Chapter 19: Problem 1
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
Step by step solution
Understand the Problem
Balance Chromium Half-Reaction (a)
Balance Arsenic Half-Reaction (b)
Balance Vanadium Half-Reaction (c)
Balance Silver Half-Reaction (d)
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Oxidation
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
Reduction
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
Half-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
Acidic Media
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
Basic Media
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