Question

Write balanced equations for the following half-reactions. Specify whether each is an oxidation or reduction. (a) \(\operatorname{Cr}(\mathrm{s}) \longrightarrow \mathrm{Cr}^{3+}(\mathrm{aq}) \quad\) (in acid) (b) \(\mathrm{AsH}_{3}(\mathrm{g}) \longrightarrow \mathrm{As}(\mathrm{s}) \quad\) (in acid) (c) \(\mathrm{VO}_{3}^{-}(\mathrm{aq}) \longrightarrow \mathrm{V}^{2+}(\mathrm{aq}) \quad\) (in acid) (d) \(\mathrm{Ag}(\mathrm{s}) \longrightarrow \mathrm{Ag}_{2} \mathrm{O}(\mathrm{s})\) (in base)

Short answer

(a) Oxidation: \( \operatorname{Cr} \rightarrow \mathrm{Cr}^{3+} + 3e^- \); (b) Oxidation: \( \mathrm{AsH}_3 + 3H^+ + 3e^- \rightarrow \mathrm{As} + 3H_2O \); (c) Reduction: \( \mathrm{VO}_3^- + 4H^+ + e^- \rightarrow \mathrm{V}^{2+} + 3H_2O \); (d) Oxidation: \( 2\mathrm{Ag} + 2OH^- \rightarrow \mathrm{Ag}_2\mathrm{O} + H_2O + 2e^- \).

Step-by-step solution

Understand the Concept of Half-Reactions

A half-reaction is either the oxidation or reduction reaction component of a redox reaction. In a redox process, oxidation refers to the loss of electrons, while reduction refers to the gain of electrons. In acidic or basic solutions, half-reactions are balanced for both charge and mass, considering the presence of H⁺ for acidic and OH⁻ for basic solutions.

Write Half-Reaction for (a)

The unbalanced half-reaction is: \( \operatorname{Cr} \rightarrow \mathrm{Cr}^{3+} \). In acidic solution, to balance the charges, we add 3 electrons to the right: \( \operatorname{Cr} \rightarrow \mathrm{Cr}^{3+} + 3e^- \). This is an oxidation reaction as Cr loses electrons.

Write Half-Reaction for (b)

The unbalanced half-reaction is: \( \mathrm{AsH}_3 \rightarrow \mathrm{As} \). Balance elements first, and in acidic solution, add 3 electrons and 3 protons to get: \( \mathrm{AsH}_3 \rightarrow \mathrm{As} + 3H^+ + 3e^- \). Then balance the hydrogen with water: \( \mathrm{AsH}_3 + 3H^+ + 3e^- \rightarrow \mathrm{As} + 3H_2O \). This is an oxidation reaction.

Write Half-Reaction for (c)

The unbalanced half-reaction is: \(\mathrm{VO}_3^- \rightarrow \mathrm{V}^{2+} \). Balance V and O by adding water, and then balance the charge with H⁺ and electrons: \( \mathrm{VO}_3^- + 4H^+ + e^- \rightarrow \mathrm{V}^{2+} + 3H_2O \). This is a reduction reaction as electrons are gained.

Write Half-Reaction for (d)

The unbalanced half-reaction is: \( \mathrm{Ag} \rightarrow \mathrm{Ag}_2\mathrm{O} \). In basic solution, use OH⁻ to balance O and H: \( 2\mathrm{Ag} + 2OH^- \rightarrow \mathrm{Ag}_2\mathrm{O}+ H_2O + 2e^- \). This reaction is an oxidation reaction due to the loss of electrons by Ag.

Key concepts

Half-Reaction Balancing

In redox chemistry, balancing half-reactions is a crucial skill. Half-reactions represent the processes of either oxidation or reduction that occur during a redox reaction. To balance these reactions, we must focus on both mass and charge balance.
To start, identify the species being oxidized or reduced, and write the chemical equation. Then, to achieve mass balance, ensure that atoms other than oxygen and hydrogen are balanced first.
For oxygen, add water molecules (Step 4's VO3- example adds water to balance oxygen). To balance hydrogen, add protons (H⁺) in acidic solutions or hydroxide ions (OH⁻) in basic solutions. In step 5's Ag to Ag2O, OH⁻ was used to balance hydroxides.
Then, balance the charge by adding electrons—place them on the side that requires charge balance. In acidic conditions, electrons are typically added to the reactant side, as shown in Step 2 with Cr to Cr³⁺.

• Ensure both sides of the equation have equal numbers of each type of atom and equal overall charge.
• Check charge and mass balance after finishing to confirm correctness.
• Balance half-reactions first, and then combine them to get the total redox equation if necessary.

Particularly useful in understanding the detailed arrangements of redox reactions, balancing half-reactions provides a cleaner, organized view.

Oxidation and Reduction

Oxidation and reduction are two sides of a redox reaction, a core concept in chemistry.
Oxidation involves the loss of electrons by a substance, while reduction happens when a substance gains electrons.
In the steps you've seen:

• Chromium (Cr) in Step 2 is oxidized to Cr³⁺, as it loses three electrons.
• Arsine (AsH₃) in Step 3 oxidizes to arsenic (As), with the release of three electrons and the subsequent balancing with protons.
• The reduction of VO3⁻ to V2+ in Step 4 shows the gain of electrons.

The mnemonic "OIL RIG" can help: Oxidation Is Loss (of electrons) and Reduction Is Gain (of electrons).
By understanding this concept, you determine the redox behavior of substances in a reactive environment. Always remember—if something is oxidized, another thing is being reduced to maintain balance. This interplay ensures that charge conservation is maintained.

Acidic and Basic Solutions

In chemistry, the conditions of the solution (acidic or basic) notably influence the balancing of redox reactions.
Acidic solutions are characterized by a high concentration of H⁺ ions. When balancing in an acidic medium, you use H⁺ ions to balance hydrogen atoms.
For example, in Step 2 and 3 involving Cr and AsH₃ respectively, protons (H⁺) are added to balance the hydrogen.

• Balancing oxygen often requires adding H₂O molecules.
• For charges, electrons are added to counterbalance the net positive or negative charge created by adding H⁺.

Basic solutions, on the other hand, have a high concentration of OH⁻ ions. In these solutions, OH⁻ ions are used instead.
For example, in Step 5 when balancing Ag to Ag₂O, OH⁻ ions are used to balance the reaction. Subsequently, H₂O is often added to clear any excess hydrogen atoms introduced.

• The final neutralization involves ensuring all charges and atoms (especially hydrogen and oxygen) are properly accounted for.

Understanding how these different conditions affect your approach ensures success in reaction balancing across varied chemical environments.