in this video we will be looking at the mole unit which is our first real kind of chemistry exclusive unit and this is the very beginnings of being able to use a mole and you're gonna find that you end up using the mole for almost all sorts of chemistry calculations so first before we get into talking about the mole let's talk a little bit about the idea of counting by Wang so I'm give you an on chemistry example to kind of illustrate this idea I want you to do is imagine you own a factory in this Factory you produce small hardware pieces you're going to make things such as nuts bolts screws washers all those little Hardware pieces that connect everything now in this factory you receive a lot of orders and therefore lots of pieces here frequently receiving orders for tens of thousands of these pieces at a time maybe hundreds of thousands how do you go about fulfilling these orders would you count them well you wouldn't count them you're the owner but pay somebody to count them but how long would it take to count out all of those tens of thousands of pieces well you probably wouldn't have somebody count them the way we would normally count things you would probably count them by weighing them you might take out a sample of one of the nuts or bolts or screws or washers weigh it figure out what one weighs then you could just start dumping these onto a scale to figure out what weight you would need to get your order for 10,000 or 20,000 of these pieces now those small manufactured pieces sometimes aren't all identical so you may recognize this so you worried about well what if that sample one that you chose to use as a representative weight was a little bit light well then average well if it's a little bit smaller than average well that's a little bit of a problem because well you'd be giving more the customer more than they ordered which isn't a problem but as a result of that you're losing inventory you don't need to lose well what if the little piece you use the sample was heavier than the average well that was heavier than the average then do have a real problem because then when you pull out the weight that you want it won't have the correct number of pieces so instead what you might do is knowing that they might not all be identical you may choose 100 random ones well 100 random ones will so we're gonna be identical but you're gonna get the occasional smaller one later one and the occasional heavier one and you're gonna get a better representation if you need to do this procedure for small hardware pieces nuts bolts screws washers you would definitely need to do this for smaller things like atoms and molecules those are so much smaller that you're never going to count out those huge numbers of items and just like all the little Hardware pieces aren't identical even for an element we know we have different isotopes you know the average for carbon is 12 if you chose 13 to be your representative thing you'd have a problem or 14 so that's why we kind of think about averages of these especially when we're dealing with that number of individual pieces so I wanted you to think about this idea of counting by weighting in a non chemical way and I'm thinking about a whole bunch of nuts bolts screws and washers you need to do that for tens of thousands of pieces the numbers you're dealing with that for things that are small like atoms and molecules is even much greater so here we're looking at the mole of unit that's going to be our counting by weighing in type unit so first off the mole though is a counting number nor just like any other counting number it just happens to be a very very large counting number one mole is 6.02 times 10 to the 23rd pretty big number but that functionality is really no different than some other things that are a little bit more familiar to us we're familiar with a dozen it's really no different than a dozen a dozen is 12 it doesn't matter what that does is up whether it's donuts eggs pencils erasers hands of soda it doesn't matter a dozen as always 12 a mole is always that counting number but because that number is so large it has limited practical uses we can count up to 12 for a dozen we can't count up that high that number is just too big for us to use but besides the counting number it also has a counting by weighing definition that we can now use in a much more practical way and this counting by Wang definition is related to the am usually c4 the elements those atomic mass units so when we looked at something like carbon we said the average mass was 12.011 am use well that 12-point amu average mass for carbon silicon McMath you nestlé's turn off made-up units that got us down by down to that small scale now has a counting by Wang definition the counting by Wang definition is instead of an amuse is that many grams of carbon twelve point oh one grams of carbon is one mole of carbon we call this relationship that it takes 12.01 grams of carbon to get a mole of carbon the molar mass the molar mass is kind of what it says how much mass does it take to give you one mole of that substance so that gives us a counting by Wang definition now we can count things that are really really small like atoms by weight then we can easily measure as opposed to individual counting numbers so this works for the average masses you see for all the other elements as well you look at something like phosphorus on the periodic table when its average mass is thirty point nine seven well that's the molar mass of that's how many grams of phosphorus it takes to give you one mole of phosphorus 40 point oh eight grams of carbon instead of am use forty point oh eight grams of carbon is one mole of carbon so what this does is this now gives up some more meaning to the periodic table some more uses we talked about the periodic table before kind of organizing the elements in groups and periods and metals and nonmetals but now this does even more the periodic table is now one gigantic unit conversion chart that you always have available being you always have that available you can use it for a whole bunch of different things periodic table has all the average mass number so long as we already talked about carbon phosphorus calcium you can do this for any of the elements out there those average mass numbers that you're seeing are now the molar masses how many grams of that substance it takes to give you one mole of that substance so we're gonna work through some examples of showing this but periodic table now just became even more useful than it was already because now we can do calculations with the information on that periodic table so we saw that we had two definitions of a mole that the mole kondal is a counting number that 6.02 times 10 to the 23rd well if we're talking about something like carbon one mole of carbon would be 6.02 times 10 to the 23rd atoms of carbon we also saw that the mole had a counting by wainy definition 12.01 grams of carbon so one way of thinking about this relationship is I kind of made a pyramid or triangle I put moles on the top and I kind of put moles at the peak of this because moles do a good job relating to counting numbers we have a way of relating moles to counting numbers how do we do that well that relationship between moles and counting numbers this one right here to go back and forth between a mole and that counting number you would end up using the definition of a mole one mole is 6.02 times 10 to the 23rd that's Avogadro's number so that's how you'd go back and forth between moles and counting numbers we also saw that moles can relate to grams that moles have that secondary counting by Wang definition so if we want to talk about the relationship between moles and grams we can talk about this relationship between our moles and our grams our moles and our grams well how are we going to deal with that our moles are grams are going to work from using the periodic table so if we want to go back and forth between moles and grams we don't do this conversion between moles and grams how are we going to do that we're going to look at the periodic table that's where we're going to get those relationships from now one part of this pyramid that you're not seeing that I didn't connect you're gonna notice that I did not connect counting number and grams together you don't see any connection running between here reason why you're not seeing any connection between there is because we really want to work through the mole if you try to connect counting number 2 grams what you're going to be dealing with are crazy small numbers that are going to be different for every element that you're working with so we don't go directly between counting number and grams we always go through the mole why we still have to use one crazy number but it's always that same crazy number and it's very large but being it's only one you don't have to deal with whole bunch of different very large or very small numbers so you wanted to go from counting numbers to grams you would go through the moles if you want to go from grams the counting number you would still go through the moles you wouldn't try to do that directly and there's conversions for each of these steps first conversion is using that counting definition of the mole is 6.02 times 10 to the 23rd you might have been familiar with this as Avogadro's number if you're going between moles and grams where you're getting that information from you're getting that information from the periodic table those average mass numbers for each of the elements so what we want to do now is we want to look at some example calculations of doing these we're gonna do some examples so our first example is diamonds are made up of pure carbon so what diamond has a mass of 315 milligrams how many atoms of carbon are present in that diamond so we had diamond and weighs 315 milligrams how many atoms of carbon are actually in there so we're using a dimensional analysis method where we can real easily show numerators denominators multiplication and division we're gonna focus on the units well what are we starting with we're starting with our 315 milligrams well 300 15 milligrams I can't do much with that I know if I ultimately want to get two atoms I'll have to be in moles and moles are going to come from grams so our first step is going to be a milligrams to grams conversion 315 milligrams of carbons what we're starting less in our numerator we want to convert that to grams so the relationship between milligrams and grams 1,000 milligrams one graph we see milligrams in the numerator milligrams in the denominator those milligrams of carbon are going to cancel remember I can't set this up as a table but this is really one gigantic division bar when we're doing dimensional analysis numerator denominator are going to cancel now I have grams of carbon now from that previous slide that we looked at we can relate grams to moles how can we relate grams to moles grams and moles get related to each other through that information on the periodic table you would look up carbon on the periodic table you see that 12.1 that molar mass of carbon that 12.1 grams of carbon is how much it takes to give you a mole of carbon those molar masses we are able to use those as conversion factors to use in problems so I have the grant as a numerator I want to go away from the grams I want the grams into known there so one mole of carbon is 12 point oh one grams of carbon grams of carbon in the numerator are going to cancel with the grams of carbon in the denominator so now I'm at moles of carbon so four moles of carbon now I'm one step closer to my goal remember I often wonder how many atoms of carbon I have well that relationship uses that actual just counting definition of the mole one mole is 6.02 times 10 to 23rd well in this case if we're dealing with carbon that would be atoms so I look at moles of carbon in the numerator I'm gonna put the moles of carbon in the denominator so they cancel the only unit I have left is a unit I want which is the atoms of carbon all my other units have cancelled off now we're ready to actually do the math part of the calculation so for the math part of the calculation everything in the numerator gets multiplied everything the denominator gets divided by so to actually get our final answer we would take 315 times 6.02 times 10 to the 23rd divided by a thousand divided by 12 and we would get our final value rounding to three significant figures because that's what our initial information was three hundred fifteen milligrams three significant figures so our final answers should be rounded to three significant figures as well we'd be looking at one point five eight times 10 to the 22nd atoms of carbon we say okay is it answer reasonable that's a lot of atoms of carbon but we recognize atoms are so small that is going to take an awful lot of them to come up to 315 milligrams let's look at another example next example is kind of almost the exact opposite here we're starting with how many atoms of an element we have you want to figure out what is the mass of that sample what is the mass of that element so here we're starting with five point seven eight times ten to twenty two atoms of iron what's the mass of that many atoms of iron no we're going to start with our given information five point seven eight times ten to twenty seconds and I want to go from atoms I'm trying to get to atoms is a counting number trying to get to grams so I'm gonna go through moles again so that's gonna be my first step is to go through moles well how can I go from counting number to moles that's using that counting definition of the mole one mole is 6.02 times 10 to 23 atoms I'm starting with atoms in the numerator so I want atoms in the denominator so atoms in the numerator and the iron will cancel now I'm going to be left with moles of iron but I want to go from moles to a mass where am I going to look I'm going to look at the periodic table for that molar mass we find the iron on the periodic table is average mass is fifty five point eight five well that's the molar mass of iron that's how grams it takes to give you one mole of that substance I want the moles to cancel so I'm starting with moles in the numerator I'm gonna put the moles in the denominator next step moles of iron well cancel the unit I'm left with is the unit I want which is grams of iron now it's just a matter of doing the math so for the calculation everything you see in the numerator is a multiplication so five point seven eight times ten and twenty second times fifty five point eight five then you're going to take that and divide it by the 6.02 times 10 to the twenty-third when you round that to three significant figures you should be looking at five point three six grams of iron now a couple of things when you're trying this so when you're going through and you are trying this on your own in doing some of these calculations whether it's this one or a similar one if you end up getting a very strange answer it might have the right number here but you get a crazy exponent something like times ten to forty four times ten to forty six or ten to forty seven what that is an indication of is that the calculator is not reading the scientific notation you entered in the way you think it should be it ended up multiplying some things that were really divided by so just something to think about when you're practicing these if you're getting all sorts of crazy exponents for a problem like this you might need to go back and look at the instruction manual in your calculator make sure you're putting in scientific notation in the way that your specific brand of calculator is going to deal with that correctly so we did a couple examples with atoms and elements but when we think about all the different matter that's out there most of the matter we deal with is not just a pure element we're much more likely to be dealing with a compound than we are just a pure element so we're going to talk a little bit about molecules and compounds everything we just did for atoms will also work for molecules and compounds we just have to treat the molecule or compound as a total collection of the atoms or the items the total for a molecule or a compound is going to equal sum of all the individual parts that make up that molecule or compound it kind of makes sense if you care about the total of something add up all the individual parts after you added up all the individual parts it has to tell you something about that total sum do some examples of dealing with molecules and compounds the first one I want to deal with deals with figuring out the molar mass of n2 v r4 so this is a molecule we want to figure out what that molar mass is how many grams of that substance do we need to make a mole and for this we just have to sum up the individual pieces figure out how many of which individual pieces we have well or the subscripts we have two nitrogens so each nitrogen comes in at 14 point O one now we look at our roamings we have four bro means so we want to put out four bro means look up the mass for the bromine at seventy nine point nine one two three four bro means if we sum together all of these all the individual parts that we listed we're going to get the total so sum total for M to be our four is three hundred forty seven point six two now was that three 47.62 really mean that three 47.62 is really the molar mass of M TBR for its how many grams of M to be R for it takes to give you one wool so three hundred forty seven point six two grams of M to be our four is equal to one mole of n2 BR for let's do another example dealing with molecules and compounds it's a compound molar mass of m2 s o4 v well here sometimes you may not want to list out everything individually but you still have to count the pieces correctly so I have manganese manganese the periodic table look comes in a fifty four point nine four or how many manganese ins do I have I have two so I need to multiply that fifty four point nine four times two and that's gonna give me the 100 nine point nine nine for the sulfur now we're looking at the sulfur here sulfur we look on the periodic table 32 point O seven so we got that how many Sulphurs do we have well sulfur is part of those polyatomic ion here's where we're using those parenthesis again each unit of sulfate has one sulfur in it and I have five units of sulfate so I'm going to have five sulfur so I'm going to take the mass of the sulfur multiply it by five to give me my total for my sulfur now for the oxygen how many oxygens do I have while oxygen comes in at 16 on the periodic table but how many do I actually have present in this compound well in this compound each unit of the sulfate gives me four oxygen atoms and I have five of those units so four times five is going to give me 20 of oxygen 20 times 16 gives me the 320i sum together all the parts and I'm gonna get five hundred ninety point three four what's that five hundred ninety point three four really represent well that's the molar mass of MN to s o four five that means it takes five hundred ninety point three four grams of that substance to give us one mole of that substance so when you're dealing with a molecule or a compound all you really need to do is sum together all of those individual pieces so we're gonna do some more examples of actually using this in our calculation so dry ice is sometimes use in shipping perishable foods to keep the item frozen or cold or dry ice actually is is it's solid co2 so we want to determine is we want to determine how many molecules of co2 are present in one in a one point five pound brick of dry ice so some useful information shows karana forests 2.2 pounds equals a kilogram so we got a way of converting between the English and the metric again this is a dimensional analysis problem we need to use dimensional analysis in order to solve this so what do we start with and only the only thing we could really start with is the pounds of the co2 so we have our pounds of the co2 ready to go I know I can't do anything really useful in those English units I have to convert to metric well I was given a way of converting between the English and the metric here so I'm going to go ahead and get out of English and get into metric right away pounds and kilograms are and get away from pounds I have pounds the numerator already so I want my pounds in the denominator so kilograms and writer panels in the denominator like pounds of carbon dioxide are going to cancel now I'll have kilograms of carbon dioxide well I know to start working in mole units I can't be in kilograms after in grams I need to do a metric to metric conversion remember these metric to metric conversions aren't provided so you need to come up with these on your own so go from kilograms to grams I need the conversion well it takes 1,000 grams to give me one kilogram I want to put the kilograms in the denominator to cancel it the kilograms already have in the numerator so one kilogram of co2 numerator kilogram and co2 in the denominator are going to cancel now that I have grams now I want to go to moles so from grams to moles how am I going to get there go from grams to moles what we need is the molar mass of that substance so we've already done this four elements now we're ready to do four compounds I need the molar mass of co2 well how do I get the molar mass of co2 and on the side I did this work it's on the left-hand side I just sum together all the pieces that go into making co2 co2 has one carbon it comes in at 12 point oh one co2 has two oxygens each one coming in at 16 so the total for co2 is 44 point oh one grams per mole I'm now using that as a conversion factor just like I use it for an individual element now I can just use that for molecules and compounds as well so I decide what I want to go away I want the grams to go away so I put the grams in the denominator grams of co2 cancel leaving me with moles in that numerator now I want to go to molecules well that's a counting number so what's my conversion for a counting number well moles and a counting number get related by that 6.02 times 10 to the 23rd here I'm not dealing with atoms with molecules the co2 that unit is called a molecule so one mole of co2 6.02 times 10 to the 23rd molecules of co2 moles in the numerator will cancel with moles in the denominator the unit I have left is a unit I want the only one I didn't cancel off is the molecules of the co2 so now I'm ready to actually do the mathematical calculation for this remember for these dimensional analysis problems anything in the numerator is a multiplied by anything the denominator is a divided by I don't taking on 1.5 you know half multiplied by 1 but multiplied by a thousand multiplied by 1 x the 6.02 times 10 to the 23rd now we're going to start the divisions divided by everything you've seen the bottom in the denominator divided by 2 point 2 divided by 40 4.01 we're going to take our answer we're looking at two significant figures for this so when you round this to two significant figures you'd be looking at nine point three times ten to the 24 molecules of co2 we ask ourselves does that make sense well we're trying to count how many molecules are in a pound and a half brick it better be a pretty large number of molecules knowing how small molecules actually are so this answer seems reasonable for us so you're going to treat molecules and compounds the exact same way we did for the atoms and the elements before except you might have to sum up all the individual pieces to figure out what's going on with the total let's do one more example using this time a compound this one asks a little bit different questions so this one asks how many atoms of oxygen are present in 436 milligrams of the calcium nitrate that we see here for this one here we're not looking for how many units of the calcium nitrate but how many oxygen atoms are within those units so this starts off very similar to the other one it's the only real starting piece of information we could start with is the milligrams of the calcium nitrate I know I can't leave them in milligrams I have to get two grams so I need to do a metric to metric conversion in the next step milligrams and grams it takes a thousand milligrams to equal one gram on place the milligrams in the denominator so they'll cancel with the milligrams in the numerator so now my milligrams of calcium nitrate are going to cancel now I'm going to have grams of calcium nitrate well I need to go from grams to moles so how can I go from grams to moles well to go from grams to moles what I'm going to have to do is I'm going to have to use the molar mass I'm gonna have to sum together all the individual pieces so I just rounded calcium to forty just to make it a little bit easier I have one calcium coming in forty two nitrogens I could have around about 214 as well but I didn't nitrogen comes in at fourteen point O one times two four twenty eight point O two for the nitrogen how many oxygens do I have well in each unit of calcium nitrate I have three oxygens I have two units of nitrate so I'm gonna get 3 times 2 or 6 units of oxygen coming out 16 times 6 is going to give us our 96 so we're gonna sum together all of our pieces when sum together all the pieces the 40 from the calcium twenty-eight point o2 from the nitrogen the ninety-six from the oxygen to give us our total of 164 point o2 grams per mole that's a molar mass for calcium nitrate now I can use that as how many grams it takes to give me one mole I want to move away from the grams so being a moving away from the grounds and put the grams of denominator such that they're going to cancel with the grams in the numerator grams the numerator cancel with the grams in the denominator now the unit I currently am at our moles of calcium nitrate well what can I do with moles of calcium nitrate I can now start working towards getting to that counting number I ultimately need a counting type number atoms of oxygen well I'm going to start getting to that counting type number well that actual counting number there's only one way to go from moles to that counting number that's to use Avogadro's number that just definition of a mole one mole is 6.02 times 10 to the 23rd regardless of what you're dealing with here I'm calling these units of calcium nitrate it's not really molecules because it's nanak compound usually we don't call ionic compounds molecules I'm just gonna leave it as units one moles gonna be 6.02 times 10 twenty-third i want moles to cancel so moles in the denominator are gonna cancel with the moles numerator and the unit i'm currently going to be at our units of calcium nitrate now that's not ultimately what I want to achieve ultimately I don't figure out how many atoms of oxygen I really need well so I need some relationship between units of calcium nitrate and atoms of oxygen well here's one this is probably the most difficult step to actually see when you're doing this problem but it's also stuff that you've actually already done in an earlier part of this problem if I have one unit of calcium nitrate how many units of oxygen do I have well we kind of already answered that if you go back down to the lower left hand corner when we did the molar mass we kind of already answered this question one unit of calcium nitrate we are a determined head six oxygen atoms that go into making that up well any true statement you can write can be used as a conversion factor so one unit of calcium nitrate in our last up contains six atoms of oxygen that's a true statement and a true statement you can make can be used as a conversion factor I want the calcium nitrate to go away so that's gonna be in the denominator such that units of calcium nitrate are going to cancel I'm gonna be left with atoms of oxygen which is what I ultimately want that's what I want to be left with are these atoms of oxygen last step is just go through the mathematical calculations for this multiply everything through the numerator 436 we don't need to multiply by one but then multiply by the 6.02 times 10 twenty-third then times six then everything in the denominator is a divided by so divided by a thousand then divided by the one 64 point zero two we're looking at rounding our final answer to three significant figures because we started with three significant figures in our initial part so we should round to three significant figures at the end and then at the end we're gonna get nine point six times ten to twenty one atoms of oxygen now again we have to ask ourselves is this reasonable is this kind of what we would expect we got a very large number should we get a very large number nine point six zero times ten twenty first is a very large number is that reasonable and here yes that is reasonable I'm trying to figure out atoms of oxygen present in 436 milligrams even though 436 milligrams isn't a lot of material we know just how small atoms actually are it's going to take a lot of atoms to get anywhere close to that amount of material so here the key things that we're doing in this in these examples that we did in this presentation is you saw that we use both definitions of the mole we ended up using the counting definition of the mole weeds and a couple different places I highlight that in purple here we used that we use that counting our accounting definition that's 6.02 times 10 twenty-third but you also see like this in green for you what you are also seeing is we're using the counting by weighing definition of the mole so you use that counting by Wang definition we're using the molar mass see that in the green you see this in all the different problems that we did we use both of the definitions of the mole and now we're at the stage of we're doing chemistry problems using this dimensional analysis technique where we're arranging our multiplications and divisions such that units are cancelling off then at the end we're multiplying things across the numerator and then anything the denominator we're dividing through by this so this was our introduction to the mole we're going to be doing some other calculations using this so key thing is this is just the beginning of our mole type calculations we use mole for a lot of different things you know make sure you have a handle on these basic mole calculations because we're going to use some of these repeatedly over and over over again especially that counting by Wang definition you're gonna see you're going to be using this all the time in chemistry it just never goes away