Problem 10 - Chemistry and Chemical Reactivity

Question

The half-cells \(\mathrm{Ag}^{+}(\mathrm{aq}) | \mathrm{Ag}(\mathrm{s})\) and \(\mathrm{Cl}_{2}(\mathrm{g}) | \mathrm{Cl}^{-}(\mathrm{aq})\) are linked to create a voltaic cell. (a) Write equations for the oxidation and reduction halfreactions and for the overall (cell) reaction. (b) Which half-reaction occurs in the anode compartment and which occurs in the cathode compartment? (c) Complete the following sentences: Electrons in the external circuit flow from the ___ electrode to the ___ electrode. Negative ions move in the salt bridge from the ___ half-cell to the ___ half-cell.

Step-by-Step Solution

Answer

(a) Oxidation: \( \mathrm{Ag} \rightarrow \mathrm{Ag}^{+} + e^- \), Reduction: \( \mathrm{Cl}_2 + 2e^- \rightarrow 2\mathrm{Cl}^- \). (b) Oxidation at anode, reduction at cathode. (c) Electrons: Ag to Cl; negative ions: Cl to Ag.

Step 1: Identify Oxidation and Reduction Half-Reactions

The two half-cells provided are \( \mathrm{Ag}^{+}( ext{aq}) | \mathrm{Ag}( ext{s}) \) for the Silver electrode and \( \mathrm{Cl}_{2}( ext{g}) | \mathrm{Cl}^{-}( ext{aq}) \) for the Chlorine electrode. Silver ions are reduced to metallic silver via the half-reaction \( \mathrm{Ag}^{+} + e^- \rightarrow \mathrm{Ag} \). Chlorine gas is reduced to chloride ions via the half-reaction \( \mathrm{Cl}_2 + 2e^- \rightarrow 2\mathrm{Cl}^- \).

Step 2: Assign Anode and Cathode Reactions

In electrochemistry, oxidation occurs at the anode and reduction occurs at the cathode. Identify which species are being oxidized or reduced: \( \mathrm{Ag} \rightarrow \mathrm{Ag}^{+} + e^- \) is the oxidation half-reaction (anode), and \( \mathrm{Cl}_2 + 2e^- \rightarrow 2\mathrm{Cl}^- \) is the reduction half-reaction (cathode).

Step 3: Write the Overall Cell Reaction

Write the balanced cell reaction by combining the two half-reactions. The overall reaction is: \( \mathrm{Cl}_2 + 2 \mathrm{Ag} \rightarrow 2 \mathrm{Cl}^- + 2 \mathrm{Ag}^+ \).

Step 4: Analyze Electron Flow in External Circuit

Electrons flow from the anode to the cathode in the external circuit. In this scenario, electrons flow from the Silver electrode (anode) to the Chlorine electrode (cathode).

Step 5: Analyze Movement of Ions in the Salt Bridge

Negative ions move through the salt bridge to balance charge. Since electrons flow from the Silver half-cell (Anode) to the Chlorine half-cell (Cathode), negative ions move from the Chlorine half-cell to the Silver half-cell to maintain electrical neutrality.

Key Concepts

Oxidation and Reduction

In a voltaic cell, oxidation and reduction reactions work hand in hand to convert chemical energy into electrical energy. Oxidation is the process where a substance loses electrons. In the given exercise, silver undergoes oxidation with the half-reaction:

• \( \mathrm{Ag} \rightarrow \mathrm{Ag}^{+} + e^- \)

The silver atom loses an electron to become a silver ion. On the other side, reduction is the gain of electrons. Chlorine gas gains electrons to form chloride ions in the reduction half-reaction:

• \( \mathrm{Cl}_2 + 2e^- \rightarrow 2\mathrm{Cl}^- \)

These two processes occur simultaneously in a voltaic cell, driving the flow of electrons.

Half-Reactions

Half-reactions are a way to represent just the oxidation or just the reduction that occurs in a redox process. They help us to see clearly what happens to each reactant in a voltaic cell. For silver, the half-reaction involves electrons being released:

• \( \mathrm{Ag} \rightarrow \mathrm{Ag}^{+} + e^- \)

For chlorine, electrons are gained:

• \( \mathrm{Cl}_2 + 2e^- \rightarrow 2\mathrm{Cl}^- \)

By writing these half-reactions separately, it becomes easier to focus on the transfer of electrons and how these movements power the cell. The overall cell reaction is derived by combining these half-reactions.

Electron Flow

Electron flow is crucial for a voltaic cell to perform its function of generating electricity. This flow occurs through an external circuit connecting the two electrodes. Electrons are released by the anode (where oxidation occurs) and are accepted at the cathode (where reduction happens). In our voltaic cell setup:

• Electrons flow from the silver electrode (anode) to the chlorine electrode (cathode).

This movement of electrons is what produces the electric current, allowing devices connected to the circuit to operate. Understanding which way electrons flow tells us the direction of energy transfer in the cell.

Salt Bridge

The salt bridge is an essential component of a voltaic cell, ensuring that the cell can continue operating efficiently. It balances the charge between the two half-cells by allowing ions to flow between them. When electrons move from the anode to the cathode:

• Negative ions from the salt bridge move from the chlorine half-cell to the silver half-cell.

This movement keeps the overall charge balanced, preventing the cell from rapidly discharging. It also maintains electrical neutrality, allowing the redox reactions to continue smoothly.

Electrode Compartments

Electrode compartments are the physical spaces where the half-reactions occur within a voltaic cell. Each compartment houses one electrode and the electrolyte solution in which its corresponding reaction takes place. Typically:

• The anode compartment is where oxidation happens - here, the silver electrode oxidizes.
• The cathode compartment is where reduction happens - here, chlorine gas reduces.

These compartments separate the reactants physically but allow electron flow and ion exchange, facilitating the voltaic cell's operation.