Balance the following skeleton reactions, and identify the oxidizing and reducing agents: (a) \(\mathrm{As}_{4} \mathrm{O}_{6}(s)+\mathrm{MnO}_{4}^{-}(a q) \longrightarrow \mathrm{AsO}_{4}^{3-}(a q)+\mathrm{Mn}^{2+}(a q)\) [acidic] (b) \(\mathrm{P}_{4}(s) \longrightarrow \mathrm{HPO}_{3}^{2-}(a q)+\mathrm{PH}_{3}(g)\) [acidic] (c) \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{CN}^{-}(a q) \longrightarrow \mathrm{MnO}_{2}(s)+\mathrm{CNO}^{-}(a q)\) [basic]

An oxidizing agent is a substance that causes another substance to lose electrons, undergoing reduction itself. It essentially 'oxidizes' the other substance. For example, in the reaction \(\text{As}_4\text{O}_6(s) + \text{MnO}_4^-(aq) \rightarrow \text{AsO}_4^{3-}(aq) + \text{Mn}^{2+}(aq)\), the oxidizing agent is \(\text{MnO}_4^-\). It gains electrons and is reduced to \(\text{Mn}^{2+}\). Identifying the oxidizing agent requires knowing what gets reduced in the reaction.

A reducing agent is a substance that donates electrons to another substance, thereby being oxidized itself. For example, in the reaction \(\text{As}_4\text{O}_6(s) + \text{MnO}_4^-(aq) \rightarrow \text{AsO}_4^{3-}(aq) + \text{Mn}^{2+}(aq)\), \(\text{As}_4\text{O}_6\) is the reducing agent. It loses electrons and is oxidized to \(\text{AsO}_4^{3-}\). To identify the reducing agent, look for the substance that gets oxidized during the reaction.

The half-reaction method is an important technique used to balance redox equations. This method involves separating the oxidation and reduction parts of the equation into two half-reactions. Here are the general steps:
1. Write the unbalanced half-reactions.
2. Balance atoms other than hydrogen and oxygen.
3. Balance oxygen atoms by adding \(\text{H}_2\text{O}\).
4. Balance hydrogen atoms by adding \(\text{H}^+\).
5. Balance the charges by adding electrons \(\text{e}^-\).
6. Multiply the half-reactions by appropriate factors so that the electrons cancel when they are added together.
7. Add the half-reactions together and simplify if necessary.
This method works under both acidic and basic conditions with slight modifications.

Balancing redox reactions in acidic conditions involves adding \(\text{H}^+\) ions to equilibrate hydrogen atoms and \(\text{H}_2\text{O}\) molecules to equilibrate oxygen atoms. The steps are:
1. Write the half-reactions.
2. Balance all atoms except hydrogen and oxygen.
3. Balance oxygen by adding \(\text{H}_2\text{O}\).
4. Balance hydrogen by adding \(\text{H}^+\).
5. Balance the charges by adding electrons.
6. Combine the half-reactions ensuring electrons on both sides cancel out.
Example: For the equation \(\text{As}_4\text{O}_6 + \text{MnO}_4^- \rightarrow \text{AsO}_4^{3-} + \text{Mn}^{2+}\), the balanced half-reactions would include \(\text{H}^+\) ions and \(\text{H}_2\text{O}\) molecules.

Balancing redox reactions under basic conditions involves adding \(\text{OH}^-\) ions in addition to \(\text{H}_2\text{O}\) molecules to balance oxygen and hydrogen atoms. The steps to follow are:
1. Write the half-reactions.
2. Balance atoms other than oxygen and hydrogen first.
3. Add \(\text{H}_2\text{O}\) to balance oxygen atoms.
4. Add \(\text{H}^+\) to balance hydrogen atoms, then add the same number of \(\text{OH}^-\) to both sides of the equation to maintain a basic medium.
5. Balance the charge by adding electrons.
6. Combine the half-reactions and simplify.
Example: For the reaction \(\text{MnO}_4^- + \text{CN}^- \rightarrow \text{MnO}_2 + \text{CNO}^-\) in basic conditions, balancing oxygen and hydrogen involves using \(\text{OH}^-\) to achieve the final balanced equation.