Balance the following skeleton reactions, and identify the oxidizing and reducing agents: (a) \(\mathrm{NO}_{2}(g) \longrightarrow \mathrm{NO}_{3}^{-}(a q)+\mathrm{NO}_{2}^{-}(a q)\) [basic] (b) \(\mathrm{Zn}(s)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{Zn}(\mathrm{OH})_{4}^{2-}(a q)+\mathrm{NH}_{3}(g)[\mathrm{basic}]\) (c) \(\mathrm{H}_{2} \mathrm{~S}(g)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{S}_{8}(s)+\mathrm{NO}(g)\) [acidic]

An oxidation state, also referred to as oxidation number, is a theoretical value representing the number of electrons an atom can gain, lose, or share during a chemical reaction. It is crucial for identifying the elements that undergo oxidation or reduction in a redox reaction.
For instance, to identify the oxidation states in the reaction \(\text{NO}_2 \rightarrow \text{NO}_3^- + \text{NO}_2^-\), we assign oxidation numbers to nitrogen in all three species:

• In \(\text{NO}_2\), nitrogen has an oxidation state of +4.
• In \(\text{NO}_3^-\), nitrogen has an oxidation state of +5.
• In \(\text{NO}_2^-\), nitrogen has an oxidation state of +3.

These oxidation states help us determine which elements are oxidized or reduced:

• Oxidation: An increase in oxidation state (loss of electrons).
• Reduction: A decrease in oxidation state (gain of electrons).

Understanding oxidation states is the first step in balancing complex redox reactions.

In redox reactions, the overall reaction is split into two parts known as half-reactions: the oxidation half-reaction and the reduction half-reaction. Each half-reaction shows either the loss or gain of electrons.
Let's break down \(\text{NO}_2 \rightarrow \text{NO}_3^- + \text{NO}_2^-\) into half-reactions:

• Oxidation half-reaction: Nitrogen in \(\text{NO}_2\) is oxidized to form \(\text{NO}_3^-\), as its oxidation state changes from +4 to +5.
• Reduction half-reaction: Nitrogen in \(\text{NO}_2\) is reduced to form \(\text{NO}_2^-\), as its oxidation state changes from +4 to +3.

Once you have these half-reactions, balance them independently by equalizing all elements except hydrogen and oxygen. Then balance oxygen atoms by adding \(\text{H}_2\text{O}\) molecules and hydrogen atoms by adding either \(\text{H}^+\) (in acidic conditions) or \(\text{OH}^-\) (in basic conditions). Finally, balance the charge by adding electrons (\(e^-\)).
Combining these balanced half-reactions will give the complete, balanced redox reaction.

An oxidizing agent, also known as an oxidant, is a substance that gains electrons in a redox reaction, thereby causing another substance to be oxidized. It is reduced in the process.
For example, in the redox reaction \(\text{H}_2\text{S} + \text{NO}_3^- \rightarrow \text{S}_8 + \text{NO}\) (under acidic conditions), nitrate ion \(\text{NO}_3^-\) acts as the oxidizing agent because it gains electrons and is reduced to \(\text{NO}\).
Identifying the oxidizing agent involves:

• Finding the substance that is reduced (a decrease in oxidation state).
• Recognizing that this substance accepts electrons.

Understanding the role of oxidizing agents is crucial for analyzing redox reactions and balancing them accurately.

A reducing agent, or reductant, is a substance that loses electrons in a redox reaction, thereby causing another substance to be reduced. It is oxidized in the process.
For instance, in the reaction \(\text{Zn} + \text{NO}_3^- \rightarrow \text{Zn}(\text{OH})_4^{2-} + \text{NH}_3\) (under basic conditions), zinc metal \(\text{Zn}\) acts as the reducing agent because it loses electrons and is oxidized to \(\text{Zn}(\text{OH})_4^{2-}\).
Identifying the reducing agent involves:

• Finding the substance that is oxidized (an increase in oxidation state).
• Recognizing that this substance donates electrons.

Understanding reducing agents is essential for deciphering redox reactions and ensuring they are correctly balanced.

Redox reactions can occur under different conditions, primarily acidic or basic, which influences how the reactions are balanced.
In acidic conditions, balance redox reactions by:

• Adding \(\text{H}_2\text{O}\) molecules to balance oxygen atoms.
• Adding \(\text{H}^+\) ions to balance hydrogen atoms.
• Adding \(\text{e}^-\) to balance the charge.

In basic conditions, balance redox reactions by:

• Adding \(\text{H}_2\text{O}\) molecules to balance oxygen atoms.
• Adding \(\text{OH}^-\) ions to balance hydrogen atoms.
• Adding \(\text{e}^-\) to balance the charge.

Understanding the conditions is critical for properly balancing each half-reaction and ensuring the overall redox reaction is accurate.