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, Mg is oxidized and Cu²⁺ is reduced. The galvanic cell consists of an anode where the oxidation half-reaction \(Mg(s) \rightarrow Mg^{2+}(aq) + 2e^-\) occurs, and a cathode where the reduction half-reaction \(Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)\) takes place. A salt bridge is used to maintain electrical neutrality in both half-cells.

Step-by-step solution

Identify the oxidation states and the redox process

In the given reaction, we can see that the oxidation states of Mg and Cu change: $$ \mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+}(a q) \\ \mathrm{Cu}^{2+}(a q) \rightarrow \mathrm{Cu}(s) $$ Mg changes from an oxidation state of 0 to +2, thus it is oxidized (loses electrons) in this redox process. Meanwhile, Cu changes from an oxidation state of +2 to 0, meaning it is reduced (gains electrons). This gives us: - Oxidized species: Mg - Reduced species: Cu

Identify the half-reactions

Since we know that Mg is oxidized and Cu is reduced, we can write the half-reactions for the given redox process: - Oxidation half-reaction (at anode): $$ \mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+}(a q) + 2 e^- $$ - Reduction half-reaction (at cathode): $$ \mathrm{Cu}^{2+}(a q) + 2 e^- \rightarrow \mathrm{Cu}(s) $$

Sketch the galvanic cell

We can now build our galvanic cell using the obtained information. The cell consists of two half-cells (anode and cathode): - Anode: Mg electrode is placed in a solution of Mg(NO₃)₂. This is where the oxidation half-reaction occurs when the metal is oxidized and releases electrons to the external circuit. - Cathode: Cu electrode is placed in a solution of Cu(NO₃)₂. This is where the reduction half-reaction occurs when Cu ions in the solution gain electrons from the external circuit and deposit as solid Cu onto the electrode. A salt bridge, typically containing KNO₃, is utilized to maintain electrical neutrality in both half-cells by allowing the flow of ions.

Summarize the results

To summarize, we have sketched a galvanic cell that uses the redox reaction: $$ \mathrm{Mg}(s)+\mathrm{Cu}^{2+}(a q) \rightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cu}(s) $$ The metal ion that is reduced is Cu²⁺, and the metal that is oxidized is Mg. The half-reaction at the anode is: $$ \mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+}(a q) + 2 e^- $$ The half-reaction at the cathode is: $$ \mathrm{Cu}^{2+}(a q) + 2 e^- \rightarrow \mathrm{Cu}(s) $$

Key concepts

Oxidation-Reduction Reaction

Oxidation-reduction reactions, also known as redox reactions, are processes that involve the transfer of electrons between two species. In a redox reaction, one substance loses electrons (oxidation) while another gains electrons (reduction). A classic example is the reaction between magnesium metal (Mg) and copper ion (Cu²⁺), which can be written as:

\[\[\begin{align*}\mathrm{Mg}(s)+\mathrm{Cu}^{2+}(aq) \rightarrow \mathrm{Mg}^{2+}(aq)+\mathrm{Cu}(s)\end{align*}\]\]
In this reaction, magnesium atoms lose two electrons, becoming Mg²⁺ ions, while copper ions gain those two electrons to form copper metal. To understand this process thoroughly, students must recognize the signs of oxidation and reduction. Oxidation corresponds to an increase in oxidation state, while reduction involves a decrease in oxidation state.

Oxidation: \( \mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+}(aq) + 2e^- \)
Reduction: \( \mathrm{Cu}^{2+}(aq) + 2e^- \rightarrow \mathrm{Cu}(s) \)

Identifying these changes in oxidation state is vital for studying the behavior of elements in a redox reaction, predicting products, and understanding the underlying chemistry of galvanic cells.

Half-Reaction

Each of the individual processes in a redox reaction—oxidation and reduction—can be represented as a 'half-reaction.' A half-reaction explicitly shows the loss or gain of electrons by a species. In the context of the magnesium and copper reaction, we have two half-reactions:

Oxidation Half-Reaction (occurs at the anode):

\( \mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+}(aq) + 2e^- \)
This half-reaction indicates that magnesium metal is being oxidized by losing two electrons. It takes place at the anode of a galvanic cell.

Reduction Half-Reaction (occurs at the cathode):

\( \mathrm{Cu}^{2+}(aq) + 2e^- \rightarrow \mathrm{Cu}(.s) \)
Conversely, the copper ions are reduced as they gain electrons, forming solid copper at the cathode.

Understanding half-reactions is crucial for students to comprehend the individual steps in a redox process, balance redox equations, and determine the flow of electrons in an electrochemical cell.

Cell Potential

The cell potential, often referred to as electromotive force (EMF), is the measure of the voltage difference between two half-cells in a galvanic cell. It is the driving force that pushes electrons from the anode to the cathode through an external circuit. The cell potential is determined by the relative tendencies of the involved redox couples to lose or gain electrons. When a metal such as magnesium is paired with a copper ion in a galvanic cell, the difference in their tendencies to undergo oxidation or reduction creates a measurable cell potential.

The magnesium/copper cell will have its own unique cell potential, which can be calculated by using standard reduction potentials from electrochemical series tables. Students should understand that

• The higher the difference in potential between the two half-cells, the greater the cell potential.
• A positive cell potential indicates a spontaneous reaction.
• Cell potential is crucial in determining the feasibility and directionality of the redox reaction.

By exploring cell potentials, students can better appreciate the energy conversions taking place in galvanic cells and their practical applications in generating electricity.