Problem 25 - Chemistry The Science in Context

Question

Super Iron Batteries In \(1999,\) scientists in Israel developed a battery based on the following cell reaction with iron(VI), nicknamed "super iron": \(\beth \mathrm{K}_{2} \mathrm{FeO}_{4}(a q)+3 \mathrm{Zn}(s) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{ZnO}(s)+2 \mathrm{K}_{2} \mathrm{ZnO}_{2}(a q)\) 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 diagram.

Step-by-Step Solution

Answer

Question: In a battery based on the following redox reaction, determine (a) the number of electrons transferred in the reaction, (b) the oxidation states of the transition metals in the reaction, and (c) draw the cell diagram: \(\mathrm{K}_{2} \mathrm{FeO}_{4}(aq) + 3\,\mathrm{Zn}(s) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3} (s) + 3\,\mathrm{ZnO}(s) +2\mathrm{K}_{2}\mathrm{ZnO}_{2}(aq)\) Answer: (a) The number of electrons transferred in the cell reaction is 6. (b) The oxidation states of the transition metals in the reaction are +6 for iron(VI), +3 for iron, 0 for zinc, and +2 for zinc in its compounds. (c) The cell diagram for the reaction is: Zn(s) | Zn^2+(aq) || Fe^6+(aq), Fe^3+(aq) | Fe(s).

Step 1: Identify the reduction and oxidation processes

To begin, we need to identify the half-reactions (reduction and oxidation) that are taking place. In the given reaction, iron is being reduced, and zinc is being oxidized: \(\mathrm{K}_{2} \mathrm{FeO}_{4}(aq) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3} (s)\) (Reduction) \(3\,\mathrm{Zn}(s) \rightarrow \mathrm{ZnO}(s) +2\mathrm{K}_{2}\mathrm{ZnO}_{2}(aq)\) (Oxidation)

Step 2: Calculate the change in oxidation states

In order to determine the number of electrons transferred in the cell reaction, we need to find the number of electrons gained and lost in the reduction and oxidation processes. First, let's determine the oxidation states of the transition metals in each compound: K: +1 Fe in \(\mathrm{FeO}_{4}\): +6 Fe in \(\mathrm{Fe}_{2}\mathrm{O}_{3}\): +3 Zn: 0 O: -2 Now, let's calculate the number of electrons exchanged in each half-reaction: Reduction: \(\mathrm{Fe}^{+6} \rightarrow \mathrm{Fe}_{2}^{+3}\), exchange of \(3 \times 2 = 6\) electrons (since two ions are involved) Oxidation: \(\mathrm{Zn}^{0} \rightarrow \mathrm{Zn}^{+2}\), exchange of \(2 \times 3 = 6\) electrons (since three atoms are involved)

Step 3: Determine the number of electrons transferred

From step 2, we can see that there are 6 electrons transferred in both the reduction and oxidation processes, which means the total number of electrons transferred in the cell reaction is 6. Answer (a): The number of electrons transferred in the cell reaction is 6.

Step 4: Write the oxidation states of the transition metals

From step 2, the oxidation states of the transition metals in the reaction are: Iron(VI) in \(\mathrm{K}_{2}\mathrm{FeO}_{4}\): +6 Iron in \(\mathrm{Fe}_{2}\mathrm{O}_{3}\): +3 Zinc in \(\mathrm{Zn}\): 0 Zinc in \(\mathrm{ZnO}\) and \(\mathrm{K}_{2}\mathrm{ZnO}_{2}\): +2 Answer (b): The oxidation states of the transition metals in the reaction are +6 for iron(VI), +3 for iron, 0 for zinc, and +2 for zinc in its compounds.

Step 5: Draw the cell diagram

In order to draw the cell diagram, we need to represent the half-cell reactions (oxidation and reduction) and the respective electrodes along with the electrolyte solution. The cell diagram can be drawn as follows: Zn(s) | Zn^2+(aq) || Fe^6+(aq), Fe^3+(aq) | Fe(s) Here, Zn is the anode (where oxidation occurs) and Fe is the cathode (where the reduction occurs). The double line (||) represents the salt bridge that allows the flow of ions to maintain charge neutrality. Answer (c): The cell diagram for the reaction is: Zn(s) | Zn^2+(aq) || Fe^6+(aq), Fe^3+(aq) | Fe(s).

Key Concepts

Galvanic Cells

Galvanic cells, also known as voltaic cells, form the foundation of battery technology. They convert chemical energy into electrical energy through spontaneous redox reactions. In these cells, an oxidation reaction occurs at the anode, where a metal tends to lose electrons. Conversely, a reduction reaction happens at the cathode, where a different metal or ion gains those lost electrons.

The flow of electrons through an external circuit creates an electric current, which can power devices. Between the half-cells, a salt bridge or a porous membrane prevents the mixing of the solutions while allowing ions to flow through it to balance the charge. The reaction that powered the 'super iron' battery, based on iron(VI), is an example of a galvanic cell reaction.

In the provided solution steps for the super iron battery, initially, the half-reactions for oxidation and reduction are identified, followed by determining the flow of electrons which essentially drives the current in the galvanic cell. By constructing the cell diagram, we visualize the setup of this electrochemical cell with zinc serving as the anode and iron compounds taking the role of the electrolyte and the cathode.

Oxidation States

Oxidation states, often called oxidation numbers, are a helpful way to keep track of electrons in chemical reactions, especially redox reactions. The oxidation state is the charge an atom would have if all its bonds were ionic, with electrons assigned to the most electronegative element. By convention, the oxidation state of an element in its standard state is zero.

In the case of our 'super iron' battery example, various oxidation states are present: Potassium always has an oxidation state of +1 due to its position in Group 1 of the periodic table, oxygen is typically assigned an oxidation state of -2 (making some exceptions), the iron changes from +6 in the reactant to +3 in the product, and zinc transitions from 0 in the metallic state to +2 in its compounds.

Determining the oxidation states is central to mapping out the electron flow within the cell and hence is a crucial step in understanding the transformation that occurs within the galvanic cell.

Electron Transfer

Electron transfer is the movement of electrons from one element or compound to another in a redox reaction. This transfer is triggered by the difference in the potential energy of the electrons in the involved substances. The substance that loses electrons is oxidized, and the substance that gains electrons is reduced, which is why these reactions are termed 'redox' (reduction-oxidation) reactions.

In the electrochemical reaction of the 'super iron' battery, we have delineated that a total of 6 electrons are transferred: 6 electrons are lost by three zinc atoms and those 6 electrons are gained by two iron atoms. This transfer is integral as it equates to the electric current that the battery can provide to an external circuit. Understanding electron transfer not only helps in following the changes in oxidation states but also gives a quantitative measure of the electrochemical cell's capability to do work, in this case, how much power the 'super iron' battery can generate.