Problem 55 - 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: (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 1: Identify the species being oxidized

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

Step 2: Balance elements excluding oxygen and hydrogen

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

Step 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: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-}\)

Step 4: 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: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 3H^{+}\)

Step 5: 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: \(HNO_{2} + H_{2}O \rightarrow NO_{3}^{-} + 3H^{+} + 2e^{-}\)

Step 6: 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##

Step 1: Identify the species being oxidized

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

Step 2: Balance elements excluding oxygen and hydrogen

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

Step 3: 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: \(N_{2} + H_{2}O \rightarrow N_{2}O\)

Step 4: 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: \(N_{2} + H_{2}O \rightarrow N_{2}O + 2H^{+}\)

Step 5: 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: \(N_{2} + H_{2}O \rightarrow N_{2}O + 2H^{+} + 2e^{-}\)

Step 6: 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.