In a Li-ion battery, the composition of the cathode is LiCoO2 when completely discharged. On charging, approximately 50% of the Li+ ions can be extracted from the cathode and transported to the graphite anode where they intercalate between the layers. (b) If the LiCoO2 cathode has a mass of 10 g (when fully discharged), how many coulombs of electricity can be delivered on completely discharging a fully charged battery?

Verified step by step guidance

Step 1: Determine the molar mass of LiCoO_2 by adding the atomic masses of lithium (Li), cobalt (Co), and oxygen (O).

Step 2: Calculate the number of moles of LiCoO_2 in the 10 g cathode using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).

Step 3: Since 50% of the Li+ ions can be extracted, calculate the moles of Li+ ions that can be extracted from the moles of LiCoO_2.

Step 4: Use Faraday's constant (approximately 96485 C/mol) to convert the moles of Li+ ions to coulombs, as each mole of Li+ ions corresponds to one mole of electrons.

Step 5: Multiply the moles of Li+ ions by Faraday's constant to find the total charge in coulombs that can be delivered on completely discharging the battery.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry of Lithium Extraction

In the context of LiCoO2, stoichiometry refers to the quantitative relationship between the lithium ions and the overall chemical reaction during charging and discharging. When the battery is charged, approximately 50% of the lithium ions (Li+) can be extracted, which is crucial for calculating the total charge delivered during discharge.

Faraday's Law of Electrolysis

Faraday's Law states that the amount of electric charge (in coulombs) required to transfer a certain amount of substance during an electrochemical reaction is directly proportional to the number of moles of electrons involved. This principle is essential for determining how many coulombs can be delivered based on the number of lithium ions extracted from the cathode.

Charge Calculation in Batteries

The total charge delivered by a battery can be calculated using the formula Q = n × F, where Q is the total charge in coulombs, n is the number of moles of electrons transferred, and F is Faraday's constant (approximately 96485 C/mol). Understanding this calculation is vital for determining the total coulombs delivered when the battery discharges completely.

Recommended video:

Guided course

00:59

Effective Nuclear Charge Calculation

Related Practice

Textbook Question

In some applications nickel–cadmium batteries have been replaced by nickel–zinc batteries. The overall cell reaction for this relatively new battery is: 2 H₂O(l) + 2 NiO(OH)(s) + Zn(s) → 2 Ni(OH)₂(s) + Zn(OH)₂(s) (c) A single nickel–cadmium cell has a voltage of 1.30 V. Based on the difference in the standard reduction potentials of Cd²⁺ and Zn²⁺, what voltage would you estimate a nickel–zinc battery will produce? (d) Would you expect the specific energy density of a nickel–zinc battery to be higher or lower than that of a nickel–cadmium battery?

Textbook Question

Li-ion batteries used in automobiles typically use a LiMn2O4 cathode in place of the LiCoO2 cathode found in most Li-ion batteries. (a) Calculate the mass percent lithium in each electrode material.

Textbook Question

Li-ion batteries used in automobiles typically use a LiMn2O4 cathode in place of the LiCoO2 cathode found in most Li-ion batteries. (b) Which material has a higher percentage of lithium? Does this help to explain why batteries made with LiMn2O4 cathodes deliver less power on discharging?

Textbook Question

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?