Question

Consider the oxidation-reduction reaction \(\mathrm{Mg}(s)+\mathrm{Cu}^{2+}(a q) \rightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cu}(s)\) Sketch a galvanic cell that uses this reaction. Which metal ion is reduced? Which metal is oxidized? What half-reaction takes place at the anode in the cell? What half-reaction takes place at the cathode?

Short answer

In the given redox reaction, magnesium (Mg) is oxidized, losing 2 electrons to become a magnesium ion (Mg\(^{2+}\)), and copper ions (Cu\(^{2+}\)) are reduced, gaining 2 electrons to become copper metal (Cu). The oxidation half-reaction is: \(Mg(s) \rightarrow Mg^{2+}(aq) + 2e^-\), and the reduction half-reaction is: \(Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)\). In the galvanic cell, the anode is where oxidation occurs (Mg electrode) and the cathode is where reduction takes place (Cu\(^{2+}\) electrode). A salt bridge connects the two containers to maintain electrical neutrality.

Step-by-step solution

Identifying the Oxidation and Reduction

In a redox reaction, oxidation refers to the loss of electrons, while reduction refers to the gain of electrons. Begin by examining the reactants and products to see how the electron count changes. In the given reaction, magnesium (Mg) becomes magnesium ion (Mg\(^{2+}\)), indicating loss of 2 electrons, so Mg is oxidized. On the other hand, copper ion (Cu\(^{2+}\)) becomes copper metal (Cu) which means gain of 2 electrons, hence Cu\(^{2+}\) is reduced.

Writing Half-Reactions

The changes in oxidation state can be represented as two separate half-reactions, one for the oxidation process and one for the reduction process. The oxidation half-reaction (loss of electrons by Mg) is: \(Mg(s) \rightarrow Mg^{2+}(aq) + 2e^-\) The reduction half-reaction (gain of electrons by Cu\(^{2+}\)) is: \(Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)\)

Identifying the Anode and Cathode

In a galvanic cell, oxidation takes place at the anode, and reduction takes place at the cathode. So, Mg is at the anode and Cu\(^{2+}\) is at the cathode. The oxidation half-reaction takes place at the anode, and the reduction half-reaction takes place at the cathode.

Sketching the Galvanic Cell

Draw two containers, one for the Mg electrode (anode) and one for the Cu electrode (cathode). Connect them with a salt bridge. Draw an arrow pointing from the anode to the cathode to represent the flow of electrons. In the left container (anode), illustrate Mg getting oxidized to Mg\(^{2+}\) and releasing 2 electrons that go through the external circuit. In the right container (cathode), show Cu\(^{2+}\) gaining these electrons to form Cu. Finally, ions from the salt bridge maintain electrical neutrality in both containers. Label the anode and cathode, clearly showing oxidation and reduction half-reactions where they occur.

Key concepts

Oxidation

Oxidation is a key concept in redox reactions, representing the loss of electrons. In our given reaction, magnesium (\(\mathrm{Mg}(s)\)) changes to magnesium ions (\(\mathrm{Mg}^{2+}(aq)\)). This shift means magnesium loses two electrons, signaling it's being oxidized.

To recognize oxidation:

• Identify the element losing electrons.
• Observe the change from a neutral state to a positively charged ion.

In this case, Mg loses its electrons, marking it as the substance that undergoes oxidation.

Reduction

Reduction involves the gain of electrons. In our reaction, copper ions (\(\mathrm{Cu}^{2+}(aq)\)) gain electrons to form copper metal (\(\mathrm{Cu}(s)\)). This gain of electrons means that copper ions are reduced.

To spot reduction:

• Find the element gaining electrons.
• Check the transition from a positively charged ion to a neutral state.

Here, \(\mathrm{Cu}^{2+}\) undergoes reduction, indicating it's the reduced species.

Galvanic Cell

A galvanic cell is an apparatus that generates electrical energy from a spontaneous redox reaction. It consists of two separate compartments, each containing an electrode and an electrolyte solution.

In our scenario:

• The anode compartment houses magnesium, where oxidation occurs.
• The cathode compartment contains copper, where reduction happens.

A salt bridge or porous barrier completes the circuit, allowing ions to flow and maintaining neutrality. This flow of electrons from anode to cathode creates the electric current.

Half-Reaction

Half-reactions are a way to separate the overall redox reaction into oxidation and reduction processes. They make it easier to understand how electrons are transferred.

For the magnesium and copper reaction:

• The oxidation half-reaction: \(\mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+}(aq) + 2e^-\)
• The reduction half-reaction: \(\mathrm{Cu}^{2+}(aq) + 2e^- \rightarrow \mathrm{Cu}(s)\)

These half-reactions ensure clarity by displaying the electron exchange distinctly.

Anode and Cathode Identification

Identifying the anode and cathode in a galvanic cell is essential for understanding where oxidation and reduction occur:

• The anode is where oxidation happens. For our example, magnesium is the anode since it loses electrons.
• The cathode is where reduction takes place. Copper ion is the cathode because it gains electrons.

Remember the mnemonic, 'An Ox, Red Cat'—oxidation at the anode, reduction at the cathode. This helps in quickly recalling their roles.