We’re being asked to determine which **cathode has a higher percentage of lithium** and if this explains why LiMn_{2}O_{4} cathodes deliver less power discharging.

Recall that **mass percent** is given by the formula:

$\overline{){\mathbf{mass}}{\mathbf{}}{\mathbf{percent}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{mass}\mathbf{}\mathbf{element}}{\mathbf{total}\mathbf{}\mathbf{mass}\mathbf{}\mathbf{of}\mathbf{}\mathbf{compound}}{\mathbf{\times}}{\mathbf{100}}}$

For the **percent by mass Li in LiMn _{2}O_{4} cathode**, the mass percent equation is

$\overline{){\mathbf{\%}}{\mathbf{}}{\mathbf{mass}}{\mathbf{}}{\mathbf{Li}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{mass}\mathbf{}\mathbf{Li}}{\mathbf{mass}\mathbf{}{\mathbf{LiMn}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{4}}}{\mathbf{\times}}{\mathbf{100}}}$

For the **percent by mass Li in LiCoO _{2} cathode**, the mass percent equation is

$\overline{){\mathbf{\%}}{\mathbf{}}{\mathbf{mass}}{\mathbf{}}{\mathbf{Li}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{mass}\mathbf{}\mathbf{Li}}{\mathbf{mass}\mathbf{}{\mathbf{LiCoO}}_{\mathbf{2}}}{\mathbf{\times}}{\mathbf{100}}}$

*We will do the following steps to solve the problem:*

*Step 1: Calculate the mass of Li, LiMn _{2}O_{4}, LiCoO_{2}*

*Step 2: Calculate the percent by mass Li in both cathodes*

*Step 3: Explain the phenomena using mass percent *

Li-ion batteries used in automobiles typically use a LiMn_{2}O_{4} cathode in place of the LiCoO_{2} cathode found in most Li-ion batteries.

1. Which material has a higher percentage of lithium?

2. Does this help to explain why batteries made with LiMn_{2}O_{4} cathodes deliver less power on discharging?

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What scientific concept do you need to know in order to solve this problem?

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