Balance each of the following skeletal equations by using oxidation and reduction half-reactions. All the reactions take place in acidic solution. Identify the oxidizing agent and reducing agent in each reaction. (a) Reaction of thiosulfate ion with chlorine gas: \(\mathrm{Cl}_{2}(\mathrm{~g})+\mathrm{S}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq}) \longrightarrow \mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq})\) (b) Action of the permanganate ion on sulfurous acid: \(\mathrm{MnO}_{4}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{SO}_{3}(\mathrm{aq}) \rightarrow \mathrm{Mn}^{2+}(\mathrm{aq})+\mathrm{HSO}_{4}^{-}(\mathrm{aq})\) (c) Reaction of hydrosulfuric acid with chlorine: \(\mathrm{H}_{2} \mathrm{~S}(\mathrm{aq})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{S}(\mathrm{s})+\mathrm{Cl}^{-}(\mathrm{aq})\) (d) Reaction of chlorine in water: $$ \mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{HClO}(\mathrm{aq})+\mathrm{Cl}^{-} \text {(aq) } $$

Understanding oxidation and reduction half-reactions is crucial when balancing redox reactions. Oxidation refers to the loss of electrons, while reduction describes the gain of electrons. To balance redox reactions, one must first split the overall reaction into two separate half-reactions.

For instance, look at reaction (a) involving the thiosulfate ion and chlorine gas:
Oxidation: \( \text{S}_2 \text{O}_3^{2-} \rightarrow \text{SO}_4^{2-} + e^- \)
Reduction: \( \text{Cl}_2 + 2e^- \rightarrow 2 \text{Cl}^- \)

After writing out these half-reactions, they are then balanced for mass and charge. Oxygen atoms are balanced by adding water molecules, hydrogen atoms by adding hydrogen ions, and the charge is balanced by adding electrons. This ensures that the number of atoms of each element and the total charge is the same on both sides of the equation.

For example, to balance the oxygen atoms in the oxidation half-reaction of thiosulfate, one might add water molecules. Additional steps include balancing hydrogen by adding hydrogen ions and ensuring that the number of electrons lost in oxidation equals the electrons gained during reduction.

Identifying oxidizing and reducing agents is key for understanding how redox reactions occur. The oxidizing agent is the substance that gets reduced by accepting electrons, while the reducing agent gets oxidized by losing electrons.

To illustrate this with reaction (a): Chlorine gas \( \text{Cl}_2 \) is the oxidizing agent because it gains electrons to form chloride ions \( \text{Cl}^- \). On the other hand, the thiosulfate ion \( \text{S}_2 \text{O}_3^{2-} \) acts as the reducing agent since it loses electrons to form sulfate ions \( \text{SO}_4^{2-} \).

Although the terms might be confusing, simply remember: the oxidizing agent gets reduced, and the reducing agent gets oxidized. By identifying these agents, we gain insight into the direction of electron flow and the driving forces behind the reaction. This information is valuable for predicting reaction outcomes and for applications in fields like energy storage and corrosion prevention.

Balancing redox reactions in an acidic solution requires a nuanced approach, as the presence of \( H^+ \) ions needs to be considered. In acidic solutions, \( H^+ \) ions are abundant and can be freely used to balance hydrogen atoms in half-reactions. Water molecules are also used to balance oxygen atoms.

Let's take the reaction between permanganate and sulfurous acid (b) as an example. In an acidic solution, you need to add \( H^+ \) ions to balance any excess oxygen after adding water to the half-reactions for balancing purposes.
In the end, you should make sure the electrons lost in oxidation match the electrons gained in reduction. Once the half-reactions are balanced for mass (oxygen and hydrogen) and charge (electrons), they can be added together, giving a full balanced equation that accurately reflects the stoichiometry and conservation principles expected of a chemical reaction. Combining half-reactions is truly an interplay between science and art that requires practice and attention to detail.