Problem 59 - Chemistry and Chemical Reactivity

Question

Magnesium metal is oxidized, and silver ions are reduced in a voltaic cell using \(\mathrm{Mg}^{2+}(\mathrm{aq}, 1 \mathrm{M}) | \mathrm{Mg}\) and \(\mathrm{Ag}^{+}(\text {aq, } 1 \mathrm{M}) |\) Ag half-cells. (a) Label each part of the cell. (b) Write equations for the half-reactions occurring at the anode and the cathode, and write an equation for the net reaction in the cell. (c) Trace the movement of electrons in the exter. nal circuit. Assuming the salt bridge contains NaNO_, trace the movement of the Nat and \(\mathrm{NO}_{3}^{-}\) ions in the salt bridge that occurs when a voltaic cell produces current. Why is a salt bridge required in a cell?

Step-by-Step Solution

Answer

Mg is the anode, Ag is the cathode; net reaction: \( \mathrm{Mg} + 2\mathrm{Ag}^{+} \rightarrow \mathrm{Mg}^{2+} + 2\mathrm{Ag} \); electrons from Mg to Ag.

Step 1: Understanding the Components

The voltaic cell consists of two half-cells. The first half-cell includes magnesium, represented as \( \mathrm{Mg}^{2+} \) (aq, 1 M) | \( \mathrm{Mg} \), and the second half-cell involves silver, represented as \( \mathrm{Ag}^{+} \) (aq, 1 M) | \( \mathrm{Ag} \). The anode is where oxidation (loss of electrons) occurs, and the cathode is where reduction (gain of electrons) takes place.

Step 2: Label Each Part of the Cell

In our magnesium-silver voltaic cell, magnesium (Mg) is the anode, because it loses electrons, and silver (Ag) is the cathode, as it gains electrons. The anode compartment contains \( \mathrm{Mg}/\mathrm{Mg}^{2+} \) and the cathode compartment contains \( \mathrm{Ag}^{+}/\mathrm{Ag} \). The salt bridge connects these two half-cells.

Step 3: Write Equations for Half-Reactions

The oxidation half-reaction at the anode is: \( \mathrm{Mg} \rightarrow \mathrm{Mg}^{2+} + 2e^- \). The reduction half-reaction at the cathode is: \( \mathrm{Ag}^{+} + e^- \rightarrow \mathrm{Ag} \). For the net equation, balance electrons by multiplying the reduction equation by 2: \( 2\mathrm{Ag}^{+} + 2e^- \rightarrow 2\mathrm{Ag} \). The net reaction is: \( \mathrm{Mg} + 2\mathrm{Ag}^{+} \rightarrow \mathrm{Mg}^{2+} + 2\mathrm{Ag} \).

Step 4: Describe Electron Flow

Electrons flow from the anode (Mg) to the cathode (Ag) along the external wire. This movement of electrons allows for the generation of electrical current.

Step 5: Trace Ion Movement in the Salt Bridge

In the salt bridge containing \( \mathrm{NaNO}_3 \), \( \mathrm{Na}^+ \) ions travel towards the cathode compartment to balance the addition of \( \mathrm{Ag}^+ \) ions from the solution, and \( \mathrm{NO}_3^- \) ions move towards the anode to balance the generation of \( \mathrm{Mg}^{2+} \) ions. The salt bridge maintains electrical neutrality by preventing charge buildup, allowing the flow of ions to complete the circuit.

Key Concepts

Voltaic cell

A voltaic cell, also known as a galvanic cell, is a device that converts chemical energy into electrical energy through a redox reaction. It consists of two compartments, called half-cells, each containing a different metal electrode and a solution of its corresponding ions.
In the case of our exercise, these half-cells are magnesium and silver, represented as \( \mathrm{Mg}/\mathrm{Mg}^{2+} \) and \( \mathrm{Ag}^{+}/\mathrm{Ag} \), respectively.
The reactions in each half-cell are connected by an external circuit where electrons flow, generating electricity. A typical voltaic cell setup includes a salt bridge, which ensures the flow of ions to maintain electrical neutrality.

Half-reaction

A half-reaction is a part of a redox reaction that involves either oxidation or reduction. It isolates the changes in electron charges that occur in each reactant.
In a voltaic cell, the half-reaction at each electrode highlights either the loss or gain of electrons. For magnesium in our voltaic cell, the half-reaction at the anode is \( \mathrm{Mg} \rightarrow \mathrm{Mg}^{2+} + 2e^- \), which represents oxidation.
At the cathode, the silver half-reaction \( \mathrm{Ag}^{+} + e^- \rightarrow \mathrm{Ag} \) depicts reduction.
These half-reactions show how electrons are transferred, lending understanding to the net cell reaction of \( \mathrm{Mg} + 2\mathrm{Ag}^{+} \rightarrow \mathrm{Mg}^{2+} + 2\mathrm{Ag} \).

Oxidation-reduction

Oxidation-reduction, or redox reactions, involve the transfer of electrons between substances. Oxidation is the process of losing electrons, while reduction is gaining electrons.
In our magnesium-silver voltaic cell, oxidation occurs at the magnesium anode \( \mathrm{Mg} \rightarrow \mathrm{Mg}^{2+} + 2e^- \) as magnesium loses electrons.
Meanwhile, at the silver cathode, reduction takes place \( \mathrm{Ag}^{+} + e^- \rightarrow \mathrm{Ag} \) as silver ions gain electrons.

• Oxidation always happens at the anode.
• Reduction always occurs at the cathode.

This transfer of electrons is essential for the generation of electric current in a voltaic cell.

Salt bridge

A salt bridge is an essential component of a voltaic cell. It connects the two half-cells and allows the movement of ions without allowing the solutions to mix directly.
This component is critical because it maintains electrical neutrality by allowing ions to move between the two half-cells. In our example with a \( \mathrm{NaNO}_3 \) salt bridge, \( \mathrm{Na}^+ \) ions migrate toward the cathode to balance the \( \mathrm{Ag}^+ \) ions being reduced, while \( \mathrm{NO}_3^- \) ions move toward the anode to balance the charge of \( \mathrm{Mg}^{2+} \) ions created through oxidation.

Without a salt bridge, the voltaic cell would quickly stop functioning as the charge would accumulate, preventing further electron flow. It ensures that the cell continues to produce electrical current efficiently.