Question

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

Short answer

(a) Oxidation, (b) Oxidation, (c) Reduction, (d) Oxidation.

Step-by-step solution

Understand the Problem

We need to write balanced half-reactions for the given equations and determine whether each represents an oxidation or a reduction process. Balancing will consider the appropriate acidic or basic media as specified.

Balance Chromium Half-Reaction (a)

Start with \( \mathrm{Cr} \rightarrow \mathrm{Cr}^{3+} \). Since it occurs in acidic solution, add \( 3\,\mathrm{e}^- \) to the right side to account for the loss of three electrons in forming \( \mathrm{Cr}^{3+} \). The balanced half-reaction is:\[ \mathrm{Cr} \rightarrow \mathrm{Cr}^{3+} + 3\, \mathrm{e}^- \]This is an oxidation reaction because electrons are lost.

Balance Arsenic Half-Reaction (b)

For \( \mathrm{AsH}_3 \rightarrow \mathrm{As} \), remove hydrogen by adding 3 protons and 3 electrons to the right side in an acidic solution. The balanced half-reaction is:\[ \mathrm{AsH}_3 \rightarrow \mathrm{As} + 3\, \mathrm{H}^+ + 3\, \mathrm{e}^- \]This is an oxidation reaction since electrons are released.

Balance Vanadium Half-Reaction (c)

Take \( \mathrm{VO}_3^- \rightarrow \mathrm{V}^{2+} \) and balance oxygen by adding water molecules to the right. Then balance the hydrogen by adding protons to the left, and finally balance charge with electrons. The balanced half-reaction is:\[ \mathrm{VO}_3^- + 4\, \mathrm{H}^+ + 3\, \mathrm{e}^- \rightarrow \mathrm{V}^{2+} + 3\, \mathrm{H}_2\mathrm{O} \]This is a reduction reaction because electrons are gained.

Balance Silver Half-Reaction (d)

For \( \mathrm{Ag} \rightarrow \mathrm{Ag}_2 \mathrm{O} \) in a basic solution, start by balancing oxygen with water on the right and hydrogen by adding \( \mathrm{OH}^- \) on the left to neutralize protons. Then balance electrons. The balanced half-reaction is:\[ 2\, \mathrm{Ag} + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{Ag}_2\mathrm{O} + 2\, \mathrm{H}^+ + 2\, \mathrm{e}^- \]This is an oxidation reaction since electrons are lost.

Key concepts

Oxidation

In chemistry, oxidation refers to the process whereby a substance loses electrons. When a material undergoes oxidation, it increases its oxidation state. This is a fundamental part of a larger class of reactions known as redox reactions, where one chemical species is oxidized and another is reduced.
Oxidation can be remembered using the acronym OIL RIG: "Oxidation Is Loss" of electrons. For instance, in the half-reaction \( \mathrm{Cr} \rightarrow \mathrm{Cr}^{3+} + 3e^- \), chromium loses three electrons, thus its oxidation state increases from 0 to +3. This confirms it is an oxidation process.

• Loss of electrons
• Increase in oxidation state
• Often involves a combining with oxygen in chemical reactions

Understanding oxidation helps in deciphering redox reactions and identifying agents that cause or undergo changes in electron number.

Reduction

Reduction is the counter process to oxidation in redox reactions. It involves the gain of electrons by a molecule, atom, or ion. As a result, the oxidation state of the substance decreases. This can be remembered by the RIG part of the acronym OIL RIG: "Reduction Is Gain" of electrons.
For example, in the balanced half-reaction \( \mathrm{VO}_3^- + 4\, \mathrm{H}^+ + 3\, \mathrm{e}^- \rightarrow \mathrm{V}^{2+} + 3\, \mathrm{H}_2\mathrm{O} \), the vanadium ion gains three electrons, reducing its oxidation state from +5 to +2. This indicates a reduction reaction.

• Gain of electrons
• Decrease in oxidation state
• Common in processes involving the donation of electrons to other chemicals

Identifying reduction is crucial in deciphering how substances interact and transform during chemical reactions.

Half-Reactions

Redox reactions are composed of two half-reactions: one for oxidation and another for reduction. Each half-reaction represents either the loss or gain of electrons, making it easier to understand and balance complex reactions.
In our examples, we write separate half-reactions for the processes. For instance, \( \mathrm{AsH}_3 \rightarrow \mathrm{As} + 3e^- + 3H^+ \) is an oxidation half-reaction where arsenic hydride loses electrons, while \( \mathrm{VO}_3^- + 4H^+ + 3e^- \rightarrow \mathrm{V}^{2+} + 3H_2O \) acts as a reduction half-reaction.

• Helps isolate each step in a redox reaction
• Essential for balancing and understanding electron transfer

Half-reactions are an essential schematic tool to systematically analyze the electron movements within a reaction, facilitating understanding and calculation.

Acidic Media

In redox reactions, acidic media refer to aqueous environments with an abundance of hydrogen ions (\(H^+\)). This environment influences how substances interact, particularly affecting which species are stable and how they react.
When balancing half-reactions in acidic media, such as \( \mathrm{AsH}_3 \rightarrow \mathrm{As} + 3\, \mathrm{H}^+ + 3\, \mathrm{e}^- \), protons are used to balance hydrogen atoms. Acidic conditions help in distributing charge and matter in reactions as protons need to be accounted for.

• Frequent presence of \(H^+\) ions
• Used to balance hydrogen atoms in reactions
• Promotes stability for different chemical species

Understanding the role of acidic media in chemical reactions is fundamental for predicting and balancing redox processes.

Basic Media

Basic media describe conditions in a solution with significant hydroxide ions (\( \mathrm{OH}^- \)) concentration. These basic environments significantly impact the course and equilibrium of redox reactions.
When dealing with balancing in basic media, such as with \( 2 \mathrm{Ag} + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{Ag}_2\mathrm{O} + 2 \mathrm{H}^+ + 2 \mathrm{e}^- \), hydroxide ions are added to balance any additional hydrogen introduced by water molecules

• Dominated by \(\mathrm{OH}^-\) ions
• Utilized to balance excess hydrogen in half-reactions
• Contributes to the neutralization of net charge in reactions

Comprehending the influences of basic media helps in mastering the balancing of chemical equations within alkaline environments.