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?

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Welcome back everyone in this example, we have the cathode lithium manganese oxide and lithium ion batteries which can be replaced by lithium iron phosphate. The use of lithium iron phosphate has received widespread market approval because of its low cost non toxicity and irons natural abundance during the charging of a certain battery with lithium iron phosphate cathodes, about 40.8% of lithium migrates from the cathode to the anodes to migrate the same amount of lithium to the graphite anodes. What fraction of the lithium in lithium manganese oxide would have to migrate in a battery that uses the lithium manganese oxide cathode. So what we need to find is our mole fraction of lithium and this will ultimately be us taking the moles of lithium that migrate in our lithium iron phosphate. And then we're going to divide that by the moles of lithium in our lithium manganese oxide. And we want to recall that from the prompt were given a percent by mass of lithium that is migrating from our cathode to are an ode. So we're going to actually interpret this in grams instead of moles. So we're going to say the grams of lithium that migrate to the grams of lithium in lithium manganese oxide and ultimately we're going to get to a mass percent. When we multiply the fraction of lithium in its mass by 100%. And that would lead us to our final answer. So let's begin by figuring out our mass of lithium in First our lithium manganese oxide and then we want to find our massive lithium in lithium iron phosphate. So this is lithium manganese oxide. So that should be M N Sub two and then 04. So beginning with lithium manganese oxide, we want to make note of our molar mass of lithium manganese oxide, Which from our periodic table we see has a molar mass of 180.817 g Permal. On the contrary, we have our molar mass of lithium iron phosphate, which is a value from a periodic table of 157.76 g per mole. When we add up the individual masses of each atom in these two compounds, we're going to get these values from our periodic table. And so to find the massive lithium in each of these, we want to make note of our Moeller massive lithium And from our periodic table we would see that that value is 6.941 g per mole. So what we're really going to find is our mass percent of lithium in both of these compounds here. So what we would do is take our individual massive lithium as 6.941 g. We're going to divide it by the total mass of lithium manganese oxide as 180.817 g and we're going to multiply this by 100%. This is going to yield a result of 3.839%. And then for our second calculation, we'll just scoot this over and let's actually use the color pink for this calculation here. So we're gonna say we have 6.941 g of lithium. We're going to divide this by our molar mass of lithium iron phosphate which we above set is 157.76 g and this is going to be multiplied by 100% to then give us our results of 4.400%. So now that we have these mass percent values, we can actually interpret them in units of grams. So we can say we have 4.400 g of lithium in lithium iron phosphate and we have 3.839 g of lithium in lithium manganese oxide. Now that we have these masses of lithium And we know that from the prompt that 40.8% of the lithium is going to be migrating from the cathode to the anodes, we want to see how that translates to a massive lithium that migrates in lithium iron phosphate. And so we would say that we know we have 4.400 g of lithium In lithium iron phosphate. And we're going to multiply this by the 40.8% that migrates to the an ode as a decimal so will say by .408. And this is going to give us a result of 1.7952 g. So now with this value, this tells us the mass of lithium that migrates to the anodes in our lithium iron phosphate and now that we have this mass, we can go back to that first formula that we outlined where we're getting the fraction of lithium Between the massive lithium that migrates in lithium iron phosphate to the massive lithium that we have in lithium manganese oxide so that we can get our final answer when we multiply by 100%. So let's follow those steps. We're going to take our massive lithium in lithium manganese oxide, which above we said is 3.839 g of lithium. We're going to divide by our mass of And sorry about that. Our numerator is supposed to be our mass of lithium that migrates so our numerator is 1.7952g of lithium. And then our denominator is our mass of lithium and lithium manganese oxide. So that was what we determined above as 3.839g of lithium And then multiplying by 100%, we're going to get that we have 46.8% of lithium as our fraction of lithium that will migrate in a lithium manganese oxide cathode. So we'll say lithium manganese oxide cathode. And this is going to be our final answer here as our fraction of lithium, I hope everything I reviewed was clear. If you have any questions leave them down below and I'll see everyone in the next practice video.

Verified Solution

Key Concepts

Lithium Migration in Batteries

Cathode Materials in Li-ion Batteries

Charge Capacity and Fractional Migration