Use the half-reaction method to balance each redox reaction occurring in acidic aqueous solution. (a) \(\mathrm{I}^{-}(a q)+\mathrm{NO}_{2}^{-}(a q) \longrightarrow \mathrm{I}_{2}(s)+\mathrm{NO}(g)\) (b) \(\mathrm{BrO}_{3}^{-}(a q)+\mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{Br}^{-}(a q)+\mathrm{N}_{2}(g)\) (c) \(\mathrm{NO}_{3}{ }^{-}(a q)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Sn}^{4+}(a q)+\mathrm{NO}(g)\)

The half-reaction method is an essential process in the field of chemistry, particularly when dealing with redox (reduction-oxidation) reactions. The method involves breaking down a complex redox reaction into two simpler parts: the oxidation half-reaction and the reduction half-reaction. Each half-reaction represents either a loss of electrons (oxidation) or a gain of electrons (reduction). By focusing on one half at a time, it becomes more manageable to balance the reaction.

To balance a redox reaction using the half-reaction method, you follow a sequence of steps. First, divide the reaction into its oxidation and reduction halves. Then, balance the atoms for each element, other than oxygen and hydrogen. Next, balance oxygen by adding water molecules and hydrogen by adding protons (H+). Finally, balance the charges by adding electrons. After the individual halves are balanced, they are recombined, ensuring that the number of electrons lost in one half equals the number gained in the other. This step-by-step approach clarifies the balancing act and helps maintain atomic and charge balance throughout the process.

Oxidation and reduction are two fundamental concepts in a redox reaction. Oxidation is the process where an atom, ion, or molecule loses electrons, and as a result, its oxidation state increases. In contrast, reduction occurs when an atom, ion, or molecule gains electrons, leading to a decrease in its oxidation state.

In the context of balancing redox reactions, identifying what gets oxidized and what gets reduced is crucial. For example, in the reaction \(\mathrm{I}^-\rightarrow \mathrm{I}_2(s)\), iodine atoms lose electrons and are oxidized, whereas in \(\mathrm{NO}_{2}^-\rightarrow \mathrm{NO}(g)\), the nitrogen dioxide gains an electron and is reduced. By recognizing these changes, we can systematically apply the half-reaction method to balance the overall redox reaction.

Redox reactions often take place in different mediums which can affect the balancing process. In an acidic aqueous solution, additional protons (H+) are available, which are used while balancing hydrogen atoms. Also, the medium provides the necessary conditions for the solvation and appropriate ionic reactions to occur.

When working with redox reactions in an acidic medium, you need to first balance all atoms except hydrogen and oxygen. Then, to balance the oxygen atoms, you typically add water molecules. To balance the hydrogen atoms, you add the protons (H+). Adjusting for these ions ensures that the reaction obeys the law of conservation of mass for both atoms and charges.

One of the most critical aspects of balancing redox reactions is ensuring atomic and charge balance. Every atom that enters a reaction must be accounted for in the products, and the net charge on both sides of the reaction must also be equal. This follows the law of conservation of matter and the principle of electrical neutrality.

To achieve atomic balance, make sure that the number of each type of atom is the same on both sides of the reaction. For the charge balance, add electrons to either the oxidation or reduction half-reaction until the net charge is the same on both sides of each half-reaction. These steps lead to a fully balanced redox equation, which is crucial for accurately representing the chemical processes occurring within the reaction. The step-by-step method involves careful attention to both atomic and charge balance, leading to a correct solution.