Write a balanced half-reaction for the product that forms at each electrode in the aqueous electrolysis of the following salts: (a) \(\mathrm{LiF} ;\) (b) \(\mathrm{SnSO}_{4}\).

Cation reduction is a core process in electrolysis, where positively charged ions gain electrons to form neutral atoms. This typically occurs at the cathode, the electrode where reduction occurs. For example, in the electrolysis of \text{SnSO}_4\, the cation \(\text{Sn}^{2+}\) undergoes reduction. The half-reaction is: \[\text{Sn}^{2+} + 2e^- \rightarrow \text{Sn} \]. Here, the tin ion gains two electrons to form solid tin metal. Understanding cation reduction helps us determine which substances will be reduced during electrolysis.

Anion oxidation is another key component of electrolysis. This occurs at the anode, the electrode where oxidation happens. Positively charged species lose electrons here. For example, during the electrolysis of \text{LiF}\, the possible oxidation of fluoride anion is represented by \(2\text{F}^- \rightarrow \text{F}_2 + 2e^- \). However, in aqueous solutions, water is more likely to be oxidized, forming oxygen gas: \[2\text{H}_2\text{O} \rightarrow \text{O}_2 + 4\text{H}^+ + 4e^- \]. Recognizing this likelihood is crucial for predicting products in an electrolysis process.

Aqueous solution electrolysis involves the breakdown of substances dissolved in water using an electric current. In such solutions, not only do the ions of the solute participate, but water molecules also play a significant role. For instance, in the electrolysis of \text{LiF}\, while one might initially consider the reduction of lithium ions and oxidation of fluoride ions, water is more likely to undergo reduction and oxidation, given its abundance: \[2\text{H}_2\text{O} + 2e^- \rightarrow \text{H}_2 + 2\text{OH}^- \] for reduction and \[2\text{H}_2\text{O} \rightarrow \text{O}_2 + 4\text{H}^+ + 4e^- \] for oxidation. This understanding helps in accurately predicting electrolysis products in aqueous solutions.

Writing balanced chemical reactions is essential to describe electrolysis processes accurately. Balancing ensures that the same number of each type of atom appears on both the reactant and product sides of a reaction. For instance, the reduction half-reaction of \(\text{SnSO}_4\) is \(\text{Sn}^{2+} + 2e^- \rightarrow \text{Sn} \), and an oxidation half-reaction of water can be \[2\text{H}_2\text{O} \rightarrow \text{O}_2 + 4\text{H}^+ + 4e^- \]. Ensuring these are balanced helps in understanding the conservation of mass and charge in chemical processes, which is fundamental for solving electrolysis problems.