Question

Balance this redox reaction (in acidic solution). $$ \mathrm{Cu}(\mathrm{s})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{NO}_{2}(\mathrm{~g}) $$

Short answer

The balanced equation is: \( \mathrm{Cu} + 2 \mathrm{H}^{+} + \mathrm{NO}_{3}^{-} \rightarrow \mathrm{Cu}^{2+} + \mathrm{NO}_{2} + \mathrm{H}_{2}O \).

Step-by-step solution

Identify Oxidation and Reduction Half-Reactions

First, determine which elements are being oxidized and reduced. Copper (Cu) is oxidized from 0 to +2, and Nitrogen in \( \text{NO}_3^{-} \) is reduced from +5 in \( \text{NO}_3^{-} \) to +4 in \( \text{NO}_2 \).

Write Oxidation Half-Reaction

The oxidation half-reaction involves copper: \[ \mathrm{Cu} \rightarrow \mathrm{Cu}^{2+} + 2e^{-} \]

Write Reduction Half-Reaction

The reduction half-reaction involves nitrate: \[ \mathrm{NO}_{3}^{-} + 2H^{+} + e^{-} \rightarrow \mathrm{NO}_{2} + H_{2}O \]

Balance Electrons between Half-Reactions

Make sure the electrons lost in the oxidation half-reaction equals electrons gained in the reduction half-reaction. We have already balanced electrons as both reactions involve 2 electrons.

Combine Balanced Half-Reactions

Add the balanced half-reactions together, ensuring that electrons cancel out:\[ \mathrm{Cu} + 2 \mathrm{H}^{+} + \mathrm{NO}_{3}^{-} \rightarrow \mathrm{Cu}^{2+} + \mathrm{NO}_{2} + \mathrm{H}_{2}O \]

Verify Atoms and Charges Balance

Check that each element is balanced on both sides, and ensure the charges match. Here, we have: Cu, two H, one N, and three O atoms on both sides, with a net charge of +1 on each side.

Key concepts

Oxidation and Reduction

Understanding oxidation and reduction is essential for solving redox reactions. These processes describe the transfer of electrons between substances. In every redox reaction, oxidation refers to the loss of electrons by a molecule, atom, or ion.
On the other hand, reduction signifies the gain of electrons.
In our example, copper (Cu) is oxidized because it loses electrons, transforming from Cu (0) to Cu\(^{2+}\). This means it loses two electrons. Meanwhile, nitrogen in nitrate ion (\(\text{NO}_3^-\)) is reduced. It gains electrons, transitioning from an oxidation state of +5 to +4 in \(\text{NO}_2\).
Always remember that the substance that gets oxidized is the reducing agent (since it donates electrons), and the one getting reduced is the oxidizing agent (as it accepts electrons). Recognizing these can help in balancing complex reactions.

Half-Reactions

Half-reactions simplify the process of balancing redox reactions by isolating the oxidation and reduction processes. They allow us to see clearly the flow of electrons.
Each half-reaction focuses on one part of the redox equation. For oxidation, we write out the species losing electrons, while for reduction, the species gaining electrons.
In our specific redox equation:

• The oxidation half-reaction is: \[ \text{Cu} \rightarrow \text{Cu}^{2+} + 2e^- \]
• The reduction half-reaction is: \[ \text{NO}_3^- + 2H^+ + e^- \rightarrow \text{NO}_2 + H_2O \]

After writing them out, it becomes easier to see how electrons are transferred and balance each half-reaction's electron count. This is necessary before combining them to ensure that the number of electrons lost equals the number gained.

Acidic Solution Balancing

Balancing redox reactions in acidic solutions involves more than just balancing charges and atoms. It includes adding \( \text{H}^+ \) ions to reflect the acidic environment.
In an acidic solution,\( \text{H}^+ \) ions not only help in balancing hydrogen atoms but can also influence the overall charge balance of the reaction.
Take a look at our reduction half-reaction from above: \[ \text{NO}_3^- + 2H^+ + e^- \rightarrow \text{NO}_2 + H_2O \]
The \( \text{H}^+ \) ions are necessary to balance the hydrogen in the final product \( \text{H}_2O \). Also, in an acidic solution, the presence of \( \text{H}^+ \) helps maintain the electrical charge across the reaction. This aspect of balancing ensures that all atoms, including hydrogen and oxygen, as well as charges, are equal on both sides of the reaction. Always double-check your final equation to verify that both mass and charge are balanced.