Question

Balance these ionic redox equations using the ion-electron method. These reactions occur in acidic solution. (a) \(\mathrm{Zn}+\mathrm{NO}_{3}^{-} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{NH}_{4}^{+}\) (b) \(\mathrm{NO}_{3}^{-}+\mathrm{S} \longrightarrow \mathrm{NO}_{2}+\mathrm{SO}_{4}^{-}\) (c) \(\mathrm{PH}_{3}+\mathrm{I}_{2} \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{2}+\mathrm{I}^{-}\) (d) \(\mathrm{Cu}+\mathrm{NO}_{4}^{-} \longrightarrow \mathrm{Cu}^{24}+\mathrm{NO}\) (c) \(\mathrm{ClO}_{4}^{-}+\mathrm{Cl}^{-} \longrightarrow \mathrm{Cl}_{2}\)

Short answer

Balance redox reactions by splitting into half-reactions, balance O and H with \( \mathrm{H}_{2}\mathrm{O} \) and \( \mathrm{H}^{+} \), balance charge with electrons, and combine the half-reactions.

Step-by-step solution

Write the Unbalanced Equations for Each Reaction

Given reactions are:(a) \( \mathrm{Zn} + \mathrm{NO}_{3}^{-} \rightarrow \mathrm{Zn}^{2+} + \mathrm{NH}_{4}^{+} \)(b) \( \mathrm{NO}_{3}^{-} + \mathrm{S} \rightarrow \mathrm{NO}_{2} + \mathrm{SO}_{4}^{2-} \)(c) \( \mathrm{PH}_{3} + \mathrm{I}_{2} \rightarrow \mathrm{H}_{3}\mathrm{PO}_{2} + \mathrm{I}^{-} \)(d) \( \mathrm{Cu} + \mathrm{NO}_{3}^{-} \rightarrow \mathrm{Cu}^{2+} + \mathrm{NO} \)(e) \( \mathrm{ClO}_{4}^{-} + \mathrm{Cl}^{-} \rightarrow \mathrm{Cl}_{2} \)

Split Each Reaction into Half-Reactions

Split each reaction into its oxidation and reduction half-reactions. For example, for part (a):Oxidation: \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} \)Reduction: \( \mathrm{NO}_{3}^{-} \rightarrow \mathrm{NH}_{4}^{+} \)

Balance Atoms in Each Half-Reaction (Other Than O and H)

Balance elements other than O and H in each half-reaction. For part (a):Oxidation: \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} \)Reduction: \( \mathrm{NO}_{3}^{-} \rightarrow \mathrm{NH}_{4}^{+} \)

Balance Oxygen Atoms by Adding \(\mathrm{H}_{2}\mathrm{O} \)

Add water molecules to balance the oxygen atoms in each half-reaction. For part (a):Oxidation: \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} \) (no change needed)Reduction: \( \mathrm{NO}_{3}^{-} + 8\mathrm{H}^{+} + 6e^{-} \rightarrow \mathrm{NH}_{4}^{+} + 3 \mathrm{H}_{2}\mathrm{O} \)

Balance Hydrogen Atoms by Adding \( \mathrm{H}^{+} \)

Add protons (\( \mathrm{H}^{+} \)) to balance hydrogen atoms in each half-reaction. For part (a):Oxidation: \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2e^{-} \)Reduction: \( \mathrm{NO}_{3}^{-} + 10\mathrm{H}^{+} + 8e^{-} \rightarrow \mathrm{NH}_{4}^{+} + 3 \mathrm{H}_{2}\mathrm{O} \)

Balance Charges by Adding Electrons (\( e^{-} \))

Add electrons to balance the charge in each half-reaction. For part (a):Oxidation: \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2e^{-} \)Reduction: \( \mathrm{NO}_{3}^{-} + 10\mathrm{H}^{+} + 8e^{-} \rightarrow \mathrm{NH}_{4}^{+} + 3 \mathrm{H}_{2}\mathrm{O} \)

Combine Half-Reactions and Simplify

Combine the half-reactions, ensuring that the electrons lost in the oxidation half-reaction equal the electrons gained in the reduction half-reaction. For part (a):Combining: \[ \mathrm{Zn} + 8\mathrm{H}^{+} + 2\mathrm{NO}_{3}^{-} \rightarrow \mathrm{Zn}^{2+} + \mathrm{NH}_{4}^{+} + 3 \mathrm{H}_{2}\mathrm{O} \]

Repeat Steps for Each Reaction

Follow steps 2 to 7 for balancing parts (b), (c), (d), and (e).

Key concepts

Ionic Redox Equations

Ionic redox equations are chemical equations that showcase the transfer of electrons between ions and molecules in redox reactions. In these reactions, one substance gets oxidized (loses electrons) while another gets reduced (gains electrons). To approach balancing these equations, you must first identify the oxidation and reduction processes. This helps in understanding how many electrons are involved in the transfer and to ensure stoichiometric consistency in the overall reactions.

Ion-Electron Method

The ion-electron method, also known as the half-reaction method, is a systematic way to balance redox equations, especially in acidic or basic solutions. This method involves splitting the overall redox reaction into two half-reactions: one for oxidation and one for reduction. The subsequent steps include balancing each half-reaction for atoms and charge, then combining the half-reactions to form a complete, balanced equation. This method ensures that both mass and charge are conserved throughout the process.
Each step simplifies understanding by focusing on individual parts of the equation before combining them.

Half-Reactions

Half-reactions are representations of the oxidation or reduction parts of a redox reaction. Each half-reaction shows how electrons are either gained (reduction) or lost (oxidation). To balance a half-reaction:

• Balance all elements except H and O.
• Add water (H₂O) to balance oxygen atoms.
• Add hydrogen ions (H⁺) to balance hydrogen atoms.
• Add electrons (e^-) to balance the charges.

After balancing, combine the half-reactions ensuring that electrons lost equal electrons gained.

Oxidation and Reduction

Oxidation and reduction are opposite processes that always occur simultaneously in redox reactions.

• Oxidation: The process where an atom, ion, or molecule loses electrons. For example, Zn is oxidized to Zn²⁺ by losing two electrons.
• Reduction: The process where an atom, ion, or molecule gains electrons. For instance, NO₃^- is reduced to NH₄⁺ by gaining electrons and protons in acidic solutions.

Understanding these processes helps identify which species is oxidized and which is reduced in a reaction.

Balancing Chemical Equations

Balancing chemical equations involves ensuring that the number of atoms of each element is the same on both sides of the equation. For redox reactions, this also includes ensuring that the total charge is balanced. Here's a simplified approach:

• Write the unbalanced equation.
• Split into oxidation and reduction half-reactions.
• Balance atoms in each half-reaction other than O and H.
• Add water to balance oxygen atoms.
• Add H⁺ to balance hydrogen atoms.
• Add electrons to balance charges.
• Combine the half-reactions, canceling out the electrons to ensure they are conserved.

This method methodically simplifies the complex process of achieving a balanced equation.