Question

Balance the following redox equations. All occur in acid solution. (a) \(\mathrm{Ag}(\mathrm{s})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{Ag}^{+}(\mathrm{aq})\) (b) \(\mathrm{MnO}_{4}^{-}(\mathrm{aq})+\mathrm{HSO}_{3}^{-}(\mathrm{aq}) \rightarrow\) \(\mathrm{Mn}^{2+}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq}\) (c) \(\mathrm{Zn}(\mathrm{s})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{N}_{2} \mathrm{O}(\mathrm{g})\) (d) \(\mathrm{Cr}(\mathrm{s})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{Cr}^{3+}(\mathrm{aq})+\mathrm{NO}(\mathrm{g})\)

Short answer

Balance the half-reactions for oxidation and reduction, ensure atoms and charges balance using H₂O, H⁺, and e⁻, then combine them.

Step-by-step solution

Identifying Oxidation and Reduction

For each equation, identify what is being oxidized and reduced. Remember, oxidation refers to the loss of electrons, while reduction means the gain of electrons.

Balancing Half-Reactions

Write separate half-reactions for the oxidation and reduction processes for each given equation. Make sure to balance all atoms other than O and H first.

Balancing Oxygen

Balance the oxygen atoms by adding water molecules (H₂O) to the side that needs oxygen in each half-reaction.

Balancing Hydrogen

Balance hydrogen atoms by adding hydrogen ions (H⁺) to the side that needs hydrogen in each half-reaction.

Balancing Charge

Balance the charges on each side of the half-reactions by adding electrons (e⁻). Ensure that the total charge is the same on both sides of the half-reaction.

Equalizing Electron Transfer

If needed, multiply the half-reactions by appropriate factors so that the electrons lost in the oxidation half-reaction equal the electrons gained in the reduction half-reaction.

Combining Half-Reactions

Add the balanced half-reactions together, ensuring that the electrons cancel each other out, combining them into the complete balanced redox equation.

Key concepts

Oxidation and Reduction

In a redox reaction, two processes occurring together are oxidation and reduction. Oxidation involves the loss of electrons from a substance, while reduction involves the gain of electrons. Identifying what gets oxidized and what gets reduced is crucial in balancing redox equations.
To determine oxidation and reduction:

• Look for changes in oxidation numbers of elements between reactants and products.
• An increase in oxidation number indicates oxidation.
• A decrease in oxidation number indicates reduction.

Example: In the reaction between silver and nitrate, Ag changes from 0 (elemental) to +1 (Ag⁺), indicating oxidation. NO₃⁻ changes from +5 (in NO₃⁻) to +3 (in NO₂), indicating reduction.

Half-Reaction Method

The half-reaction method is a systematic approach to balancing redox equations. It breaks the overall reaction into two separate parts: the oxidation half and the reduction half. This allows you to address each part of the redox process individually.
Here’s how to use the half-reaction method:

• Write the half-reactions for both reductions and oxidations separately.
• Balance all atoms except oxygen and hydrogen first.
• Add water ( H₂O) molecules to balance oxygen, as oxygen in acidic solutions can be balanced with water.
• Balance hydrogen using hydrogen ions (H⁺) since the reaction occurs in an acidic solution.
• Finally, add electrons to balance the charge on each side of the half-reaction.

This method is particularly useful in complex reactions, as it simplifies the process by focusing on changes in each species' oxidation state.

Balancing Chemical Equations

Balancing chemical equations ensures that the same number of each type of atom appears on both sides of the equation. In redox chemistry, this involves not just balancing atoms, but also the charges.
Steps for balancing redox reactions include:

• Ensure each atom type is balanced, adding water for oxygen and hydrogen ions for hydrogen.
• Balance the charge by adding electrons where needed. The number of electrons lost in the oxidation half should match the electrons gained in the reduction half.
• Combine the two half-reactions together, making sure the electrons cancel out so that they do not appear in the final equation.

By meticulously following these steps, we can achieve a balanced and chemically correct equation, preserving the conservation of mass and charge.

Acidic Solution Redox Chemistry

In acidic solutions, balancing redox reactions involves certain additional steps due to the presence of H⁺ ions. These steps ensure that both mass and charge are conserved in the equation.
When using the half-reaction method in acidic solutions:

• First, balance all elements in the equation except hydrogen and oxygen.
• Use water molecules to balance the oxygen atoms in each half-reaction.
• Add H⁺ ions to balance the hydrogen atoms that result from adding water molecules.
• Balance the electrical charge by including electrons. The number of electrons added should make the charges on both sides equal.

This method accommodates the acidic environment, allowing for the proper balancing of hydrogen ions and other atoms involved in the chemical reaction. Through this process, it's ensured that the redox reactions conform to real-life situations, like those found in cellular respiration and other biological processes.