Balance the equations below assuming they occur in an acidic solution. (a) \(\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{Sn}^{2+} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{Sn}^{4+}\) (b) \(\mathrm{PbO}_{2}+\mathrm{Hg} \longrightarrow \mathrm{Hg}_{2}^{2+}+\mathrm{Pb}^{2+}\) (c) \(\mathrm{Al}+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \longrightarrow \mathrm{Al}^{3+}+\mathrm{Cr}^{3+}\)

Understanding oxidation and reduction is crucial for balancing redox reactions. In terms of chemical processes, oxidation refers to the loss of electrons by a molecule, atom, or ion. Conversely, reduction is the gain of electrons. These processes always occur together; when one species undergoes oxidation, another undergoes reduction. This simultaneous action justifies the term redox reaction, as it encompasses both reduction and oxidation steps.

In a redox reaction, the substance that donates electrons (the one oxidized) is known as the reducing agent, while the one that gains electrons (the one reduced) is the oxidizing agent. The movement of electrons from one species to another is key to understanding how to balance redox reactions and predict the direction and feasibility of chemical reactions.

Assigning oxidation numbers to the atoms in a chemical equation is the first step in the method for balancing redox reactions. Oxidation numbers represent the theoretical charges on atoms if the compound was composed of ions. They help identify which elements are oxidized and which are reduced. To assign oxidation numbers, one follows a set of rules such as: elements in their elemental form have an oxidation number of zero; for a simple monoatomic ion, the oxidation number is equal to the charge of the ion; in compounds, fluorine is assigned a -1 oxidation number, oxygen is generally -2 (with exceptions), and hydrogen is usually +1 (with exceptions).

By comparing oxidation numbers before and after the reaction, you can determine which species have increased (oxidation) or decreased (reduction) their oxidation state, which is essential for balancing the reaction properly.

Balancing redox reactions requires an understanding of the interplay between oxidation states and electron transfer. To balance redox reactions, particularly in acidic solutions, the following steps are essential: First, assign oxidation numbers to determine which atoms are oxidized and reduced. Then, write out the separate half-reactions for the oxidation and reduction processes. Next, balance the atoms that undergo changes in oxidation state, followed by balancing the oxygen atoms by adding water molecules as needed, and then balance the hydrogen atoms by adding H⁺ ions. Finally, balance the overall charge by adding electrons.

Remember, it is crucial that the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction. Once the half-reactions are balanced separately, they can be combined to give the balanced overall equation. The coefficients from the balanced half-reactions should multiply through to all species in those half-reactions, adjusting the coefficients for the other compounds in the overall reaction as needed to ensure mass and charge balance.

The half-reaction method is a systematic process for balancing redox reactions. It splits the overall reaction into two separate half-reactions: one for oxidation and another for reduction. Each half-reaction is balanced independently, which simplifies the complexity of the process.

Here's a general approach to using the half-reaction method:

• Write down each half-reaction and balance the main elements involved, excluding oxygen and hydrogen.
• Balance oxygen by adding H₂O molecules.
• Balance hydrogen by adding H⁺ ions (in acidic solution).
• Balance the charge by adding electrons to one side of the half-reaction.
• Ensure that the number of electrons is balanced by multiplying the half-reactions by coefficients that equalize the electrons transferred.
• Add the balanced half-reactions together, cancel out identical entities on both sides, and confirm that atoms and charges are balanced in the final equation.

This method is particularly useful for complex redox reactions and provides a clear path for students to follow to ensure accuracy in their solutions.