so let's spend some time talking about the mole defining what the mole is understanding the mole and then start using the mole for conversions and talk about smaller Mass first what is a mole the definition of mole states that a mole is the SI unit for substance the quantity of a substance that contains the same number of entities as the number of atoms in exactly 12 grams of carbon-12 the definition itself can be difficult for students to understand so let's back up a little bit a mole is a number word what do I mean by a number word I mean it represents a specific number of things such as if I said one dozen eggs I know that that means 12 eggs if I said baker's dozen I know that represents 13 of whatever I'm talking about if I say a couple of tacos the word couple means to so this would be two tacos a gross of pencils now less people tend to know what a gross means but gross itself means 144. so this would be 144 pencils so if I'm saying a mole of something I'm saying a specific number of that item it tells me it's the SI Universe substance from a side that's our standard units and so of a substance the quantity of substance that contains the same number of entities as the number of atoms in exactly 12 grams of carbon-12 so if I have exactly 12 grams of carbon 12 I have one mole of carbon-12 but what is that number that is what we call Avogadro's number 6.022 times 10 to the 23rd now you may see that written somewhere at 6.02 in my class you need to use 6.022 it gives me four sig figs this way and that's a really big number if I took that out of scientific notation it would be and I have to do this by Counting 6022 so one two three four five six seven eight nine 12 13 14 15 16 17 18 19 20 21 22 23. I then go ahead and put all my commas in to separate out all my zeros which are hard to see one two three I don't think I put those in the right spot three one two three one two oops three three there you go sorry about that I'm just trying to show you like just how big this bumper really is it's a really big number um that number is hard bigger and harder for most people to understand that number is bigger than if I took the entire population of the world right now we would have less than one mole of people it's a very large number but what does that number really mean it means if I have exactly 12 grams of carbon 12 atoms I have that many carbon-12 atoms that's insane right that's a huge massive number what I want you to think about is just how small a carbon or any atom is atoms are very very very small smaller than we can see with our human eye without without some kind of instrument to help and honestly there's more than most of us can really comprehend it's just tiny so it takes a lot of them to equal up to one mole of material and so if I wanted one mole of particles I would have 6.022 times 10 to the 23rd particles if I want one mole of atoms I have 6.022 times 10 to the 23rd atoms five one mole of electrons I have 6.022 times 10 to the 23rd electrons and if I have one mole of molecules I have 6.022 times 10 to the 23rd molecules again one mole is representing a very large number for us but it's specifically based on carbon 12 why carbon 12 because as we talked about previously the entire periodic table is correlated or based on carbon 12. 1 Amu is equal to 1 12 of a carbon-12 atom so the table has been normalized so that one mole is 12 grams of carbon we figure out exactly how many particles are in exactly 12 grams of carbon we find it to be 6.022 times 10 the 23rd we know how much one mole is also this little guy here this is our mascot from the American Chemical Society it represents our mole so how does this help us well we can count atoms by using moles if we can find the mass of a particular number of atoms we can use this information to convert the mass of an element sample into the number of atoms of that sample so let's go ahead and look at Copper I know that if I have one mole of anything I have 6.022 times 10 to the 23rd of that thing so therefore if I have one mole of copper atoms I have 6.022 times 10 to the 23rd copper atoms but remember when we have an equality like this that is giving me a conversion factor but I also know by looking at the periodic table I can look at the table we're going to talk about this as well so we get atomic mass or molar mass Atomic meaning for one atom one type of atom molar or um molecular mass molar mass molecular weight meaning for an entire molecule or compound I know that one mole of carbon atoms will equal 63.55 grams of carbon atoms where do I get this number periodic table we've already talked about how to correlate that number how to develop that number with the isotopic isotopes of carbon of copper and the ratios of copper so I know that that number is 63.55 is on my periodic table I know I get that by looking at the Isotopes of copper and how abundant they are and I use their fractional abundance to figure out the overall number there but that means that one mole of copper atoms weighs 63.55 grams of copper so if I have one mole of copper atoms that contains 6.022 times 10 or 23rd copper atoms and it weighs 63.55 grams of copper just for visual on your side 22 copper pennies contains approximately one mole of copper atoms so if you have 22 copper pennies you've got approximately 6.022 times 10 to the 23rd copper atoms and this brings us to what we call molar mass molar means per mole so the mass per mole the mass in grams of one mole of a substance and it's the average masks again it comes from the relative abundances of the Isotopes of that element so the molar mass of copper is 63.55 grams per mole meaning it takes 63.55 grams to make one mole of that material so this is just kind of conversions that we can do now I much prefer you do these as actual conversion factors but students sometimes just getting practice and getting started need to see it a little bit differently if you are going to try to convert between grams molecules atoms particles things generally speaking any of it we have to go through moles so every time you have to go through moles first moles is your middle ground you cannot convert from grams straight to molecules atoms particles are things you cannot convert from molecules atoms particles or things straight to grams you have to go through moles first so use your moles first if you are going between grams and moles you use your Atomic or molar mass again Atomic just means for one specific atom of something so like copper carbon Nitro nitrogen is a diatomic copper carbon zinc sodium any of that that's Atomic molar mass is for anything that's not a single element so we've got diatomics we're talking about in chapter three Like Oxygen is a diatomic it doesn't actually exist as just oxygen um the auction we breathe I mean it's actually considered O2 uh carbon dioxide carbon monoxide sodium chloride all of those would be molar masses because it'd be for more than one particle together if I'm trying to go between grams and moles though I'm using my Atomic and molar masses so that again is listed as grams per mole if I am going from moles to grams so we can see the arrow here I'm multiplying and if I'm going from grams to moles I'm dividing again if you just do this as a conversion factor you won't have to remember this it'll be easier but some students again have to get a background down before they can do the rest if I'm going from moles to grams I am multiplying because I a mole represents a very very large number a gram is more realistic to what we're going to see in the real world we're going to multiply to get there if I'm going from grams to moles I'm going to be dividing because I'm going to represent something that's a very very big number a mole is a very big number Final in between molecules atoms particles and things I'm using Avogadro's number that is that 6.022 times 10 to the 23rd things per one mole of things whatever that thing maybe molecule atom particle ion compound doesn't matter and same thing we see if we're going from um if we're going from moles to molecules atoms particles or things for multiplying if we're going from molecules as particles or things back to moles we are dividing but again I recommend just doing this conversion factor it will make your life a lot easier and you will get the question right more often than not if you're doing the rest of your stuff correctly that is but again this is grams per mole it's a conversion factor and this is Avogadro's number as your conversion factor so let's go ahead and work an example what do I mean by this well how many molecules are present in 2.35 moles of molecules we're gonna do the same thing that we started in chapter one when we do dimensional analysis first thing we're going to do is write down what we're trying to find if we read the question it's asking us for molecules and it's telling us we're starting with 2.35 moles of molecules so I want to know the number of molecules write down what you're trying to find next write down what you are given 2.35 moles of molecules now I'm going to think about my conversion factors I am trying to get rid of moles of molecules I'm trying to get to molecules the one conversion I have that goes between number of things and moles is Avogadro's number I know that one mole of anything is equal to 6.022 times 10 to the 23rd of that thing so 6.022 times 10 to the 23rd molecules for every one mole of molecules they're cancel out my molecule that cancels out I apologize that cancels out my moles of molecules and gives me my molecules calculate that out and so in your calculator be careful depends on what calculator you have you are typing 2.35 times 6.022 and you should have some kind of e button most of the time it's a double e this e and these E's are not the same E's this is a natural log thing most of the time you're going to see it with a button like that do not use that button please that is not correct like that or it may say e to the x that is not the correct button but ee 23 that's how I'm able to type into my calculator I actually have to hit the second button to get that e button to activate so you're going to try to find your scientific notation and connected if you don't know where to find it 1.42 times 10 to the 24th molecules and so we have our final answer now with this next question number of moles of atoms how many moles of atoms are present in 9.5 times 10 to the 15th atoms so we want to know number of moles of atoms and we're told we have 9.5 times 10 to the 15th atoms using the same conversion here I've got a number of things and I'm trying to get some moles of things my numerator I'm going to put what I'm trying to get to number of moles of atoms my denominator I'm putting what I'm trying to get rid of 6.022 times 10 to the 23rd atoms how do I know it goes in denominator because if something is in the numerator and in the denominator it cancels itself out I also am trying to get to moles of atoms and by putting it in my numerator it now gives you my answer in moles of atoms calculate that through and I get 1.6 times 10 to the negative 8 atoms and I forgot to discuss sig figs here but let's go ahead and do that really quickly so in this question here this had three sig figs so my final answer had to have three sig figs remember the times 10 to the 24 that is just your sine notation that is not your sig figs second question 9.5 two sig figs again that 10 to the 15th is telling you how big the number is it's not your sig figs 9.5 is my sig figs my final answer two sig figs as well so two sig figs in my measurement two sig figs of my final answer I'm not I'm using avocados number to four sig figs so that will not limit my calculations so we've talked about converting between moles and atoms of things but what if we want to start using it for actual elements how do we do this well the mole this word mole relates to Mass one mole of carbon if I look at the periodic table I look up carbon I'm going to find a box that looks something like this it's going to have a c in the middle it's going to have a 12.01 in the bottom and it's gonna have a six in the top and we talked about this we said you know up here is your atomic number which tells you your number of protons tells you number of electrons in a neutral species um this is your elemental symbol and this your average s but this also tells you your moles so you may see it say 12.01 it may say 12.011 depending on how accurate your table is some go up to successful places but one mole of carbon is equal to 12.01 grams per mole so this number down here is telling me how many grams do I have in one mole of that substance if I looked up if I want to add up the molar mass of water I would look up on the table I would find that my I would find hydrogen I'm going to pretend that's a box has a one and a 1.008 and if I looked up oxygen 15.999 or some will just say flat out 16. remembering our formulas I know that water H2O has two hydrogens so this would be two times one point zero zero eight grams per mole one oxygen one times fifteen point nine nine nine grams per mole add this all up and most of the time too big um I'm gonna and so it matches my answer so I want to recalculate this right now I'm gonna most often write 16 grams per moles most tables you're going to see they'll either be 15.99 or they'll just be a flat 16 but a 16 is what I have memorized here and then I don't have to calculate things quick but this adding up would give me 18.02 grams per mole water so I apologize that means that one mole of carbon is 12.01 grams um one mole of H2O is 18.02 grams but that gives me my conversion factor that means that one mole of carbon 12.01 grams of carbon 12.1 grams of carbon to one mole of carbon same with the water one mole of water 18.02 grams of water 18.02 grams of water to one mole of water what if I look up at the one down here uh aluminum sulfate let's go ahead and I gotta move the screen up a little bit let's go ahead and add this up if I look up aluminum two aluminums would be 2 times 26.98 grams per mole again I'm getting that 26.98 from the periodic table itself when I look up aluminum that's what I see I've got so the two goes to the aluminum here the three goes to this entire polyatomic meaning I have three sulfurs 3 times 32.07 grams per mole and 3 times 4 oxygens 12 oxygens 12 times 16.00 grams per mole when I add all this up together I get 342.2 grams per mole so one mole of aluminum sulfate is equal to 342.2 grams of aluminum sulfate so if I had exactly 342.2 grams aluminum sulfate I would have one mole of that material molar masses are really useful because we can use these to convert from grams to moles and moles to grams again this is called molar mass you may also see it called molecular weight molecular mass formula weight formula mass it represents the mass of one mole of material the difference between molecular and formula we're going to talk about this a little bit in the next chapter but when we have ionic compounds like say sodium chloride NaCl this is a formula unit versus water which is H2O is a molecule and it's what that means is sodium chloride it's not just one sodium ion and one chloride ion that hang out together that's why we write it for simplification simplification but really it's a huge array of compounds together it's an alternating pattern of sodium chloride sodium chloride sodium chloride sodium ion is what I mean by that but sodium chloride and sodium chloride ion alternating in a huge 3D crystal structure the simplest unit of that is one formula unit whereas water is one individual molecule there's water molecules can hang out together but it's one individual molecule we'll talk about more of that in chapter three though that's what you'll see things like molecular mass versus formula mass and a very useful formula for molar mass is remembering its mass over number of moles now that may seem intuitive like well you just told me that yes but there will be example questions we do where the question says you Analyze This Mass sample and through the math you can find the moles of that sample and then with that information you can actually figure out the molecular weight of the compound itself and identify what your unknown would be so let's work a few more examples what is the molar mass of ammonium nitrate nh4no3 so I got ammonium nitrate and it gives me my formula I see I have two nitrogens two times 14.01 grams per mole this gives me 28.02 grams per mole for the nitrogen I've got four hydrogens four times one point zero zero eight grams per mole gives me 4.032 grams per mole my sig figs and three oxygen 3 times 16. grams per mole is 48 grams per mole sum this up together when I put this in the calculator I get 80.052 that is grams formal but again I need to look at my sig figs here this is precise to the hundredths this is for size to the thousands and I forgot to mark up this precise to the hundreds meaning my final answer is hundredths so my final answer here is 80.05 grams per mole and it's usually sufficient to leave your molar masses to four four sig figs overall no if you are ever have a measurement that's more than four sig figs you should measure your molar mass out to more sig figs as well to not let your molar mass limit your sig figs in your calculation or limit your Precision your measurement but most often four will be sufficient for what we do let's see we've also got calcium permanganate cmno42 we've got one calcium again there's no subscript here so that just means one calcium I look up calcium and table and I see it's atomic weight is 40.08 grams per mole now this two here applies to the entire polyatomic so I've got two manganese 2 times 54.94 grams per mole 109.88 I'm going to underline my sig figs there grams per mole calcium of course being 40.08 grams per mole and two times that entire polytonic but I've got a 4 here meaning overall I have eight oxygen eight times 16 grams per mole gives me 128. I got to put the point zero there to keep my sig figs grams per mole that happened up here on auction as well make sure you're not letting your sig figs drop sum this together and I get 277 0.96 grams per mole but hundredths place tens place tens place I have to limit this to the tens place I'm gonna have to round I'm going to cut my number right here I'm dropping a six I need to round up this is going to round up to 278.0 I need to include that point zero to keep my significant figures in place molar mass 278.0 grams per mole for a lot more practice we're gonna do a lot more practice in the next video but this is just kind of give you guys a basis to start