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Chemistry / Chemistry: The Central Science 13 / Chapter 20 / Problem 20.80

Chemistry: The Central Science | 13th Edition | ISBN: 9780321910417 | Authors: Theodore E. Brown; H. Eugene LeMay; Bruce E. Bursten; Catherine Murphy; Patrick Woodward; Matthew E. Stoltzfus

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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? (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? (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?

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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? (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? (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?

ANSWER:

Problem 20.80

Li-ion batteries used in automobiles typically use a LiMn2O4 cathode in place of the $\mathrm{LiCoO_{2}}$ cathode found in most Li-ion batteries.

(a) Calculate the mass percent lithium in each electrode material?

(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?

(c) In a battery that uses a $\mathrm{LiCoO_{2}}$ cathode approximately 50% of the lithium migrates from the cathode to the anode on charging. In a battery that uses a $\mathrm{LiMn_{2}O_{4}}$ cathode what fraction of the lithium in $\mathrm{LiMn_{2}O_{4}}$ would need to migrate out of the cathode to deliver the same amount of lithium to the graphite anode?

Step by step solution

Step 1 of 3

(a)

From the given,

Mass of Li in one mole of $\mathrm{LiMn_{2}O_{4}}$ = 6.94 g

Molar mass of $\mathrm{LiMn_{2}O_{4}}$ = 180.81 g

Let’s calculate the mass percentage of Li in $\mathrm{LiMn_{2}O_{4}}$

$$$ \mathrm{Mass\,percent\,of\,Li\,in\,LiMn_{2}O_{4}}=\frac{\mathrm{Mass\,of\,Li}}{\mathrm{Molar\,mass\,LiMn_{2}O_{4}}}$

$$$ =\frac{\mathrm{6.94 \,g}}{\mathrm{180.81\,g}} \times 100 =3.8 \%$

Therefore, mass percentage of lithium in $\mathrm{LiMn_{2}O_{4}}$ is 3.8 %.

From the given,

Mass of Li in $\mathrm{LiCoO_{2}}$ = 6.94 g

Molar mass of $\mathrm{LiCoO_{2}}$ = 97.87 g

Let’s calculate the mass percentage of “Li” in $\mathrm{LiCoO_{2}}$ .

$$$ \mathrm{Mass\,percentage\,of\,Li} = \frac{ \mathrm {Mass\,of\,Li}} { \mathrm{ Molar\,mass\,of}\, \mathrm {LiCoCO_{2}}}$

$$$ =\frac{6.94 \mathrm{g}}{97.87 \,\mathrm{g}}\times 100 \% = 7.09 \%$

Therefore, mass percent of Li in $\mathrm{LiCoO_{2}}$ is 7.09

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