Question

Write complete balanced half-reactions for (a) oxidation of nitrous acid to nitrate ion in acidic solution, (b) oxidation of \(\mathrm{N}_{2}\) to \(\mathrm{N}_{2} \mathrm{O}\) in acidic solution.

Short answer

The balanced half-reactions are: (a) Oxidation of HNO2 to NO3- in acidic solution: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 3H^{+} + 2e^{-}\) (b) Oxidation of N2 to N2O in acidic solution: \(N_{2} + H_{2}O \rightarrow N_{2}O + 2H^{+} + 2e^{-}\)

Step-by-step solution

Identify the species being oxidized

The species being oxidized in this process is nitrous acid (HNO2), and the product is the nitrate ion (NO3-).

Balance elements excluding oxygen and hydrogen

There is only one nitrogen atom on both sides, so the nitrogen atoms are already balanced: \(HNO_{2} \rightarrow NO_{3}^{-}\)

Balance oxygen atoms

There are two oxygen atoms in HNO2 and three in NO3-. Add one H2O molecule to the left side to balance the oxygens: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-}\)

Balance hydrogen atoms

There are now three hydrogen atoms on the left side of the equation and none on the right side. Add three H+ ions to the right side to balance the hydrogens: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 3H^{+}\)

Balance electrical charges

The left side has a total charge of 0 while the right side has a total charge of +2. Add two electrons (e-) to the right side to balance the electrical charges: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 3H^{+} + 2e^{-}\)

Verify the balanced half-reaction

The resulting balanced half-reaction looks like this: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 3H^{+} + 2e^{-}\) We can verify that it is correctly balanced, as there is an equal number of atoms of each element on both sides of the equation, and the overall charges are equal. ##Oxidation of N2 to N2O in acidic solution##

Identify the species being oxidized

The species being oxidized in this process is nitrogen gas (N2), and the product is nitrous oxide (N2O).

Balance elements excluding oxygen and hydrogen

There are two nitrogen atoms on both sides, so the nitrogen atoms are already balanced: \(N_{2} \rightarrow N_{2}O\)

Balance oxygen atoms

There are no oxygen atoms in N2, but one in N2O. Add one H2O molecule to the left side to balance the oxygen: \(N_{2} + H_{2}O \rightarrow N_{2}O\)

Balance hydrogen atoms

There are two hydrogen atoms on the left side of the equation and none on the right side. Add two H+ ions to the right side to balance the hydrogens: \(N_{2} + H_{2}O \rightarrow N_{2}O + 2H^{+}\)

Balance electrical charges

The left side has a total charge of 0 while the right side has a total charge of +2. Add two electrons (e-) to the right side to balance the electrical charges: \(N_{2} + H_{2}O \rightarrow N_{2}O + 2H^{+} + 2e^{-}\)

Verify the balanced half-reaction

The resulting balanced half-reaction looks like this: \(N_{2} + H_{2}O \rightarrow N_{2}O + 2H^{+} + 2e^{-}\) We can verify that it is correctly balanced, as there is an equal number of atoms of each element on both sides of the equation, and the overall charges are equal.