welcome to unit 7 which I like to call math of chemistry though your teacher may call it Stoichiometry depending on how deep you go into this unit um it could get really complex many high school students just take this a few steps in and it can still be tough my goal here is to make this as easy for you as possible but it is important to recognize that you may not need all of the information that I'm going to teach in this unit so make sure to check with your teacher to find out exactly how much of this unit you need to know the very first lesson is on moles and formula mass and the question of the day is how do chemists measure things that they can't see atoms and molecules you know are too small to be handled individually so how on Earth do chemists actually do this a mole is a bundle of atoms scientists have determined that we're going to collect atoms into bundles we call those bundles holes when you have a bundle of atoms they're a lot easier to handle in fact it's the only way we can handle atoms is by grouping them together in to make to make a bigger Blobs of atoms we make substances really and we've decided on the size of a mole by using carbon as our reference so the number of atoms that are present in exactly 12 grams of carbon 12 is the quantity that is a mole now you may think of mole and think of this cute little guy or like a freckle we're talking moles like chemistry moles so anytime you have to Google something you have to make sure to Google a chemistry mole um it's also a shortened version of molecule that's where the word came from so getting back to that initial question how do chemists measure things that they can't see well they bundle or lump those atoms into groups that we can see and we call those groups moles so a way I like to think about it is sand castles if you've ever built a sand castle before you know that you take large bundles of grains of sand and lump them together into a bucket or a sand castle mold I'm going to use Bucket from here on out this way it doesn't sound like mole but if you have a sand castle you're going to fill this bucket full of sand and then you're going to flip it upside down lift the bucket up and then you have all of your grains of sand put together it would be really ridiculous to try to build a sand castle by stitching together individual grains of sand it would take you forever and in a lot of cases it would be near impossible because you go to touch one grain of sand and a bunch of others are going to get stuck to your fingers so this is kind of the same concept with Scientists except the grains of sand are way tinier and you literally cannot pick them up there's no tweezer tiny enough to just grab one atom um so we take our atoms which we can't see at all because they're even tinier than grains of sand and we lump them together so a grain of sand would be like an atom and the bucket that we use would be the mole we use that to kind of lump them all together and in this case you can count how many um buckets are overturned to figure out like the size of your sand castle we kind of do the same thing with atoms we use these bundles called moles to figure out exactly how many atoms we're working with so what exactly is a mole well the number is really big it's 6.02 times 10 to the 23rd that's how many carbon atoms there are in 12 grams of carbon 12. that is 602 sextillion so you move the decimal two times to get behind the two and then you add 21 zeros and then you'd have the full number 602 times 10 to the 23rd we call that Avogadro's number it's named after the guy who originally came up with this idea he didn't quite have the number 6.02 times 10 to the 23rd but he had the concept A bunch of physicists figured out the number and then credited that number to the man Avogadro um so each element we know has its own Mass if you look at the periodic table you know that hydrogen has a mass of one helium is four carbon is 12. silicon is 28. blah blah blah each of these masses represents one mole of that element so up until this point we've been looking at the periodic table and the masses as atomic mass units now we're going to look at them as grams that's the cool thing about moles is that when you have just the right number you don't have to do a unit conversion between atomic mass units and grams because that crazy number 6.02 times 10 to the 23rd kind of did that for us so we just read these as if they have different units we read them as grams instead so we know that each element has its own mass and we're looking at one mole of each of these elements when we are talking about their masses and how much they are so all of the moles are going to have the same quantity if you have a mole of donuts a mole of golf balls a mole of carbon atoms you're going to have 6.02 times 10 to the 23rd of these things it's kind of like the word dozen a dozen just means 12 of something a mole just means 602 sextillion of those things so because all moles have the same quantity we can use moles in place of molecules when we talk about chemical reactions in a chemical reaction you would say that three moles of ammonia breaks into no two moles of ammonia breaks into one mole of nitrogen and three moles of hydrogen we can use mole or molecule either way they're interchangeable so the mole of ammonia would have a different Mass from a mole of nitrogen or from a mole of hydrogen because they're made of elements that have different masses um I like to think of it as a mole of elephants and a mole of butterflies two different animals a mole of elephants is going to be gigantic probably like larger than planet Earth um and then a mole of butterflies is definitely smaller but it's going to be less massive um like volume wise it's smaller but Mass wise it's going to be smaller as well because a single butterfly is smaller than a single elephant if that makes sense so if you had a mole of hydrogen and a mole of I don't know tin a mole of hydrogen is going to be much lighter than a mole of tin simply because hydrogen is lighter than tin if you have 12 hydrogens and 12 tins the 12 hydrogens are still going to be lighter all we're doing is replacing dozen with this giant number of the mole and the reason the number for a mole is so large is because atoms are so tiny you have to get a lot of them bundled together before they're really like tangible so the only way that we know that we have a mole of a substance is to find out its mass because we can't count these individual atoms so instead we are going to use the periodic table to add together all of the masses convert them to grams just by pulling them from the periodic table and totaling them up so previously we would look at this as one molecule not quite but one unit molecule of potassium permanganate in this we have one potassium one manganese and four oxygens well if I had a mole of these then I would have a mole of potassium and a mole of Manganese and four moles of oxygen see what I'm getting at here so previously we would look at this as single atoms and we would look at the whole thing as a molecule now we're going to take a bunch of these potassium permanganates and lump them together so that we can actually physically work with them you and I cannot work with a single potassium permanganate it's too tiny so we take a bunch of them lump them together and make a mole of potassium permanganates we can't possibly sit here and count them all out there's not even enough seconds in your lifetime to count to a mole because it's such a large number so instead what we're going to do is count by weighing we're going to find the mass of this on a scale and because every element has its own Mass you can't just like pile stuff onto a scale until the scale tells you you have one mole of stuff you'd have to tell the scale what you were measuring so the first thing that we're going to do for this is count up all of the atoms that we have in the molecule or really the number of moles we have in a mole of this molecule so we have one potassium one manganese and four oxygens per one mole of potassium permanganate we're going to look up the masses on the periodic table and because we are talking about a mole of this substance meaning a large bundle of these atoms um well not even a large amount we're looking at a specific number of these atoms we are going to pull those masses and because we're talking about moles they're going to be in grams instead of atomic mass units so here I'm just working in whole numbers for the sake of um ease here uh this entire unit I don't focus on significant figures I think that's one extra thing that we just don't need your teacher May care about significant figures so make sure that you are minding your significant figures rules if that is the case but potassium is actually 39.10 manganese is 54.94 round that to 55 and then oxygen comes in at a solid 16 it's 16.00 so what I like to do is this qmt chart the quantity mass in total this is going to help us throughout the unit as we move through um this concept of moles and taking tiny little intangible atoms and bulking them up to a place where humans can actually work with them so we are going to multiply going across so this 39 is 1 times the 39 giving me the total mass of all of my potassiums same thing happens here for the manganese and then lastly I have a four oxygens coming in at 16 grams a piece giving me 64 grams in total of oxygen per mole of the potassium permanganate when I add that all up this is going to tell me the mass of one mole of potassium permanganate so if I'm in a lab and I needed for my chemical reaction let's say one mole right my chemical reaction is maybe going to say potassium permanganate decomposes into its elements so I would have a one here and then this would decompose into one potassium one permanganate and two diatomic oxygens giving me four in total the big two times the little two um I would know that I had one mole of it when I had 158 grams of it that's how you count them that's how you know that you have one bundle of potassium permanganates so in this case the scale or the balance is going to tell you you have 158 grams and that's when you know that you had a mole of it now if you doubled the 158 then you would have two moles of potassium permanganate if you cut it in half you would have half a mole of potassium permanganate I mean even think about buying Donuts or Bagels if you go to the bakery and ask for a half dozen donuts you're gonna get six donuts you can cut these numbers in half that's fine you can get two dozen donuts that would be 24. we're kind of doing the same thing here but in this case we're just working with one for now when we have 158 grams of potassium permanganate that's when I know that I have 600 into sextillion potassium permanganate molecules so let's say for a chemical reaction I needed one mole of calcium hydroxide well how would I know when I had a mole the only way to know is to get its mass so I'm going to find the mass of this entire calcium hydroxide and figure out when I need to stop shoveling calcium hydroxide onto my balance so the process here is to list all of your elements just like this and then I like I said like to do the qmt which stands for quantity mass and total q m t and I know for some of you this will be pretty tedious but when we get into percent by mass um this total column is going to help you quite a bit so I definitely recommend that you stick with this qmt chart at least for a little bit so quantity just means that we're counting how many we have so we have one calcium and then remember this little two outside the parentheses is going to distribute in telling me I have two oxygens and two hydrogens the mass I'm going to pull from the periodic table and throughout this unit you will get really good at remembering all of the masses I know that calcium is 40. oxygen is 16 and hydrogen is one when you multiply these counted quantity measurements really they have an infinite number of zeros behind them meaning that it has way more significant figures than the mass does so when you multiply you're going to stick to the number of significant figures on the mass and remember you multiply going across so this is going to come out to 40 and you should match your significant figures on the total to the Mass 2 times 16 is 32. if you didn't know your 16 times tables I Promise by the end of your Stoichiometry unit you'll know them and then 2 times 1 is 2. so this tells me that I have 40 grams of calcium 32 grams of oxygen and 2 grams of hydrogen per mole of calcium hydroxide so I'm going to add this all going down and that is going to give us um let's see four and seven 74 grams per mole I have 74 grams every time I have a mole of calcium hydroxide if I wanted two moles then I would double that 74 if I wanted half a mole I would divide that 74 in half all right here is another example here we have aluminum carbonate and the question is how many grams per mole or what is the formula mass of an aluminum carbonate so we are going to list all of the elements aluminum carbon and oxygen and then we're going to fill out that qmt chart I have two aluminums three carbons and nine oxygens massive in aluminum is 27. carbon is 12. and oxygen is 16. 2 times 27 is 54. 3 times 12 is 36. and 9 times 16 I don't remember 144. we're going to add all of these going down the total column and that comes out to 234 grams per mole come on and there you have it that's how you figure out the formula mass again the more you work with moles the more it kind of makes sense um it's really just a practice thing the formula mass once you learn the process is very simple but the mole concept itself is really tough to wrap your brain around it's important to remember that atoms and molecules we often call them particles are super super small and at this point we don't have the technology to work with individual atoms and molecules so instead we lump them into groups that we call moles all of those mole moles are of equivalent quantity meaning that if you have a mole of carbon a mole of gold a mole of aluminum carbonate you will have the same number of particles this helps us to work in ratios so it's almost kind of like um doubling a recipe right if you wanted to make a cake you would use a certain number of ingredients if you wanted to make a mole of cakes you would need a mole of each ingredient if you wanted to make two cakes you would have to double your recipe if you wanted four cakes you'd have to quadruple your recipe if you want a mole of cakes you would have to multiply all of your ingredients by a mole that's kind of what we're working with here a mole is just a name for a very large number and that number is 6.02 times 10 to the 23rd 602 sextillion and that is called Avogadro's Number we'll talk about him more when we get to gases because that is where the concept of a mole came from um but his number is not something that he came up with he just came up with the concept of bundling atoms into groups of equal size and that's it that is everything please leave any questions you have in the comment section below the video I'd be happy to get them answered for you subscribe so you don't miss the next lesson where we really get into this qmt chart I hope to see you there bye