. \[ \mathrm{N_{2}} + \mathrm{H_{2}O} \rightarrow \mathrm{N_{2}O} + 2e^{-} \] Now, we balance the hydrogen atoms by adding 2 protons \(\mathrm{H^{+}}\) to the right side. \[ \mathrm{N_{2}} + \mathrm{H_{2}O} \rightarrow \mathrm{N_{2}O} + 2e^{-} + 2\mathrm{H^{+}} \] The balanced half-reaction for the oxidation of dinitrogen is: \[ \mathrm{N_{2}} + \mathrm{H_{2}O} \rightarrow \mathrm{N_{2}O} + 2e^{-} + 2\mathrm{H^{+}} \]