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Difficulty: MediumBalancing Redox Equations and Half-Reactions

Complete the balanced reduction half-reaction equation for the conversion of nitrate ions to nitrogen monoxide gas in an acidic medium by providing the missing stoichiometric coefficients. What are the values of the coefficients for hydrogen ions and electrons?

Answer:NO3−(aq)+【4】H+(aq)+【3】e−→NO(g)+2H2O(l)\text{NO}_3^-(\text{aq}) + 【4】\text{H}^+(\text{aq}) + 【3】e^- \rightarrow \text{NO}(\text{g}) + 2\text{H}_2\text{O}(\text{l})

Answer

The balanced reduction half-reaction requires 4 hydrogen ions (H⁺) and 3 electrons (e⁻).
The balanced half-reaction is NO₃⁻(aq) + 4H⁺(aq) + 3e⁻ → NO(g) + 2H₂O(l). Four hydrogen ions balance the four hydrogens present in the two water molecules on the right. Three electrons balance the net charge (+3 on the left reactant side versus 0 on the neutral product side), confirming that nitrogen is reduced from oxidation state +5 in NO₃⁻ to +2 in NO.

Step-by-Step Solution

1
Balance oxygen atoms using water molecules
One nitrate ion (NO₃⁻) has 3 oxygen atoms, and NO has 1 oxygen atom, requiring 2 H₂O molecules on the product side: NO₃⁻ → NO + 2 H₂O
In aqueous acid media, oxygen atoms are balanced by adding H₂O molecules to the oxygen-deficient side.
2
Balance hydrogen atoms using hydrogen ions
The right side has 4 hydrogen atoms in 2 H₂O, so 4 H⁺ ions must be added to the left side: NO₃⁻ + 4 H⁺ → NO + 2 H₂O
Hydrogen atoms in acidic media are balanced by adding H⁺ ions to the hydrogen-deficient side.
3
Balance electrical charge using electrons
Left side net charge = (-1) + 4(+1) = +3. Right side net charge = 0. Adding 3 electrons (3 e⁻) to the left side gives a net charge of 0 on both sides: NO₃⁻ + 4 H⁺ + 3 e⁻ → NO + 2 H₂O
Electrons are added to the side with the higher net positive charge to satisfy conservation of charge.

Key Concept

Half-Reaction Method for Balancing Redox Equations in Acidic Medium
Estimated Time:1m 30s
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Topics

Balancing Redox Equations and Half-Reactions

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