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Worked example: Calculating molar mass and number of moles

The molar mass of a substance is the mass in grams of 1 mole of the substance. As shown in this video, we can obtain a substance's molar mass by summing the molar masses of its component atoms. We can then use the calculated molar mass to convert between mass and number of moles of the substance. Created by Sal Khan.

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Video transcript

- [Instructor] We are asked to calculate the number of moles in a 1.52 kilogram sample of glucose. So like always, pause this video and try to figure this out on your own and this periodic table of elements will prove useful. All right, now if we're trying to figure out the number of moles, remember, mole is really, you can view it as a quantity of something. If I said a dozen of something, you'd say oh, that's 12 of that thing. If I say a mole of something, I'm saying that's Avogadro's number of that thing. And so we have a 1.52 kilograms sample of our molecule in question, of glucose so if we can figure out the mass per mole, or another way to think about it, the molar mass of glucose, well then we just divide the mass of our sample by the mass per mole and we'll know how many moles we have. So what is the molar mass of glucose? Well to figure that out, and that's why this periodic table of elements is useful, we just have to figure out the molar mass of the constituent elements. So if we first look at carbon, carbon, we see from this periodic table of elements, has a molar mass of 12.01 grams per mole. We've talked about it in other videos, you could view this 12.01 as a relative atomic mass of a carbon atom, of as the average atomic mass of a carbon atom, or what's useful, and this is where Avogadro's Number is valuable, if you have Avogadro's Number of carbons, it is going to have a mass of 12.01 grams. So carbon has a molar mass of 12.01 grams per mole and now we can think about hydrogen in the same way. Hydrogen has a molar mass of 1.008 grams per mole, 008 grams per mole. And then last but not least, we have oxygen here. Oxygen, we can see from our periodic table of elements, it has a molar mass of 16.00 grams per mole. And so now we have all the information we need from our periodic table of elements. So the molar mass of glucose is going to be six times the molar mass of carbon plus 12 times the molar mass of hydrogen plus six times the molar mass of oxygen. So it's going to be six times 12.01 grams per mole plus 12 times 1.008 grams per mole plus every molecule of glucose has six oxygen plus six times 16.00 grams per mole. Six times 12.01 plus 12 times 1.008 plus six times 16 is equal to, and if we're thinking about significant figures here, the molar mass of hydrogen goes to the thousandths place but we only go to the hundredths for carbon and for oxygen, we're adding all of these up together so it's going to be 180. I can only go to the hundredths place for significant figures, so 180.16. So that's equal to 180.16 grams per mole. And we could say grams of glucose, C6H12O6 per mole of glucose, C6H12O6 and then we can use this 1.52 kilograms to figure out how many moles we have. So if we start off with 1.52 kilograms of glucose, so that's C6H12O6, well first we can convert it to grams 'cause here, our molar mass is given in terms of grams, so times, we're going to want kilograms in the denominator and grams in the numerator, so how many grams are there per kilograms? Well, we have 1,000 grams for every one kilogram. So when you multiply these two out, this is going to give you the number of grams we have of glucose which would be 1,520 and if you have your mass in terms of grams, you can then divide by your molar mass or you can view it as multiplying it by the moles per gram. So for every one mole of glucose, C6H12O6, we have 180.16 grams of glucose, C6H12O6, and this is going to get us, we get 1.52 times 1,000 is equal to, this is the number of grams of glucose we have, and then we're going to divide by 180.16, divide by 180.16, gives us this number, and let's see, if we see significant figures, we have three significant figures here, we have five here so we wanna round it to three significant figures, so it will be 8.44 moles of glucose. So our kilograms cancel with our kilograms and then our grams of glucose cancel with our grams of glucose and we are left with 8.44 moles of glucose, moles of C6H12O6. And we are done.