Li-ion batteries used in automobiles typically use a LiMn2O4 cathode in place of the LiCoO2 cathode found in most Li-ion batteries. (c) In a battery that uses a LiCoO2 cathode, approximately 50% of the lithium migrates from the cathode to the anode on charging. In a battery that uses a LiMn2O4 cathode, what fraction of the lithium in LiMn2O4 would need to migrate out of the cathode to deliver the same amount of lithium to the graphite anode?

Verified step by step guidance

1. Identify the chemical formula for the cathodes: LiCoO_2 and LiMn_2O_4.
2. Understand that in LiCoO_2, 50% of the lithium migrates to the anode during charging.
3. Calculate the amount of lithium in LiMn_2O_4 that would need to migrate to deliver the same amount of lithium as in LiCoO_2.
4. Recognize that LiMn_2O_4 has a different stoichiometry, with one lithium per formula unit compared to LiCoO_2.
5. Determine the fraction of lithium migration in LiMn_2O_4 by comparing the stoichiometry and migration percentage of LiCoO_2.

Key Concepts

Lithium Migration in Batteries

In lithium-ion batteries, lithium ions move between the anode and cathode during charging and discharging. This migration is crucial for the battery's operation, as it allows for the storage and release of electrical energy. Understanding the fraction of lithium that migrates is essential for comparing different cathode materials and their efficiency in energy delivery.

Cathode Materials in Li-ion Batteries

Different cathode materials, such as LiCoO2 and LiMn2O4, have distinct electrochemical properties that affect their performance in batteries. LiCoO2 is known for its high energy density, while LiMn2O4 offers better thermal stability and safety. The choice of cathode material influences the amount of lithium that can be effectively utilized during the charging process.

Charge Capacity and Fractional Migration

The charge capacity of a battery refers to the total amount of charge it can store, which is directly related to the amount of lithium that migrates from the cathode to the anode. To deliver the same amount of lithium to the anode, it is necessary to calculate the fraction of lithium that must migrate from the cathode, which can vary based on the specific material properties and design of the battery.