The following steps are unbalanced half-reactions involved in the nitrogen cycle. Balance each half-reaction to show the number of electrons lost or gained, and state whether it is an oxidation or a reduction (all occur in acidic conditions): (a) \(\mathrm{N}_{2}(g) \longrightarrow \mathrm{NO}(g)\) (b) \(\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow \mathrm{NO}_{2}(g)\) (c) \(\mathrm{NH}_{3}(a q) \longrightarrow \mathrm{NO}_{2}^{-}(a q)\) (d) \(\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{NO}_{2}^{-}(a q)\) (c) \(\mathrm{N}_{2}(g) \longrightarrow \mathrm{NO}_{3}^{-}(a q)\)

When you're trying to balance chemical equations, the goal is to ensure that the number of each type of atom on the reactant side (left side) equals the number on the product side (right side). This involves several steps.

First, write down the unbalanced half-reactions. For example, let's take (a): \(\mathrm{N}_{2}(g) \rightarrow \mathrm{NO}(g)\).

Next, balance the nitrogen atoms. Since there are two nitrogen atoms in \(\text{{N}}_{2}\), you need two \(\text{{NO}}\) molecules on the product side: \(\text{{N}}_{2}(g) \rightarrow 2 \text{{NO}}(g)\).

Then, balance the oxygen atoms by adding water (\(\text{{H}}_{2}\text{{O}}\)) molecules if necessary. In example (b), \(\text{{N}}_{2} \text{{O}}(g) \rightarrow \text{{NO}}_{2}(g)\), you have one oxygen in \(\text{{N}}_{2} \text{{O}}\) and two in \(\text{{NO}}_{2}\).

Add water to the left side if needed: \(\text{{N}}_{2} \text{{O}}(g) + \text{{H}}_{2}\text{{O}} \rightarrow 2 \text{{NO}}_{2}(g)\).

After that, balance hydrogen atoms by adding \(\text{{H}}^{+}\) ions. In acidic conditions, this is how you account for any extra hydrogen atoms: \(\text{{N}}_{2} \text{{O}}(g) \rightarrow 2 \text{{NO}}_{2}(g) + 2 \text{{H}}^{+}\).

Finally, balance the charge by adding electrons (\(\text{{e}}^{-}\)). If the right side of the equation is more positive, add electrons to it, and vice versa. This ensures both sides have the same electrical charge.

Redox reactions involve the transfer of electrons between two species. The term 'redox' stands for reduction-oxidation.

In these reactions:

• Reduction is the gain of electrons (more negative).
• Oxidation is the loss of electrons (more positive).

In balancing redox equations, you must first assign oxidation states to the atoms in each chemical species.

For instance, in reaction (a) \(\text{{N}}_{2}(g) \rightarrow 2 \text{{NO}}(g)\), nitrogen starts with an oxidation state of 0 in \(\text{{N}}_{2}\) and changes to +2 in \(\text{{NO}}\), indicating it loses electrons.

This means nitrogen is oxidized. The equation can then be written as: \(\text{{N}}_{2}(g) \rightarrow 2 \text{{NO}}(g) + 4 \text{{H}}^{+} + 4 \text{{e}}^{-}\). Here, \(\text{{4 e}}^{-}\) are the lost electrons.

In step (d), \(\text{{NO}}_{3}^{-}(aq) \rightarrow \text{{NO}}_{2}^{-}(aq)\), nitrogen is reduced from an oxidation state of +5 in \(\text{{NO}}_{3}^{-}\) to +3 in \(\text{{NO}}_{2}^{-}\). So, it gains electrons and is reduced.

Understanding whether an atom is oxidized or reduced helps you track the number of electrons lost or gained in the reaction.

Balancing redox reactions in acidic conditions means you'll likely need to use H+ ions and water (H2O) to balance hydrogen and oxygen atoms.

Here are the steps specific to acidic solutions:

Add H2O to balance oxygen atoms.

• For example, in step (e): \(\text{{N}}_{2}(g) \rightarrow 2 \text{{NO}}_{3}^{-}(aq) \), you'd add H2O to the left side if balancing is needed.

Add \( \text{{H}}^{+} \) ions to balance hydrogen atoms.

• In reaction (c): \(\text{{NH}}_{3}(aq) \rightarrow \text{{NO}}_{2}^{-}(aq)\), you'd add \( \text{{H}}^{+} \) to the right side for balance.

Adjust for charge by adding electrons \( \text{{e}}^{-} \). After ensuring the atoms are balanced, count the charge on both sides.

• If the charges aren't balanced, add electrons to the more positive side so both sides have the same charge. In step (a): \(\text{{N}}_{2}(g) \rightarrow 2 \text{{NO}}(g) + 4 \text{{H}}^{+} + 4 \text{{e}}^{-}\).

These adjustments account for the acidic environment and ensure a properly balanced redox reaction.

Remembering these key points in balancing reactions under acidic conditions will make it simpler to follow through on the steps and correctly balance the equations.