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Worked example: Calculating molar mass and number of moles

AP.Chem:
SPQ‑1 (EU)
,
SPQ‑1.A (LO)
,
SPQ‑1.A.1 (EK)
,
SPQ‑1.A.3 (EK)

Video transcript

we are asked to calculate the number of moles in a 1.5 to 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 a really you confuse a quantity of something if I set 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 one point five two kilogram 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 in other videos you could view this 12.01 as the 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 zero zero eight 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 point zero zero 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 armen plus 12 times the molar mass of hydrogen plus 6 times the molar mass of oxygen so it's going to be 6 times 12.01 grams per mole plus 12 times one point zero zero eight grams per mole plus every molecule of glucose has six oxygens plus 6 times 16 point zero zero grams per mole six times twelve point zero one plus twelve times one point zero zero eight plus six times 16 is equal to and if we're thinking about significant figures here the molar mass of hydrogen goes to the thousands place but we only go to the hundredths for carbon and for oxygen we're adding all these up together so it's going to be 180 point I can only go to the hundreds place for significant figures so 180 point one six so that's equal to 180 point one six grams per mole and we could say grams of glucose c6h12o6 per mole of glucose c6h12o6 and then we can use this one point five two kilograms to figure out how many moles we have so if we start off with one point five two kilograms of glucose so that's c6 h-12 o-6 well first we can convert it to grams because 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 kilogram 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 1520 and if you have your mass in terms of grams you can then divide by your molar mass or you could view it as multiplying it by the moles per gram so for every 1 mole of glucose c6h12o6 we have 180 0.16 grams of glucose C c6 h-12 o-6 and this is going to get us we get 1 point 5 2 times 1000 is equal to this is the number of grams of glucose we have and then we're going to divide by 180 point 1 6 divided by 180 point 1 6 gives us this number and let's see if we see significant figures we have three significant figures here we have five years we want to round it to three significant figures so it will be eight point four four 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 eight point four four moles of glucose moles of c6 h-12 o-6 and we are done