Problem 57 - Chemistry: The Central Science

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.

Step-by-Step Solution

Answer

The balanced half-reactions are as follows: (a) Oxidation of nitrous acid to nitrate ion in acidic solution: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 4H^{+} + 2e^{-}\) (b) Oxidation of N2 to N2O in acidic solution: \(N_{2} + 2H_{2}O + 4e^{-} \rightarrow 2N_{2}O\)

Step 1: 1. Determine the oxidation states of nitrogen in the reactants and products

Nitrous acid (HNO2) has an oxidation state of +3 for nitrogen. In the nitrate ion (NO3-), the oxidation state of the nitrogen atom is +5. This indicates that the nitrogen atom has been oxidized from +3 to +5.

Step 2: 2. Write unbalanced half-reaction equations

Write the unbalanced half-reaction equations for the oxidation of HNO2 to NO3-. This gives: \(HNO_{2} \rightarrow NO_{3}^{-}\)

Step 3: 3. Balance the atoms

We balance the oxygen atoms by adding a water molecule (H2O) to the left side of the equation: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-}\) Now balance the hydrogen atoms by adding four hydrogen ions (4H+) to the right side of the equation: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 4H^{+}\)

Step 4: 4. Balance the charges by adding electrons

Lastly, balance the charges by adding the appropriate number of electrons (e-) to the right side of the equation: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 4H^{+} + 2e^{-}\) Now we have a balanced half-reaction for the oxidation of nitrous acid to nitrate ion in acidic solution: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 4H^{+} + 2e^{-}\) (b) Oxidation of N2 to N2O in acidic solution: First, we need to determine the oxidation states of nitrogen in N2 and N2O.

Step 5: 1. Determine the oxidation states of nitrogen in the reactants and products

In the nitrogen gas (N2), the oxidation state of the nitrogen atoms is 0. In nitrous oxide (N2O), the oxidation state of the nitrogen atoms is +2. This indicates that the nitrogen atom has been oxidized from 0 to +2.

Step 6: 2. Write unbalanced half-reaction equations

Write the unbalanced half-reaction formulas for the oxidation of N2 to N2O: \(N_{2} \rightarrow N_{2}O\)

Step 7: 3. Balance the atoms

Balance the nitrogen atoms by multiplying the right side of the equation by 2: \(N_{2} \rightarrow 2N_{2}O\) Now balance the oxygen atoms by adding two water molecules (2H2O) to the left side of the equation: \(N_{2} + 2H_{2}O \rightarrow 2N_{2}O\)

Step 8: 4. Balance the charges by adding electrons

Lastly, balance the charges by adding the appropriate number of electrons (e-) to the left side of the equation: \(N_{2} + 2H_{2}O + 4e^{-} \rightarrow 2N_{2}O\) Now we have a balanced half-reaction for the oxidation of N2 to N2O in acidic solution: \(N_{2} + 2H_{2}O + 4e^{-} \rightarrow 2N_{2}O\)