Write equations for the half-reactions that occur in the electrolysis of molten potassium bromide.

During the electrolysis of molten potassium bromide, a key process that occurs is the reduction half-reaction. This reaction takes place at the cathode, which is the negatively charged electrode. Ions that gain electrons during electrolysis are reduced, and this process is critical for transforming ions into their elemental form.

For the given exercise, the reduction half-reaction involves potassium ions (\(K^+\)). These ions gain electrons to become neutral atoms of potassium metal (\(K(s)\)). The equation representing this change is: \[ K^+ + e^- \rightarrow K(s) \] This simple equation also encapsulates the concept of electroplating, where a metal is deposited onto an electrode.

In electrolysis, the reduction half-reaction is vital because it produces the substance the process aims to extract. Understanding this half-reaction helps students realize the transformations occurring at the cathode during electrolysis.

In parallel to the reduction at the cathode, an oxidation half-reaction occurs at the anode, which is the positively charged electrode in the process of electrolysis. Oxidation involves the loss of electrons from a species. The liberated electrons then travel through the external circuit to the cathode, enabling the reduction process to take place.

For molten potassium bromide (\(KBr\)), the oxidation half-reaction concerns the bromide ions (\(Br^-\) ions). These ions release electrons, thereby transforming into bromine gas (\(Br_2(g)\)). The equation for this transformation is: \[ 2Br^- \rightarrow Br_2(g) + 2e^- \]It's important to note that oxidation is not just about the loss of electrons; it also encompasses the overall increase in oxidation states, which in this scenario involves going from \text{-}1 in bromide ions to 0 in bromine gas. Mastery of oxidation reactions is essential for understanding various chemical processes, including battery operations and corrosion.

To ensure that the chemical equation accurately reflects the conservation of mass and charge, balancing half-reactions is a critical step in the process of electrolysis. In the context of our exercise, the half-reactions represent the transformations of potassium ions and bromide ions separately. The balancing process ensures that the number of electrons lost in oxidation equals the number of electrons gained in reduction.

In our particular example, the half-reactions are:

• Reduction at cathode: \( K^+ + e^- \rightarrow K(s) \)
• Oxidation at anode: \(2Br^- \rightarrow Br_2(g) + 2e^- \)

These reactions are already balanced in terms of atoms and charge. For every two bromide ions that lose a total of two electrons, there are two potassium ions each gaining one electron. Instruction in balancing equations is fundamental for students because it lays the groundwork for understanding complex redox reactions and stoichiometry in chemistry.