Question

(a) Which ion is smaller, \(\mathrm{Co}^{3+}\) or \(\mathrm{Co}^{4+} ?(\mathbf{b})\) In a lithium-ion battery that is discharging to power a device, for every \(\mathrm{Li}^{+}\) that inserts into the lithium cobalt oxide electrode, a \(\mathrm{Co}^{4+}\) ion must be reduced to a \(\mathrm{Co}^{3+}\) ion to balance charge. Using the CRC Handbook of Chemistry and Physics or other standard reference, find the ionic radii of \(\mathrm{Li}^{+}, \mathrm{Co}^{3+},\) and \(\mathrm{Co}^{4+} .\) Order these ions from smallest to largest. (c) Will the lithium cobalt oxide cathode expand or contract as lithium ions are inserted? (d) Lithium is not nearly as abundant as sodium. If sodium ion batteries were developed that function in the same manner as lithium ion batteries, do you think "sodium cobalt oxide" would still work as the electrode material? Explain. (e) If you don’t think cobalt would work as the redox-active partner ion in the sodium version of the electrode, suggest an alternative metal ion and explain your reasoning.

Short answer

In summary: (a) Co⁴⁺ is smaller than Co³⁺. (b) The order of ions from smallest to largest is Co⁴⁺ < Co³⁺ < Li⁺. (c) The lithium cobalt oxide cathode will expand as lithium ions are inserted. (d) Sodium cobalt oxide might not be the ideal choice for an electrode material in sodium-ion batteries due to stability and performance issues caused by the large size of sodium ions. (e) An alternative metal ion for the sodium version of the electrode could be manganese (Mn³⁺/Mn⁴⁺), as it has a larger ionic radius compatible with the size of sodium ions, stable oxidation states for redox processes, and is more abundant and less toxic than cobalt.

Step-by-step solution

(a) Comparing Co³⁺ and Co⁴⁺ ion sizes

When comparing ions from the same element, each additional positive charge will attract the electrons stronger towards the nucleus, resulting in a smaller ionic radius. Therefore, the ion with a higher charge will be smaller: Co⁴⁺ is smaller than Co³⁺.

(b) Finding ionic radii and ordering ions

Using the CRC Handbook of Chemistry and Physics or another standard reference, we find the following ionic radii: - Li⁺: 76 pm - Co³⁺: 54.5 pm - Co⁴⁺: 51 pm Now we can order these ions from smallest to largest: Co⁴⁺ < Co³⁺ < Li⁺.

(c) Expansion or contraction of lithium cobalt oxide cathode

When lithium ions are inserted into the lithium cobalt oxide electrode, they are larger than the cobalt ions they replace (Li⁺ > Co³⁺). As a result, the cathode will expand to accommodate the larger lithium ions.

(d) Feasibility of sodium cobalt oxide as an electrode material

Sodium ions are larger than lithium ions. While it is possible that a sodium-ion battery may work similarly to a lithium-ion battery, the larger size of sodium ions may lead to a significant expansion in the sodium cobalt oxide electrode during charge/discharge cycles. This could result in decreased stability and performance over time. Therefore, sodium cobalt oxide might not be the ideal choice for an electrode material in sodium-ion batteries.

(e) Suggesting an alternative metal ion for the sodium version of the electrode

Considering that using cobalt as the redox-active partner ion with sodium might lead to stability issues, we could search for a metal ion with similar redox properties but a larger ionic radius, more compatible with the size of sodium ions. One possible candidate could be the manganese ion (Mn³⁺/Mn⁴⁺). This ion has a larger ionic radius than cobalt ions, and its stable oxidation states are compatible with the redox process needed for a sodium-ion battery's functionality. Additionally, manganese is more abundant and less toxic than cobalt, which could be advantageous for large-scale battery production.

Key concepts

lithium-ion battery

Lithium-ion batteries are a staple in modern rechargeable battery technology. They are widely used due to their high energy density, low self-discharge rate, and long lifespan. These batteries function by moving lithium ions between the anode and cathode through an electrolyte. As the battery discharges, lithium ions travel from the anode to the cathode, powering the connected device. This flow of ions, combined with the flow of electrons through an external circuit, generates electrical energy.

Key benefits include:

• High efficiency in energy storage and release.
• Lightweight and compact design making them ideal for portable electronics.
• Lower maintenance requirements compared to other battery types.

Understanding the workings of lithium-ion batteries is crucial for innovations in energy storage solutions.

lithium cobalt oxide

Lithium cobalt oxide (LiCoO₂) plays a significant role as a cathode material in lithium-ion batteries. It serves as the positive electrode, where lithium ions are hosted during the discharging and charging process. The lithium ions' interaction with cobalt ions results in crucial redox reactions necessary for the battery's operation. Lithium cobalt oxide has favorable properties, such as high theoretical capacity and good cycling stability.

Important features include:

• High voltage platforms, providing better energy output.
• Reliable performance under various temperature ranges.
• Efficient lithium-ion transfer capability maximizing energy efficiency.

However, it's essential to consider issues such as the rarity and toxicity of cobalt when evaluating its long-term use.

sodium-ion battery

Sodium-ion batteries are gaining interest as an alternative to lithium-ion batteries due to the abundance and affordability of sodium. Like their lithium counterpart, these batteries operate by the movement of sodium ions between electrodes. Although similar in mechanism, the larger ionic size of sodium compared to lithium presents some challenges, such as increased electrode expansion and reduced energy density.

Advantages of sodium-ion batteries:

• More sustainable due to the abundance of sodium resources.
• Potentially lower costs due to cheaper raw materials.
• Environmentally friendly, offering a viable option for scaling up production.

These batteries are being actively researched to overcome the structural challenges posed by sodium's larger size.

transition metal ions

Transition metal ions are crucial components in battery chemistry, especially in the cathode materials like lithium cobalt oxide. These ions, such as cobalt, manganese, and nickel, undergo redox reactions, alternating between oxidation states to facilitate the flow of electric current. For instance, cobalt ions cycle between Co³⁺ and Co⁴⁺ during lithium-ion battery operation, enabling the storage and release of energy.

Benefits of transition metal ions include:

• Ability to participate in multiple electron transfer reactions.
• Contribution to high energy densities in batteries.
• Stability under repeated redox cycles increasing battery life.

Selection of appropriate transition metal ions is key to the performance and longevity of rechargeable batteries.

cathode expansion

Cathode expansion is a phenomenon where the cathode material of a battery increases in volume during charge and discharge cycles. This is particularly noticeable in lithium-ion batteries when lithium ions, which are larger than cobalt ions, insert into the lithium cobalt oxide cathode.

Challenges include:

• Potential mechanical stress leading to cathode degradation over time.
• Possible reduction in battery efficiency due to structural changes.
• Impact on the longevity and safety of the battery.

Managing cathode expansion is crucial to maintaining the structural integrity and operational efficiency of rechargeable batteries.

redox reactions

Redox reactions, short for reduction-oxidation reactions, are chemical processes involving the transfer of electrons between two substances. In the context of batteries, these reactions facilitate the storage and release of electrical energy as ions migrate between electrodes.

Key points about redox reactions:

• Drive the conversion of chemical energy to electrical energy.
• Involve oxidation, where a substance loses electrons, and reduction, where a substance gains electrons.
• Integral to the cycling stability and energy output of batteries, affecting their overall performance.

Understanding redox reactions is essential for developing efficient battery technologies and improving existing ones.