Problem 29 - Chemistry: The Central Science

Question

A voltaic cell similar to that shown in Figure \(20.5\) is constructed. One electrode half-cell consists of a silver strip placed in a solution of \(\mathrm{AgNO}_{\mathrm{g}}\) and the other has an iron strip placed in a solution of \(\mathrm{FeCl}_{2}\). The overall cell reaction is $$ \mathrm{Fe}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+2 \mathrm{Ag}(s) $$ (a) What is being oxidized, and what is being reduced? (b) Write the half-reactions that occur in the two half-cells. (c) Which electrode is the anode, and which is the cathode? (d) Indicate the signs of the electrodes. (e) Do electrons flow from the silver electrode to the iron electrode or from the iron to the silver? (f) In which directions do the cations and anions migrate through the solution?

Step-by-Step Solution

Answer

(a) Iron is being oxidized and silver is being reduced. (b) Oxidation half-reaction: \(\mathrm{Fe}(s) \longrightarrow \mathrm{Fe}^{2+}(aq) + 2e^-\), Reduction half-reaction: \(2\mathrm{Ag}^+(aq) + 2e^- \longrightarrow 2\mathrm{Ag}(s)\). (c) Anode = Iron electrode, Cathode = Silver electrode. (d) Anode (Iron electrode) = Negative, Cathode (Silver electrode) = Positive. (e) Electrons flow from the iron electrode (anode) to the silver electrode (cathode). (f) Cations migrate towards the cathode (silver electrode), and anions migrate towards the anode (iron electrode).

Step 1: Identify Oxidation and Reduction

The given overall cell reaction is: \(\mathrm{Fe}(s) + 2\mathrm{Ag}^+(aq) \longrightarrow \mathrm{Fe}^{2+}(aq) + 2\mathrm{Ag}(s)\) In this reaction, iron (Fe) is losing electrons and becoming Fe²⁺ ions. This is an oxidation process. On the other hand, silver ions (Ag⁺) are gaining electrons, and becoming silver metal (Ag). This is a reduction process. So, iron is being oxidized and silver is being reduced.

Step 2: Write Half-reactions

Now, we can write the half-reactions for oxidation and reduction separately. Oxidation half-reaction (occurring at anode): \(\mathrm{Fe}(s) \longrightarrow \mathrm{Fe}^{2+}(aq) + 2e^-\) Reduction half-reaction (occurring at cathode): \(2\mathrm{Ag}^+(aq) + 2e^- \longrightarrow 2\mathrm{Ag}(s)\)

Step 3: Identify Anode and Cathode

Based on the half-reactions: The anode is where oxidation occurs, i.e., the iron electrode: Anode = Iron electrode The cathode is where reduction occurs, i.e., the silver electrode: Cathode = Silver electrode

Step 4: Determine Signs of Electrodes

Identifying the signs of electrodes: Anode: Since oxidation takes place at the anode, it is the source of electrons, which are negatively charged, so the anode is negative: Anode (Iron electrode) = Negative Cathode: Since reduction takes place at the cathode, it receives electrons, so it is positive: Cathode (Silver electrode) = Positive

Step 5: Direction of Electron Flow

Electrons flow from the electrode where oxidation takes place (anode) to the electrode where reduction takes place (cathode). Therefore, electrons flow from the iron electrode (anode) to the silver electrode (cathode).

Step 6: Migration of Cations and Anions

In the solution: - Cations (positively charged ions) will migrate towards the cathode (silver electrode), which is negatively charged - Anions (negatively charged ions) will migrate towards the anode (iron electrode), which is positively charged

Key Concepts

Oxidation and Reduction

In a voltaic cell, oxidation and reduction processes occur simultaneously to drive the electrochemical reactions. Oxidation is the process in which a substance loses electrons. In our example, iron (Fe) undergoes oxidation as it loses two electrons to form \(\mathrm{Fe}^{2+}(aq)\). This process is crucial because free electrons are needed for the cell to function.On the other hand, reduction is the process where a substance gains electrons. Silver ions (\(\mathrm{Ag}^{+}\)) gain electrons to form silver metal (\(\mathrm{Ag}(s)\)). Reduction completes the circuit by using the electrons supplied by oxidation, ensuring that energy flows smoothly within the system.

Electrode Classification

Electrodes are fundamental components of voltaic cells, serving as sites for oxidation and reduction. In this cell, we have two electrodes: an iron electrode and a silver electrode. The anode is the electrode where oxidation occurs, which in this case, is the iron electrode, as Fe loses electrons. Meanwhile, the cathode is the site of reduction, situated at the silver electrode, where Ag⁺ gains electrons. Additionally, electrodes are classified by their role in the cell's electron transfer process:

• Anode: The negative electrode as it loses electrons.
• Cathode: The positive electrode as it gains electrons.

This classification helps understand how electrons move and where chemical changes happen in the cell.

Electron Flow

Understanding electron flow in a voltaic cell is key to grasping how these cells generate electrical energy. Electrons originate from the oxidation process at the anode. In this voltaic cell, electrons flow from the iron anode, where Fe is oxidized and releases electrons, towards the silver cathode, where the reduction process occurs. This movement is vital because it represents the flow of electrical current, which powers any connected external circuit or device. In summary:

• Direction of electron flow: From anode (iron) to cathode (silver)
• Purpose: To carry electrical energy through the circuit

Ion Migration

Ion migration balances the charge in the voltaic cell's solution, supporting continuous reaction flow. In electrochemical cells, ions move to compensate for electrons leaving or entering the electrodes. In this example, the positively charged ions (cations) migrate towards the negatively charged cathode (silver electrode), while negatively charged ions (anions) move toward the positively charged anode (iron electrode). This ion migration ensures that charge balance is maintained in the cell so that reactions can continue without disruption. Key points to remember include:

• Cation migration direction: Towards the cathode
• Anion migration direction: Towards the anode

Half-Reactions

Half-reactions are detailed depictions of the oxidation and reduction processes in an electrochemical cell. They provide insights into the electron exchange occurring at each electrode site. For example:

• Oxidation half-reaction: \(\mathrm{Fe}(s) \rightarrow \mathrm{Fe}^{2+}(aq) + 2e^-\)
• Reduction half-reaction: \(2\mathrm{Ag}^{+}(aq) + 2e^- \rightarrow 2\mathrm{Ag}(s)\)

These reactions reflect the changes occurring at each electrode, with the oxidation reaction showing the loss of electrons by Fe, and the reduction reaction representing the gain of electrons by Ag⁺. By writing these half-reactions, we get a clear picture of electron flow and chemical changes within the voltaic cell.