Problem 65 - General Chemistry

Question

Balance the following oxidation-reduction reactions by the half-reaction method. a. \(\mathrm{CuCl}_{2}(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{AlCl}_{3}(a q)+\mathrm{Cu}(s)\) b. \(\mathrm{Cr}^{3+}(a q)+\mathrm{Zn}(s) \longrightarrow \mathrm{Cr}(s)+\mathrm{Zn}^{2+}(a q)\)

Step-by-Step Solution

Answer

a. Balanced equation: \( 3\mathrm{Cu}^{2+}(aq) + 2\mathrm{Al}(s) \rightarrow 3\mathrm{Cu}(s) + 2\mathrm{Al^{3+}}(aq) \). b. Balanced equation: \( 2\mathrm{Cr}^{3+}(aq) + 3\mathrm{Zn}(s) \rightarrow 2\mathrm{Cr}(s) + 3\mathrm{Zn}^{2+}(aq) \).

Step 1: Write the Unbalanced Equation for Reaction (a)

The given chemical equation is: \( \mathrm{CuCl}_{2}(aq) + \mathrm{Al}(s) \rightarrow \mathrm{AlCl}_{3}(aq) + \mathrm{Cu}(s) \). Separate it into oxidation and reduction half-reactions.

Step 2: Identify Oxidation and Reduction in Reaction (a)

For oxidation: \( \mathrm{Al}(s) \rightarrow \mathrm{Al^{3+}}(aq) \). For reduction: \( \mathrm{Cu}^{2+}(aq) \rightarrow \mathrm{Cu}(s) \).

Step 3: Balance Each Half-Reaction for Reaction (a)

Balance the atoms and charges: - Oxidation: \( \mathrm{Al}(s) \rightarrow \mathrm{Al^{3+}}(aq) + 3e^- \) (add 3 electrons to the right side).- Reduction: \( \mathrm{Cu}^{2+}(aq) + 2e^- \rightarrow \mathrm{Cu}(s) \) (add 2 electrons to the left side).

Step 4: Equalize Electrons for Reaction (a)

Make the electrons equal in both half-reactions. Multiply oxidation by 2 and reduction by 3:- Oxidation becomes: \( 2 \mathrm{Al}(s) \rightarrow 2 \mathrm{Al^{3+}}(aq) + 6e^- \).- Reduction becomes: \( 3\mathrm{Cu}^{2+}(aq) + 6e^- \rightarrow 3\mathrm{Cu}(s) \).

Step 5: Combine the Half-Reactions for Reaction (a)

Add the balanced oxidation and reduction half-reactions:\[ 3\mathrm{Cu}^{2+}(aq) + 2\mathrm{Al}(s) \rightarrow 3\mathrm{Cu}(s) + 2\mathrm{Al^{3+}}(aq) \]

Step 6: Write the Unbalanced Equation for Reaction (b)

The given chemical equation is: \( \mathrm{Cr}^{3+}(aq) + \mathrm{Zn}(s) \rightarrow \mathrm{Cr}(s) + \mathrm{Zn}^{2+}(aq) \). Separate it into oxidation and reduction half-reactions.

Step 7: Identify Oxidation and Reduction in Reaction (b)

For oxidation: \( \mathrm{Zn}(s) \rightarrow \mathrm{Zn}^{2+}(aq) \). For reduction: \( \mathrm{Cr}^{3+}(aq) \rightarrow \mathrm{Cr}(s) \).

Step 8: Balance Each Half-Reaction for Reaction (b)

Balance the atoms and charges: - Oxidation: \( \mathrm{Zn}(s) \rightarrow \mathrm{Zn}^{2+}(aq) + 2e^- \) (add 2 electrons to the right side).- Reduction: \( \mathrm{Cr}^{3+}(aq) + 3e^- \rightarrow \mathrm{Cr}(s) \) (add 3 electrons to the left side).

Step 9: Equalize Electrons for Reaction (b)

Make the electrons equal in both half-reactions. Multiply oxidation by 3 and reduction by 2:- Oxidation becomes: \( 3 \mathrm{Zn}(s) \rightarrow 3 \mathrm{Zn}^{2+}(aq) + 6e^- \).- Reduction becomes: \( 2 \mathrm{Cr}^{3+}(aq) + 6e^- \rightarrow 2 \mathrm{Cr}(s) \).

Step 10: Combine the Half-Reactions for Reaction (b)

Add the balanced oxidation and reduction half-reactions:\[ 2\mathrm{Cr}^{3+}(aq) + 3\mathrm{Zn}(s) \rightarrow 2\mathrm{Cr}(s) + 3\mathrm{Zn}^{2+}(aq) \]

Key Concepts

Half-Reaction Method

The half-reaction method is a systematic approach used to balance complex oxidation-reduction reactions. In redox reactions, it is essential to ensure that the electrons lost in oxidation are equal to the electrons gained in reduction. This method breaks down the overall reaction into two separate equations: one for oxidation and one for reduction.

• **Oxidation Half-Reaction**: This involves the species that loses electrons. For instance, in reaction (a), aluminum goes through oxidation: \( \mathrm{Al}(s) \rightarrow \mathrm{Al}^{3+}(aq) + 3e^- \).
• **Reduction Half-Reaction**: This deals with the species that gains electrons. For copper in reaction (a), the reduction is: \( \mathrm{Cu}^{2+}(aq) + 2e^- \rightarrow \mathrm{Cu}(s) \).

To balance the reactions, we adjust atoms and charges in each half-reaction. Electrons are then equalized across both equations, usually by multiplying each equation by a factor that makes the number of electrons the same. Finally, the balanced half-reactions are combined to form a complete balanced redox equation.

Oxidation-Reduction Reaction

An oxidation-reduction reaction, commonly known as a redox reaction, is a type of chemical reaction that involves the transfer of electrons between two species. This type of reaction is fundamental in chemistry and powers many essential processes in everyday life, from energy generation to metabolism in living organisms.

• **Oxidation**: This process involves the loss of electrons by a molecule, atom, or ion. As seen in reaction (b), zinc undergoes oxidation: \( \mathrm{Zn}(s) \rightarrow \mathrm{Zn}^{2+}(aq) + 2e^- \).
• **Reduction**: This is the gain of electrons by a molecule, atom, or ion. For chromium in reaction (b), reduction happens as: \( \mathrm{Cr}^{3+}(aq) + 3e^- \rightarrow \mathrm{Cr}(s) \).

Every oxidation is paired with a reduction; hence, electrons lost by one species are gained by another. This complementary process can be remembered by the mnemonic "OIL RIG" - Oxidation Is Loss, Reduction Is Gain of electrons.

Electron Transfer

Electron transfer is the essence of any redox reaction. The movement of electrons from one species to another is what drives the chemical changes within a redox reaction. Understanding how electron transfer occurs is crucial to grasp more complex chemical phenomena.
In the scenarios provided (a and b), electrons move from the oxidizing agent to the reducing agent:

• In reaction (a), aluminum is the source of electrons, or the reducing agent, while copper ions serve as the oxidizing agent, accepting electrons.
• Likewise, in reaction (b), zinc donates electrons and acts as a reducing agent as chromium ions capture those electrons and are reduced.

The interplay of electron transfer is what allows the balanced equations to represent a real chemical change. Recognizing which species are donors and acceptors is essential in profiling the redox behavior, providing insights into the reactivity and strength of different elements as oxidizing or reducing agents.