Chapter 21: Problem 13

Balance the following skeleton reactions, and identify the oxidizing and reducing agents: (a) \(\mathrm{O}_{2}(g)+\mathrm{NO}(g) \longrightarrow \mathrm{NO}_{3}^{-}(a q)[\) acidic \(]\) (b) \(\mathrm{CrO}_{4}^{2-}(a q)+\mathrm{Cu}(s) \longrightarrow \mathrm{Cr}(\mathrm{OH})_{3}(s)+\mathrm{Cu}(\mathrm{OH})_{2}(s)[\) basic \(]\) (c) \(\mathrm{AsO}_{4}^{3-}(a q)+\mathrm{NO}_{2}^{-}(a q) \longrightarrow \mathrm{AsO}_{2}^{-}(a q)+\mathrm{NO}_{3}^{-}(a q)[\) basic \(]\)

Short Answer

Expert verified

Balanced reactions: (a) \(\text{3NO}(g) + 4 \text{H}_{2}\text{O}(l) + \text{O}_{2}(g) \rightarrow \text{3NO}_{3}^{-}(aq) + 4 \text{H}^{+}(aq) \), (b) \(\text{3Cu}(s) + 2 \text{CrO}_{4}^{2-}(aq) + 5 \text{OH}^{-}(aq) + 4 \text{H}_{2}\text{O}(l) \rightarrow \text{3Cu}(OH)_{2}(s) + 2 \text{Cr}(OH)_{3}(s) \), (c) \(\text{4NO}_{2}^{-}(aq) + \text{AsO}_{4}^{3-}(aq) + 8 \text{OH}^{-}(aq) \rightarrow 4 \text{NO}_{3}^{-}(aq) + \text{AsO}_{2}^{-}(aq) + 4 \text{H}_{2}\text{O} \). Oxidizing agents: (a) \(\text{O}_{2}(g) \), (b) \(\text{CrO}_{4}^{2-}(aq) \), (c) \(\text{NO}_{2}^{-}(aq) \). Reducing agents: (a) \(\text{NO}(g) \), (b) \(\text{Cu}(s) \), (c) \(\text{AsO}_{4}^{3-}(aq) \).

Step by step solution

Write the unbalanced half-reactions for reaction (a)

For reaction (a), first separate the oxidation and reduction half-reactions. One possible set of half-reactions is: Oxidation: \(\text{NO}(g) \rightarrow \text{NO}_{3}^{-}(aq)\)Reduction: \(\text{O}_{2}(g) \rightarrow \text{H}_{2}\text{O}(l) \)

Balance the atoms other than oxygen and hydrogen in reaction (a)

Write the balanced half-reactions for each species:Oxidation: \(\text{NO}(g) \rightarrow \text{NO}_{3}^{-}(aq) \) Reduction: \(\text{O}_{2}(g) \rightarrow \text{H}_{2}\text{O}(l) \)

Balance oxygen atoms in each half-reaction for reaction (a)

Balance oxygen by adding \(\text{H}_{2}\text{O}(l) \): Oxidation: \(\text{NO}(g) + 2 \text{H}_{2}\text{O}(l) \rightarrow \text{NO}_{3}^{-}(aq) \) Reduction: \(\text{O}_{2}(g) \rightarrow 2 \text{H}_{2}\text{O}(l) \)

Balance hydrogen atoms in each half-reaction for reaction (a)

Balance hydrogen by adding \(\text{H}^{+}(aq)\): Oxidation: \(\text{NO}(g) + 2 \text{H}_{2}\text{O}(l) \rightarrow \text{NO}_{3}^{-}(aq) + 4 \text{H}^{+}(aq) \) Reduction: \(\text{O}_{2}(g) + 4 \text{H}^{+}(aq) \rightarrow 2 \text{H}_{2}\text{O}(l) \)

Balance the charges by adding electrons in reaction (a)

Add electrons to balance the charges:Oxidation: \(\text{NO}(g) + 2 \text{H}_{2}\text{O}(l) \rightarrow \text{NO}_{3}^{-}(aq) + 4 \text{H}^{+}(aq) + 3 e^{-} \)Reduction: \(\text{O}_{2}(g) + 4 \text{H}^{+}(aq) + 4 e^{-} \rightarrow 2 \text{H}_{2}\text{O}(l) \)

Combine balanced half-reactions for reaction (a)

Multiply the half-reactions to equalize electrons and then add them: Oxidation: \(\text{NO}(g) + 2 \text{H}_{2}\text{O}(l) \rightarrow \text{NO}_{3}^{-}(aq) + 4 \text{H}^{+}(aq) + 3 e^{-} \) Reduction: \(\text{O}_{2}(g) + 4 \text{H}^{+}(aq) + 4 e^{-} \rightarrow 2 \text{H}_{2}\text{O}(l) \)Combined: \(\text{3NO}(g) + 4 \text{H}_{2}\text{O}(l) + \text{O}_{2}(g) \rightarrow 3 \text{NO}_{3}^{-}(aq) + 4 \text{H}^{+}(aq) \)

Identify oxidizing and reducing agents in reaction (a)

Oxidizing agent: \(\text{O}_{2}(g) \) (gets reduced) Reducing agent: \(\text{NO}(g) \) (gets oxidized)

Write the unbalanced half-reactions for reaction (b)

For reaction (b), separate into half-reactions:Oxidation: \(\text{Cu}(s) \rightarrow \text{Cu(OH)}_{2}(s) \) Reduction: \(\text{CrO}_{4}^{2-}(aq) \rightarrow \text{Cr(OH)}_{3}(s) \)

Balance the atoms other than oxygen and hydrogen in reaction (b)

Oxidation: \(\text{Cu}(s) \rightarrow \text{Cu(OH)}_{2}(s) \) Reduction: \(\text{CrO}_{4}^{2-}(aq) \rightarrow \text{Cr(OH)}_{3}(s) \)

Balance oxygen atoms in each half-reaction for reaction (b)

Balance oxygen by adding \(\text{H}_{2}\text{O}(l) \): Oxidation: \(\text{Cu}(s) + 2 \text{H}_{2}\text{O}(l) \rightarrow \text{Cu(OH)}_{2}(s) \) Reduction: \(\text{CrO}_{4}^{2-}(aq) + 4 \text{H}_{2}\text{O}(l) \rightarrow \text{Cr(OH)}_{3}(s) \)

Balance hydrogen atoms in each half-reaction for reaction (b)

Balance hydrogen by adding \(\text{OH}^{-}(aq) \): Oxidation: \(\text{Cu}(s) + 2 \text{H}_{2}\text{O}(l) \rightarrow \text{Cu(OH)}_{2}(s) + 2 \text{OH}^{-}(aq) \) Reduction: \(\text{CrO}_{4}^{2-}(aq) + 4 \text{H}_{2}\text{O}(l) + 8 \text{OH}^{-}(aq) \rightarrow \text{Cr(OH)}_{3}(s) + 4 \text{H}_{2}\text{O}(l) \)

Balance the charges by adding electrons in reaction (b)

Add electrons to balance the charges:Oxidation: \(\text{Cu}(s) \rightarrow \text{Cu(OH)}_{2}(s) + 2 \text{OH}^{-}(aq) + 2 e^{-} \) Reduction: \(\text{CrO}_{4}^{2-}(aq) + 4 \text{H}_{2}\text{O}(l) + 8 \text{OH}^{-}(aq) \rightarrow \text{Cr(OH)}_{3}(s) + 4 \text{H}_{2}\text{O}(l) + 3 e^{-} \)

Combine balanced half-reactions for reaction (b)

Multiply the half-reactions to equalize electrons and then add them: Oxidation: \(\text{Cu}(s) + 2 \text{OH}^{-}(aq) \rightarrow \text{Cu}(OH)_{2}(s) + 2 e^{-} \) Reduction: \(\text{CrO}_{4}^{2-}(aq) + 4 \text{H}_{2}\text{O}(l) + 3 e^{-} \rightarrow \text{Cr}(OH)_{3}(s) + 5 \text{OH}^{-}(aq) \)Combined: \(\text{3Cu}(s) + 2 \text{CrO}_{4}^{2-}(aq) + 5 \text{OH}^{-}(aq) + 4 \text{H}_{2}\text{O}(l) \rightarrow 3 \text{Cu}(OH)_{2}(s) + 2 \text{Cr}(OH)_{3}(s) \)

Identify oxidizing and reducing agents in reaction (b)

Oxidizing agent: \(\text{CrO}_{4}^{2-}(aq) \) (gets reduced) Reducing agent: \(\text{Cu}(s) \) (gets oxidized)

Write the unbalanced half-reactions for reaction (c)

For reaction (c), separate into half-reactions:Oxidation: \(\text{NO}_{2}^{-}(aq) \rightarrow \text{NO}_{3}^{-}(aq) \) Reduction: \(\text{AsO}_{4}^{3-}(aq) \rightarrow \text{AsO}_{2}^{-}(aq) \)

Balance the atoms other than oxygen and hydrogen in reaction (c)

Oxidation: \(\text{NO}_{2}^{-}(aq) \rightarrow \text{NO}_{3}^{-}(aq) \) Reduction: \(\text{AsO}_{4}^{3-}(aq) \rightarrow \text{AsO}_{2}^{-}(aq) \)

Balance oxygen atoms in each half-reaction for reaction (c)

Balance oxygen by adding \(\text{H}_{2}\text{O}(l) \): Oxidation: \(\text{NO}_{2}^{-}(aq) \rightarrow \text{NO}_{3}^{-}(aq) \) Reduction: \(\text{AsO}_{4}^{3-}(aq) + 2 \text{H}_{2}\text{O}(l) \rightarrow \text{AsO}_{2}^{-}(aq) \)

Balance hydrogen atoms in each half-reaction for reaction (c)

Balance hydrogen by adding \(\text{OH}^{-}(aq) \): Oxidation: \(\text{NO}_{2}^{-}(aq) \rightarrow \text{NO}_{3}^{-}(aq) + e^{-} \) Reduction: \(\text{AsO}_{4}^{3-}(aq) + 2 \text{H}_{2}\text{O}(l) + 4 \text{OH}^{-}(aq) \rightarrow \text{AsO}_{2}^{-}(aq) + 2 \text{H}_{2}\text{O}(l) \)

Balance the charges by adding electrons in reaction (c)

Add electrons to balance the charges:Oxidation: \(\text{NO}_{2}^{-}(aq) \rightarrow \text{NO}_{3}^{-}(aq) + e^{-} \) Reduction: \(\text{AsO}_{4}^{3-}(aq) + 2 \text{H}_{2}\text{O}(l) + 4 \text{OH}^{-}(aq) \rightarrow \text{AsO}_{2}^{-}(aq) + 2 \text{H}_{2}\text{O}(l) + 4 e^{-} \)

Combine balanced half-reactions for reaction (c)

Multiply the half-reactions to equalize electrons and then add them: Oxidation: \(\text{NO}_{2}^{-}(aq) + e^{-} \rightarrow \text{NO}_{3}^{-}(aq) \) Reduction: \(\text{AsO}_{4}^{3-}(aq) + 4 e^{-} + 8 \text{OH}^{-}(aq) \rightarrow \text{AsO}_{2}^{-}(aq) + 6 \text{H}_{2}\text{O} \)Combined: \(\text{4NO}_{2}^{-}(aq) + \text{AsO}_{4}^{3-}(aq) + \text{8OH}^{-}(aq) \rightarrow \text{4NO}_{3}^{-}(aq) + \text{AsO}_{2}^{-}(aq) + 4 \text{H}_{2}\text{O} \)

Identify oxidizing and reducing agents in reaction (c)

Oxidizing agent: \(\text{NO}_{2}^{-}(aq) \) (gets reduced) Reducing agent: \(\text{AsO}_{4}^{3-}(aq) \) (gets oxidized)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Oxidizing Agents

In redox reactions, the oxidizing agent is the substance that accepts electrons. It gets reduced as it gains electrons. For example, in reaction (a), the oxidizing agent is \(\text{O}_2(g)\) because it gains electrons and is transformed into water. Oxidizing agents are very important because they drive the oxidation process, which involves the loss of electrons by another substance. In general, common oxidizing agents include halogens, oxygen, and compounds like \(\text{H}_2\text{O}_2\). When identifying the oxidizing agent in a reaction, look for the substance whose oxidation number decreases. This indicates that it has gained electrons.

Reducing Agents

Reducing agents do the opposite of oxidizing agents. They donate electrons and thereby get oxidized themselves. In the context of reaction (a), the reducing agent is \(\text{NO}(g)\) because it loses electrons, transforming into \(\text{NO}_3^{-}(aq)\). Reducing agents are crucial for driving the reduction process, where the oxidation number of another species increases due to electron gain. Examples of common reducing agents include metals like sodium, and hydrogen gas. When identifying the reducing agent, find the substance whose oxidation number increases, indicating it has lost electrons.

Half-Reaction Method

The half-reaction method is an efficient way to balance redox reactions. By splitting the reaction into two half-reactions (oxidation and reduction), it becomes easier to balance atoms and charges. Here are the general steps:

Write the unbalanced half-reactions.
Balance all elements except for hydrogen and oxygen.
Balance oxygen atoms by adding water (\(\text{H}_2\text{O}\)).
Balance hydrogen atoms by adding hydrogen ions (\(\text{H}^{+}\)) if in acidic solution or hydroxide ions (\(\text{OH}^-\)) if in a basic solution.
Balance the charges by adding electrons (\(e^-\)).
Combine the balanced half-reactions, making sure the number of electrons lost in the oxidation half equals the number gained in the reduction half.

Applying this method to each of the given reactions ensures that they are properly balanced and clarifies the roles of the oxidizing and reducing agents.