Problem 20 - Chemistry: An Atoms-Focused Approach

Question

In a flow battery, two solutions are pumped into each voltaic cell, and oxidation and reduction half-reactions take place at two inert electrodes. One such cell is based on the reduction of \(\mathrm{Sn}^{4+}(a q)\) to \(\mathrm{Sn}^{2+}(a q)\) and the oxidation of \(\mathrm{Fe}^{2+}(a q)\) to \(\mathrm{Fe}^{3+}(a q)\) a. Write half-reactions for the cell's anode and cathode. b. Write a balanced cell reaction. c. How many electrons are transferred in the cell reaction?

Step-by-Step Solution

Answer

Question: In a flow battery, two half-reactions occur where Sn4+ is reduced to Sn2+ and Fe2+ is oxidized to Fe3+. Write the half-reactions for the anode and cathode, the balanced cell reaction, and determine the number of electrons transferred in the cell reaction. Answer: The half-reactions for the anode (oxidation) and cathode (reduction) are as follows: Anode: Fe2+(aq) → Fe3+(aq) + e– Cathode: Sn4+(aq) + 2e– → Sn2+(aq) The balanced cell reaction is: 2(Fe2+(aq)) + Sn4+(aq) → 2(Fe3+(aq)) + Sn2+(aq) The number of electrons transferred in the cell reaction is 2.

Step 1: Identify the anode and cathode half-reactions

For a redox reaction, oxidation occurs at the anode, and reduction occurs at the cathode. In this case, the reduction of Sn\(^{4+}\) to Sn\(^{2+}\) is a reduction reaction, and the oxidation of Fe\(^{2+}\) to Fe\(^{3+}\) is an oxidation reaction. Thus, the anode half-reaction is for the oxidation of Fe\(^{2+}\), and the cathode half-reaction is for the reduction of Sn\(^{4+}\).

Step 2: Write the anode and cathode half-reactions

We will now write the half-reactions for both the anode and cathode. Anode (oxidation): Fe\(^{2+}(aq) \rightarrow\) Fe\(^{3+}(aq) + e^-\) Cathode (reduction): Sn\(^{4+}(aq) + 2e^- \rightarrow\) Sn\(^{2+}(aq)\)

Step 3: Write a balanced cell reaction

To obtain the balanced cell reaction, we need to balance the half-reactions such that the number of electrons lost in the anode half-reaction is equal to the number of electrons gained in the cathode half-reaction. We can achieve this by multiplying the anode half-reaction by 2 and then adding both half-reactions. Anode (oxidation): \(2\times(\)Fe\(^{2+}(aq) \rightarrow\) Fe\(^{3+}(aq) + e^-\) \()\) Cathode (reduction): Sn\(^{4+}(aq) + 2e^- \rightarrow\) Sn\(^{2+}(aq)\) Balanced cell reaction: \(2\times(\)Fe\(^{2+}(aq))\) + Sn\(^{4+}(aq) \rightarrow 2 \times\)Fe\(^{3+}(aq)\) + Sn\(^{2+}(aq)\)

Step 4: Determine the number of electrons transferred in the cell reaction

Finally, identify the number of electrons transferred in the balanced cell reaction. In this case, two electrons are transferred as the reactions proceed. The number of electrons transferred in the cell reaction is 2.

Key Concepts

Flow Battery

A flow battery is a type of rechargeable battery where energy is stored in two chemical solutions contained in external tanks. These solutions are then pumped into a chamber, or cell, where the energy conversion happens. Flow batteries stand out due to their flexibility in size and capacity, allowing them to be scaled up simply by using larger tanks. This makes them incredibly useful for grid-scale energy storage, where they help balance the supply and demand of electricity. In these systems, the tanks store the materials responsible for producing electricity, unlike conventional batteries where all components are contained in a single unit.

Some key features of flow batteries include:

• Energy Storage Flexibility: The capacity can be increased easily by enlarging the storage tanks.
• Longevity: They provide long cycle life and can withstand many charge and discharge cycles.
• Immediate Response: Flow batteries can switch from charge to discharge instantly, making them quick to respond to changes in electricity demand.

Because of these characteristics, flow batteries are becoming a crucial part of the modern sustainable energy infrastructure.

Oxidation-Reduction

Oxidation-reduction, often termed as redox reactions, involves the transfer of electrons between two species. In a redox reaction, one species loses electrons (oxidation) while another gains electrons (reduction). These reactions are the cornerstone of energy conversion processes in batteries, including flow batteries.

The essence of a redox reaction can be understood by remembering the acronym **LEO** the lion says **GER**:

• LEO (Lose Electrons Oxidation): When a substance loses electrons, it is oxidized.
• GER (Gain Electrons Reduction): When a substance gains electrons, it is reduced.

In the context of chemical reactions within a battery, oxidation occurs at the anode whereas reduction occurs at the cathode. Understanding the process of electron exchange in these reactions is vital for grasping how batteries produce electric current.

Half-Reactions

Half-reactions are a way to break down the overall redox reaction into two parts, showcasing the individual processes of oxidation and reduction separately. They provide a detailed look at each step, allowing us to see exactly what is happening to each reactant.

In the flow battery example from the exercise, two half-reactions were identified:

• Anode (Oxidation): Fe\(^{2+}(aq)\) to Fe\(^{3+}(aq)\) with the release of an electron \(e^-\).
• Cathode (Reduction): Sn\(^{4+}(aq)\) gains electrons to become Sn\(^{2+}(aq)\).

To construct a balanced full redox equation, these half-reactions must be adjusted such that electrons lost and gained match. This balancing ensures the conservation of charge, an essential principle for maintaining consistent and reliable operation of the battery.
Comprehending half-reactions aids significantly in visualizing the intricate processes occurring within a flow battery.

Electron Transfer

Electron transfer is at the heart of how batteries generate electricity. Electrons flow from one substance to another during redox reactions, creating a current. This transfer occurs due to the natural tendency of some chemical species to donate electrons and others to accept them.

In the exercise situation within a flow battery cell:

• Electrons are released from Fe\(^{2+}(aq)\) as it becomes Fe\(^{3+}(aq)\) at the anode.
• These electrons move through an external circuit to Sn\(^{4+}(aq)\), reducing it to Sn\(^{2+}(aq)\) at the cathode.

This flow of electrons through the external circuit generates electrical energy.
The number of electrons transferred, in this case, is 2, as established through balancing the half-reactions. The controlled movement and harnessing of electrons are what make batteries such valuable sources of portable power. Understanding electron transfer processes is fundamental for appreciating how chemical energy is transformed into electrical energy in electrochemical cells.