Balance the half-reactions in Problem 19.42, assuming that they occur in acidic solution.

Verified step by step guidance

1. Identify the oxidation and reduction half-reactions from the given chemical equation. In each half-reaction, focus on the species that undergoes a change in oxidation state.
2. For the oxidation half-reaction, add water molecules to the side lacking oxygen to balance the oxygen atoms. Then, add hydrogen ions (H+) to the side lacking hydrogen to balance the hydrogen atoms.
3. For the reduction half-reaction, similarly add water molecules to the side lacking oxygen and hydrogen ions (H+) to the side lacking hydrogen to balance the atoms accordingly.
4. Balance the charges in each half-reaction by adding electrons (e-) to the side that has a higher positive charge for reduction, or to the side with a higher negative charge for oxidation.
5. Combine the balanced half-reactions. Adjust the coefficients of the entire equation so that the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction, ensuring that the overall charge and mass are balanced.

Key Concepts

Half-Reaction Method

The half-reaction method involves separating a redox reaction into its oxidation and reduction components. Each half-reaction is balanced individually for mass and charge, allowing for a clearer understanding of electron transfer. This method is essential for balancing complex redox reactions, especially in acidic or basic solutions.

Acidic Solution Conditions

In acidic solutions, the presence of hydrogen ions (H+) is crucial for balancing redox reactions. When balancing half-reactions in acidic conditions, H+ ions are added to the side lacking hydrogen atoms, and water molecules are used to balance oxygen atoms. Understanding how to manipulate these species is vital for achieving a balanced equation.

Charge Balance

Charge balance is a fundamental principle in balancing chemical equations, particularly in redox reactions. Each half-reaction must have equal total charges on both sides of the equation. This often involves adding electrons to one side to ensure that the overall charge is balanced, which is critical for the accuracy of the final balanced equation.