Question

Draw the voltaic cell represented by this reaction and label the cathode, the anode, the salt bridge, the oxidation half cell, the reduction half cell, the positive electrode, and the negative electrode. Use Figure 14.1 "A Redox Reaction in Which the Two Half Reactions Are Physically Separated" as a guide. $$ 3 \mathrm{Mg}+2 \mathrm{Cr}^{3+} \rightarrow 3 \mathrm{Mg}^{2+}+2 \mathrm{Cr} $$

Short answer

Anode: Mg, Cathode: Cr; Anode is negative, Cathode is positive.

Step-by-step solution

Identify the Half-Reactions

The given reaction is \( 3 \mathrm{Mg}+2 \mathrm{Cr}^{3+} \rightarrow 3 \mathrm{Mg}^{2+}+2 \mathrm{Cr} \). First, split it into two half-reactions. The oxidation half-reaction is \( 3 \mathrm{Mg} \rightarrow 3 \mathrm{Mg}^{2+} + 6e^- \), and the reduction half-reaction is \( 2 \mathrm{Cr}^{3+} + 6e^- \rightarrow 2 \mathrm{Cr} \).

Determine Anode and Cathode

The oxidation half-reaction occurs at the anode and involves magnesium losing electrons. Therefore, the anode is where the \( \mathrm{Mg} \) --> \( \mathrm{Mg}^{2+} \) reaction occurs. The reduction half-reaction occurs at the cathode, where \( \mathrm{Cr}^{3+} \) ions gain electrons to form \( \mathrm{Cr} \), making this the site of the cathode.

Label the Electrodes

In electrochemical cells, oxidation occurs at the anode, making it the negative electrode. Reduction occurs at the cathode, making it the positive electrode. Therefore, label the anode as negative and the cathode as positive.

Add the Salt Bridge

A salt bridge is necessary to maintain the charge balance. Connect the anode and cathode solutions with a salt bridge, which allows the ions to flow and completes the circuit without allowing the solutions to mix.

Draw the Voltaic Cell

Draw the cell with two half-cells separated, featuring a container for magnesium and its ions on one side and for chromium and its ions on the other. Connect them with a salt bridge and indicate the compartments, electrodes, and flow of electrons.

Key concepts

Oxidation Reaction

In an oxidation reaction, a substance loses electrons, increasing its oxidation state. The reaction for magnesium in the provided exercise is a prime example. Magnesium (\( \mathrm{Mg} \)) loses electrons to form magnesium ions (\( \mathrm{Mg}^{2+} \)) by the equation: \( 3 \mathrm{Mg} ightarrow 3 \mathrm{Mg}^{2+} + 6e^- \).
Oxidation occurs at the anode in a voltaic cell, where it's characterized by the loss of electrons. This process leads to magnesium's conversion from its pure metallic form into ions, which results in the flow of electrons into the external circuit.
To remember oxidation, use the mnemonic 'OIL RIG'—Oxidation Is Loss (of electrons). This concept is crucial for understanding how energy is generated from chemical reactions in voltaic cells.

Reduction Reaction

Reduction is essentially the opposite of oxidation—it involves the gain of electrons by a molecule, atom, or ion. In our reaction involving chromium, chromium ions (\( \mathrm{Cr}^{3+} \)) gain electrons. This can be written as:\( 2 \mathrm{Cr}^{3+} + 6e^- ightarrow 2 \mathrm{Cr} \).
Reduction occurs at the cathode in an electrochemical cell. During this process, electrons provided by the external circuit are used to convert the \( \mathrm{Cr}^{3+} \) ions into chromium metal. This is a critical reaction because it is the site where the gain of electrons occurs, thus completing the circuit.
To easily recall reduction, use the mnemonic 'OIL RIG'—Reduction Is Gain (of electrons), providing a straightforward way of understanding these complementary processes.

Electrochemical Cell

An electrochemical cell is a device capable of generating electrical energy from chemical reactions or facilitating chemical reactions through the introduction of electrical energy. In a voltaic or galvanic cell, like the one described in the exercise, the spontaneous reaction between chemicals generates electrical energy.

• Anode: Site of oxidation; electrons are liberated here.
• Cathode: Site of reduction; electrons are accepted here.
• Salt Bridge: Connects the two half-cells and balances charge by allowing ions to travel between them.

In these cells, two half-cells are used: one for the oxidation reaction and the other for the reduction reaction. The flow of electrons from the anode to the cathode through an external circuit provides electrical energy.

Half-Reactions

Half-reactions are part of a redox reaction, indicating the oxidation or reduction process that occurs separately. Each half-reaction either adds electrons or removes them, highlighting the electron movement.

• Oxidation Half-Reaction: \( 3 \mathrm{Mg} ightarrow 3 \mathrm{Mg}^{2+} + 6e^- \) - Magnesium loses electrons and is oxidized.
• Reduction Half-Reaction: \( 2 \mathrm{Cr}^{3+} + 6e^- ightarrow 2 \mathrm{Cr} \) - Chromium ions gain electrons and are reduced.

The beauty of using half-reactions is in simplifying the complex transformations in a redox reaction. By looking at each half separately, it's easier to follow where electrons are moving and how they're contributing to the larger reaction. This understanding is foundational in constructing voltaic cells.