Problem 27 - Chemistry Principles and Practice

Question

Complete and balance each half-reaction in acid solution, and identify it as an oxidation or a reduction. (a) \(\mathrm{UO}_{2}^{2+}(\mathrm{aq}) \rightarrow \mathrm{U}^{4+}(\mathrm{aq})\) (b) \(\mathrm{Zn}(\mathrm{s}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})\) (c) \(\mathrm{IO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{I}^{-}(\mathrm{aq})\)

Step-by-Step Solution

Answer

(a) Reduction: \(\mathrm{UO}_{2}^{2+} + 4\mathrm{H}^+ + 2\mathrm{e}^- \rightarrow \mathrm{U}^{4+} + 2\mathrm{H}_2\mathrm{O}\); (b) Oxidation: \(\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2\mathrm{e}^-\); (c) Reduction: \(\mathrm{IO}_{3}^- + 6\mathrm{H}^+ + 6\mathrm{e}^- \rightarrow \mathrm{I}^- + 3\mathrm{H}_2\mathrm{O}\)."

Step 1: Identify Type of Equation (a)

Check the charges on each side of the equation for \(\mathrm{UO}_{2}^{2+} \rightarrow \mathrm{U}^{4+}\):- On the left side, uranium has a +6 oxidation state because \(\mathrm{UO}_{2}^{2+}\) implies \(\mathrm{U}^{2+}\) + 2x(-2) from oxygen = +6.- On the right side, uranium has a +4 oxidation state because it's \(\mathrm{U}^{4+}\).This change from +6 to +4 indicates a reduction is happening because the oxidation state decreases.

Step 2: Balance Half-Reaction (a)

The equation is \(\mathrm{UO}_{2}^{2+} \rightarrow \mathrm{U}^{4+}\). To balance the electrons and charges in acidic solution:1. Balance uranium: already 1 on both sides.2. Balance the oxygen atoms by adding 2 \(\mathrm{H}_2\mathrm{O}\) to the right side: \(\mathrm{UO}_{2}^{2+} \rightarrow \mathrm{U}^{4+} + 2\mathrm{H}_2\mathrm{O}\).3. Balance the hydrogen by adding 4 \(\mathrm{H}^+\) to the left side: \(\mathrm{UO}_{2}^{2+} + 4\mathrm{H}^+ \rightarrow \mathrm{U}^{4+} + 2\mathrm{H}_2\mathrm{O}\).4. Balance the charge by adding 2 electrons to the left: \(\mathrm{UO}_{2}^{2+} + 4\mathrm{H}^+ + 2\mathrm{e}^- \rightarrow \mathrm{U}^{4+} + 2\mathrm{H}_2\mathrm{O}\).

Step 3: Identify Type of Equation (b)

Check the changes in oxidation state for \(\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+}\):- Zinc changes from oxidation state 0 to +2.This indicates an oxidation process, as the oxidation state increases.

Step 4: Balance Half-Reaction (b)

The equation is \(\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+}\). Balance the electrons:1. Zinc is already balanced in terms of the element.2. Add 2 electrons to the right side to balance the charge: \(\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2\mathrm{e}^-\). This reaction is complete for acidic conditions.

Step 5: Identify Type of Equation (c)

Analyze the transformation in oxidation number for \(\mathrm{IO}_{3}^- \rightarrow \mathrm{I}^-\):- In \(\mathrm{IO}_{3}^-\), iodine is in a +5 oxidation state.- In \(\mathrm{I}^-\), iodine is in a -1 oxidation state.This indicates a reduction since the oxidation state decreases.

Step 6: Balance Half-Reaction (c)

For the equation \(\mathrm{IO}_{3}^- \rightarrow \mathrm{I}^-\), balance elements and charges:1. Iodine is already balanced with 1 atom on each side.2. Balance the oxygens by adding 3 \(\mathrm{H}_2\mathrm{O}\) to the right side: \(\mathrm{IO}_{3}^- \rightarrow \mathrm{I}^- + 3\mathrm{H}_2\mathrm{O}\).3. Balance the hydrogen by adding 6 \(\mathrm{H}^+\) to the left side: \(\mathrm{IO}_{3}^- + 6\mathrm{H}^+ \rightarrow \mathrm{I}^- + 3\mathrm{H}_2\mathrm{O}\).4. Add 6 electrons to the left to balance the charge: \(\mathrm{IO}_{3}^- + 6\mathrm{H}^+ + 6\mathrm{e}^- \rightarrow \mathrm{I}^- + 3\mathrm{H}_2\mathrm{O}\).

Key Concepts

Oxidation

In chemistry, oxidation refers to a process where an atom, ion, or molecule loses electrons. This is commonly associated with an increase in oxidation state.
Understanding oxidation is crucial in identifying redox reactions, such as when \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} \).
Here, the zinc atom starts with an oxidation state of 0 and changes to +2, indicating it has lost two electrons.
These electrons are typically added to the other side of the equation to balance the charge as shown in the half-reaction equation: \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2\mathrm{e}^- \).
Key points to remember about oxidation:

• Loss of electrons
• Increase in oxidation state
• Often involves metals, such as zinc or iron

Identifying and balancing oxidation half-reactions is essential for comprehensively understanding redox processes.

Reduction

Reduction is a fundamental concept in redox chemistry, and it contrasts oxidation by involving the gain of electrons. This gain typically results in a decrease in the oxidation state of the involved species.
For instance, in the half-reaction \( \mathrm{UO}_{2}^{2+} \rightarrow \mathrm{U}^{4+} \),
uranium's oxidation state decreases from +6 to +4, indicating it has gained electrons.
This process is balanced by adding electrons to the side where the reduction occurs, as seen in the full balanced equation: \( \mathrm{UO}_{2}^{2+} + 4\mathrm{H}^+ + 2\mathrm{e}^- \rightarrow \mathrm{U}^{4+} + 2\mathrm{H}_2\mathrm{O} \).Essentials of reduction:

• Gain of electrons
• Decrease in oxidation state
• Can involve various agents, such as molecules containing oxygen

Grasping reduction is key to solving and balancing redox equations with precision.

Half-Reaction Balancing

Balancing half-reactions is a crucial skill in understanding redox reactions as it ensures that both mass and charge are conserved. When balancing, you need to consider:- **Elemental Balance**: Ensure each type of atom has the same amount on both sides of the equation.- **Charge Balance**: The total charge on each side must be equal.For example, to balance \( \mathrm{IO}_{3}^- \rightarrow \mathrm{I}^- \) in acidic solution,
follow these steps:

• Add water molecules to balance oxygen: \( 3 \mathrm{H}_2\mathrm{O} \) to the right side.
• Add \( \mathrm{H}^+ \) ions to balance hydrogen: \( 6 \mathrm{H}^+ \) to the left side.
• Add electrons to balance charge: \( 6 \mathrm{e}^- \) to the left side.

Resulting in the balanced equation: \( \mathrm{IO}_{3}^- + 6\mathrm{H}^+ + 6\mathrm{e}^- \rightarrow \mathrm{I}^- + 3\mathrm{H}_2\mathrm{O} \). Each element's atoms and the net charge on both sides are equal, ensuring the accuracy of the half-reaction balance.

Acidic Solution

In redox chemistry, the type of solution often dictates how a reaction should be balanced, particularly in the addition of hydrogen ions (\( \mathrm{H}^+ \)) and water molecules (\( \mathrm{H}_2\mathrm{O} \)).
In an acidic solution, these components are vital in balancing oxygen and hydrogen atoms.
Understanding redox reactions in acidic conditions is important for solving equations involved in electrochemistry and environmental chemistry.
Consider the equation \( \mathrm{UO}_{2}^{2+} \rightarrow \mathrm{U}^{4+} \)
in which water and \( \mathrm{H}^+ \) ions are used to ensure balanced reactions:

• Add \( 2\mathrm{H}_2\mathrm{O} \) to the right to balance oxygen atoms.
• Add \( 4\mathrm{H}^+ \) to the left to balance hydrogen atoms from the added water.

These added components are crucial for both balancing the half-reaction accurately and maintaining the acid-based environment needed for the reaction to occur. Understanding how to manipulate reactions in acidic solutions ensures chemists can accurately predict and explain chemical processes.