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 for the given reactions in acidic solution are as follows: (a) Oxidation of nitrous acid to nitrate ion (HNO₂ → NO₃⁻): \[ \mathrm{HNO_2} \rightarrow \mathrm{NO_3^-} + \mathrm{H_2O} + 2\mathrm{H^+} \] (b) Oxidation of nitrogen gas to nitrous oxide (N₂ → N₂O): \[ \mathrm{N_2} + \mathrm{H_2O} \rightarrow \mathrm{N_2O} \]

Step-by-step solution

Write the unbalanced equation

For nitrous acid (HNO₂) oxidation: HNO₂ → NO₃⁻

Balance atoms other than oxygen and hydrogen

The nitrogen atom is already balanced.

Balance the oxygen atoms

There are 2 oxygen atoms on the left and 3 on the right: HNO₂ → NO₃⁻ + H₂O

Balance the hydrogen atoms

Now, there are 4 hydrogen atoms on the left and 2 on the right. Balance by adding 2 hydrogen ions: HNO₂ → NO₃⁻ + H₂O + 2H⁺

Balance the charges

The charges on both sides are equal (+1). Thus, the half-reaction for the oxidation of nitrous acid in acidic solution is: HNO₂ → NO₃⁻ + H₂O + 2H⁺ (b) Oxidation of nitrogen gas to nitrous oxide (N₂ → N₂O)

Write the unbalanced equation

For nitrogen gas (N₂) oxidation: N₂ → N₂O

Balance atoms other than oxygen and hydrogen

The nitrogen atoms are already balanced.

Balance the oxygen atoms

There is one oxygen atom on the right side: N₂ + H₂O → N₂O

Balance the hydrogen atoms

There are 2 hydrogen atoms on the left, so no additional hydrogen ions are needed.

Balance the charges

The charges on both sides are equal (0). Thus, the half-reaction for the oxidation of nitrogen gas in acidic solution is: N₂ + H₂O → N₂O