Problem 22 - Chemistry: An Atoms-Focused Approach

Question

Super Iron Batteries In \(1999,\) scientists in Israel developed a battery based on the following cell reaction with iron(V1), nicknamed "super iron": \(2 \mathrm{K}_{2} \mathrm{FeO}_{4}(a q)+3 \mathrm{Zn}(s) \rightarrow \mathrm{Fc}_{2} \mathrm{O}_{3}(s)+\mathrm{ZnO}(s)+2 \mathrm{K}_{2} \mathrm{ZnO}_{2}(a q).\) a. Determine the number of electrons transferred in the cell reaction. b. What are the oxidation states of the transition metals in the reaction? c. Draw the cell.

Step-by-Step Solution

Answer

Iron (Fe) starts with an oxidation state of +6 and ends with an oxidation state of +3. Zinc (Zn) starts with an oxidation state of 0 and ends with an oxidation state of +2. c. Draw the cell. The cell can be represented as: \(Zn(s) | Zn^{2+}(aq) || Fe^{6+}(aq), Fe^{3+}(aq) | Fe_2O_3(s)\) In this cell, zinc serves as the anode (where oxidation occurs) and iron serves as the cathode (where reduction occurs).

Step 1: a. Determine the number of electrons transferred in the cell reaction

Firstly, we need to identify the species that are changing their oxidation states during the reaction. For this, we can look at the balanced equation: \(2 K_2FeO_4(aq) + 3 Zn(s) \rightarrow Fe_2O_3(s) + ZnO(s) + 2 K_2ZnO_2(aq)\) In this reaction, we can see that iron (Fe) and zinc (Zn) change their oxidation state. Let's determine the initial and final oxidation states for both elements: Iron starts as a part of \(K_2FeO_4\), which contains the Fe(VI) ion (as mentioned in the problem). Iron ends as a part of \(Fe_2O_3\), in which it has an oxidation state of +3. Zinc starts as the elemental form, \(Zn(s)\), with an oxidation state of 0. Zinc ends as a part of \(ZnO\) and \(K_2ZnO_2\), in which it has an oxidation state of +2. Now we can calculate the number of electrons that are transferred. We know that 2 moles of \(K_2FeO_4\) and 3 moles of \(Zn\) are participating in the reaction: For iron: Initial oxidation state: +6 Final oxidation state: +3 Change in oxidation state: -3 Since there are 2 moles of \(Fe\) present, the total change in oxidation state is \(-3 \times 2 = -6\) (6 electrons are gained). For zinc: Initial oxidation state: 0 Final oxidation state: +2 Change in oxidation state: +2 Since there are 3 moles of \(Zn\) present, the total change in oxidation state is \(+2 \times 3 = +6\) (6 electrons are lost). The number of electrons transferred in the cell reaction is therefore 6.

Step 2: b. What are the oxidation states of the transition metals in the reaction?

We already determined the oxidation states in part a. For clarity, let's reiterate the oxidation states of the transition metals in the reaction: Iron (Fe): Starts with an oxidation state of +6 (in \(K_2FeO_4\)) and ends with an oxidation state of +3 (in \(Fe_2O_3\)). Zinc (Zn): Starts with an oxidation state of 0 (in \(Zn\)) and ends with an oxidation state of +2 (in \(ZnO\) and \(K_2ZnO_2\)).

Step 3: c. Draw the cell

To draw the cell, we first need to determine which half-reaction is the oxidation reaction and which half-reaction is the reduction reaction: Oxidation half-reaction: \(Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-\) Reduction half-reaction: \(Fe^{6+}(aq) + 3e^- \rightarrow Fe^{3+}(aq)\) The cell can now be represented as: \(Zn(s) | Zn^{2+}(aq) || Fe^{6+}(aq), Fe^{3+}(aq) | Fe_2O_3(s)\) In this cell, zinc serves as the anode (where oxidation occurs) and iron serves as the cathode (where reduction occurs).

Key Concepts

Oxidation States

Understanding oxidation states is crucial in chemistry, especially when analyzing redox reactions. The oxidation state, or oxidation number, indicates the degree of oxidation of an atom in a compound. It is a hypothetical charge an atom would have if all bonds to atoms of different elements were 100% ionic. For example, in the compound \( K_2FeO_4 \), iron has an oxidation state of +6. This high value is due to its bonding with more electronegative oxygen atoms.

In contrast, elemental zinc \( (Zn) \) has an oxidation state of 0 as it is not combined with any other element. By following these changes, we can determine how electrons are transferred in a reaction. Identifying the change in oxidation states helps us understand the movement of electrons, which is central to redox reactions.

Redox Reactions

Redox reactions involve the transfer of electrons between two species. They are composed of two half-reactions: oxidation, where a species loses electrons, and reduction, where a species gains electrons. In the exercise, zinc undergoes oxidation, losing electrons to move from an oxidation state of 0 to +2. Meanwhile, iron undergoes reduction, gaining electrons to decrease its oxidation state from +6 to +3.

Understanding redox reactions requires identifying the oxidizing and reducing agents. Here, zinc is the reducing agent since it donates electrons, and iron is the oxidizing agent as it accepts electrons. Recognizing these agents helps us grasp how chemical energy is transferred and transformed during the reaction.

Electrochemical Cells

Electrochemical cells, like the one described in the exercise, convert chemical energy into electrical energy through redox reactions. These cells consist of two electrodes: an anode and a cathode.

• The anode is where oxidation occurs. In this case, zinc is oxidized at the anode.
• The cathode is where reduction takes place. Iron is reduced at the cathode.

In our cell, zinc metal serves as the anode, releasing electrons into the external circuit. Iron ions in the solution are reduced at the cathode.

The cell is often represented with a cell diagram that shows the flow of electrons and the movement within the cell. It's an important tool to visualize the process, showing zinc ions \( (Zn^{2+}) \) traveling through the solution and electrons flowing through the external circuit to the iron ions \( (Fe^{3+}) \), which are reduced. Understanding how these cells work underpins battery technology and numerous other applications in modern life.