okay we need to go ahead and talk about the mole so here's our mole not even joking he is absolutely our little mascot there he is in his little lab coat and it says acs on it um acs is the american chemical society and yes we are very proud of our little mole i have a key chain of him i want the stuffed animal he's really cute anyway he's safe he's doing reactions he should wear gloves and you know shoes but he's got his safety goggles on his lab coat but we use the mole as our mascot because we talk about this number of a mole all the time in chemistry when you are unsure what to do and you're going to be doing math you're probably going to convert to moles but what is a mole the definition of a mole states the a mole is quote the s i unit for amount of 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. great what the heck does that even mean we've got this 12 grams of carbon 12 here well that's because the entire table is based on avogadro's number the entire table is based on carbon 12. um so 12 grams of carbon 12 contain a certain number of carbon atoms 12 grams of carbon 12 contains 6.022 x 10 to the 23rd carbon atoms it's a really big number six let's see zero two two i think i got all the zeros in there don't quote me i kind of get lost when i'm counting all of them out that looks right yeah really big number 12 grams of carbon it's not very much it contains that many carbon atoms this really big number is known as avogadro's number or we'll write capital n subscript a avogadro's number is equal to 6.022 times 10 to the 23rd 6.22 times 10 to the 23rd what whatever you're looking for atoms ions people cars trees doesn't matter it's avogadro's number and it means that it has that many of something this is where we get the word mole so we write you know the word mole we abbreviate and write mol and yes we've only dropped the e we realized how ridiculous that is we're still we're still going to drop that e all the time and so are you because you're getting used to it but the mole is a number word so what do i mean by that i mean if i tell you can you pick up a dozen eggs you know you're going to pick up 12 eggs a package of 12 eggs is a dozen eggs a couple of tacos a couple means two a gross of pencils you may or may not know this one um but a gross means 144 a mole is just that it's a number word so if i tell you one mole of particles i mean 6.022 times 10 to the 23rd particles one mole of atoms is 6.022 times 10 to the 23rd atoms one mole of electrons 6.022 times 10 to the 23rd electrons and i know you figured out the pattern by now one mole of molecules is 6.022 times 10 to the 23rd molecules why do i care well you may not recognize it right here but all of these things are written as equalities what can i do as equalities i can treat equalities as conversion factors in dimensional analysis so if i told you i had 18 eggs i could say times one dozen divided by 12x i know i have 1.5 dozen eggs i'm going to do the same thing with the number of moles of something i'm going to use this as a conversion factor so counting 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 or elemental sample into the number of atoms in that sample and if i can look at the number of atoms i can talk more about what's actually happening chemically in the system why well because if i've got two atoms of hydrogen reacting with one oxygen to form one water that's piece by piece that's not weight though that's not by mass an oxygen atom weighs different than a hydrogen atom so i can't compare it by mass i need to compare by number to number so for example here looking at copper i know that one mole of copper atoms equals 6.022 times 10 to the 23rd copper atoms because this is avogadro's number so if i have one mole of anything i have 6.02 times 10 to the 23rd of that thing i also though know that one mole of copper atoms is going to equal the amu or atomic mass unit of copper because that's how what's reported on the periodic table is how many it takes to reach one mole of that species all those mass numbers written on the table account for 6.022 times 10 to the 23rd of that atom that's how it's correlated back to carbon 12. so i know one mole of carbonate are copper atoms copper cu one molar of copper atoms weighs 63.55 grams so if i have 63.55 grams of copper atoms or 63.55 grams of copper i have exactly one mole of copper 22 copper pennies contain approximately one mole of copper atoms so 22 pennies and you've got almost an about an entire mole of copper just amazing to me how much how much that is those numbers are so big for my brain uh molar mass so we we're getting more mass this entire entire chemistry career whether you stop after gen chem organic or if you're a full chemistry major and you're going out for a phd you're going to use molar mass all the time molar mass is the mass in grams of one mole of a substance specifically the average mass so the molar mass of copper is 63.55 molar meaning per mole and mass meaning mass so mass so molar mass means mass per mole so molar mass what is the mass in grams of one mole of that substance um this diagram is probably one of my absolute favorites and you should recreate this in your notes you should if you can recreate this you guys can convert between atoms ions molecules any piece back to moles back to grams the trick here is that we can never convert straight from grams to atoms straight from grams to ions are straight from grams to molecules because each species weighs a different amount it has a different number of protons neutrons and electrons in its nucleus if we convert through moles we're talking about the numbers of them we can convert through moles always so to go from grams to moles we need to divide by your atomic or molar mass to go from atoms or ions or molecules to moles we need to divide by avogadro's number moles are very moles take very big numbers and bring them down into reasonable numbers why because again one mole equals 6.022 times 10 to the 23rd a mole is a huge huge number so in order to go from grams to moles i need to divide because i need to make that number smaller in order to go from atoms ions or molecules i need to divide because that number means to get smaller on the flip side of that going from moles back to grams i need to multiply because moles is a really moles represents a really big number grams is smaller so i need to actually multiply here so i can bring this back into what is actually there in the number of grams i have so i'm going to multiply by the atomic or molar mass to go from moles to atoms ions molecules particles whatever you want you're going to multiply by avogadro's number so if you can recreate this diagram if you can remember first always no exceptions convert to moles just kind of cement that into your brain there's there is instances where you will not be converting to moles yes but a lot of the time you need to convert to moles more often than not you need to convert to moles and sometimes if you get stuck and you really don't know where to go convert to moles and you'll be back on track but when converting to moles you have to divide when converting away from moles to either grams or atoms ions molecules you must multiply now what you're dividing by or multiplying by is dependent on where you're going between grams and moles you use atomic or molar mass atomic mass meaning of a single element molar mass meaning of a molecule or a compound and between moles and atoms ions molecules you use avogadro's number so let's look at an example here how many molecules are present in 2.35 moles of molecules well i know based on avogadro's number one mole of anything is equal to 6.022 times 10 to the 23rd of that thing so here i'm going to first highlight what am i given i'm told i have 23 moles of molecules and i want to know how many molecules this is so i want to know the number of molecules i have 20 or 2.35 moles of these molecules i want to go from moles to number of molecules so in my numerator i'm going to put molecules because that's what i'm trying to get to in my denominator i'm going to have moles of molecules because that's what i'm trying to cancel out so i need to arrange this in its inequality in its ratio here to appropriately cancel what i need i'm going to write 6.022 times 10 to the 23rd molecules divided by one mole of molecules if i do this my moles of molecules will cancel and i'll be left with molecules be careful entering this into your calculator uh most calculators you're going to put 6.022 ee 23. um if your calculator is different i'm not sure that's just how i know most work but please be careful putting this in your calculator you should find the answer to be 1.42 times 10 to the 24th molecules why did i keep three sig figs here well here i have four sig figs here i have three sig figs so i'm going to round my final answer to three significant figures another example how many moles of atoms are present in 9.5 times 10 to the 15th atoms okay so what do i want to know i want to know how many moles i'm told i have 9.5 times 10 to the 15th atoms so i'm going to write down what i want to know first is number of moles and in this case i'm looking at atoms it's always good to write down what you're actually looking for there because right now we're looking for one thing specifically yes but in future chapters we're going to be calculating moles of multiple species and so it's better to identify what that moles is of so that you don't mix up what you're doing i know i have 9.5 times 10 to the 15th atoms and i want to get to moles so i'm going to put moles of atoms in my numerator because that's what i want to get to and number of atoms or just atoms in my denominator because that's what i'm trying to cancel out i know one mole of atoms is equal to 6.022 times 10 to the 23rd atoms that cancels out my atoms and here i find the answer to be 1.6 times 10 to the minus eighth moles of atoms four sig figs here two sig figs here another thing you want to start doing is being able to kind of check yourself and say does my answer make sense does this answer actually make logical sense to me and when these numbers are so big it's really hard to do that and i understand that but i still want you to think about it what i want you to think about in this first example here i've got 2.35 moles of a species i know one mole is 6.02 times 10 to the 23rd my final answer is definitely bigger than that now does it look like it's 2.35 times bigger than that well these numbers are so big i can't tell to be honest with you but i know it's bigger and so therefore i'm probably on the right track here i want to know in the second example how many moles i'm starting with less than the number of atoms it takes to make up one mole and i see that my number is in fact pretty small and um it's pretty small and it's less than one mole this is a one i don't remember if i specified that or not there is a one right here though one point six didn't look like a one um it's less than one mole and that makes sense because i started with less than a mole of atoms so it's always good to try to check yourself some examples will be easier to mentally check but always kind of mentally check yourself and say does this answer make sense to me because we all make mistakes i make mistakes but then i go back and look at it i'm like oh what what that's not right and like because i'm mentally checking myself and i know that comes with practice but the more practice you do the more problems you're comfortable with the better you'll be able to check yourself and catch yourself so you don't make those mistakes when it comes to an assessment okay let's work another example an aluminum sphere contains 8.55 times 10 to the 22nd aluminum atoms what is the radius of the sphere in centimeters the density of aluminum is 2.7 grams per centimeter cubed so now i gotta remember sphere what is the sphere the volume of a sphere is four thirds pi r cubed why do i want volume well because i got density here density is grams per um is mass over volume and so i'm probably gonna have to get volume at some point let's see what do i want here i know that this aluminum sphere contains 8.55 times 10 to the 22nd aluminum atoms i want to know the radius of that sphere in centimeters and i know that the density of aluminum is 2.7 grams per centimeter cubed so i've got density i know i'm looking for radius i'm probably going to need the volume first thing i want to do though is figure out if i have this many aluminum atoms how much does that weigh i want to know the number of grams of aluminum i have why because if i can figure out the grams of aluminum i can use density to convert back to volume once i get volume i can convert back to radius so number grams of aluminum if i have 8.55 times 10 to the 22nd aluminum atoms i've got atoms i want to get to grams i have to convert through moles there is no direct conversion from atoms to grams of any species you must must without exception convert through moles so i'm going to say times 1 mole of aluminum atoms and divide that by avogadro's number 6.022 times 10 to the 23rd aluminum atoms if i check right now this cancels out my aluminum atoms and i have moles of aluminum atoms which is excellent i'm halfway there i really want how many grams does this contain though so i can use that density the other conversion we haven't done an example with yet but i saw on that table i could convert between grams of a species and moles using the atomic mass i get this mass from the periodic table and we will talk about this we'll do more examples with this as well but what i find is that one mole of aluminum equals 26.98 grams of aluminum so i'm gonna say 26.98 grams of aluminum divided by one mole of aluminum why did i put it in that order well first i need to cancel out my moles of aluminum atoms secondly i really need grams of aluminum so i need this in my numerator calculate this out and you should get a value of 3.83 grams of aluminum now i have grams of aluminum fantastic now i can use the density to figure out the volume so this was step one find the mass step two is determine the volume of that based on that mass and then step three is determine radius so let's go ahead and work on step two i know density is equal to mass over volume and it can be used as a conversion factor i've got the density though and i've got the mass i need the volume so i'm gonna say volume is equal to mass over density this equals 3.83 grams of aluminum and you can either just divide right here by density or you can write out by dimensional analysis i don't care either way times one centimeter cubed divided by 2.70 grams of aluminum note this cancels out my grams aluminum gives me centimeters cubed i'm going to leave it in centimeters cubed i'm not going to convert this over to milliliters because i don't need to um remember one centimeter cubed equals one milliliter i don't need it that way though i need centimeters so i can figure out the radius here of the sphere in centimeters so this is perfect the unit's exactly that i want eventually i find this to be 1.42 centimeters cubed so the volume that can be made of aluminum sphere from eight point five five times ten to twenty second aluminum atoms has a volume of one point four two centimeters cubed let's go ahead and plug that in and solve for r one point four two centimeters cubed is equal to four thirds pi r cubed to solve for r i'm going to take the cubed root of 1.42 centimeters cubed times 3 divided by 4 pi and that is cubed root to enter cube root in your calculator please make sure you can do that correctly normally you can put something in parentheses and then put raise this most of the time to raise you put the little triangle symbol raise this to one third that's the same as taking the cubed root unless you have a cube root button on your calculator some people do some people don't r here though we find the radius here to be point six nine seven centimeters cubed so a lot of work to get there highlight this in a different color a lot of work to get there but we have all the resources we have all the tools now to figure out what is the radius of the sphere in centimeters if i have an aluminum sphere that contains 8.55 times 10 of the 20 second aluminum atoms and i tell you that the density is 2.7 grams per centimeter cubed we've got everything we need so the mole the mole again relates to mass one mole of carbon equals 12.01 grams of carbon why do i know this well if i look at the periodic table i've got carbon it's gonna have a six up here which is its atomic number let me put these in different colors you guys a six up here which is the atomic number it's going to say 12.01 or possibly one one this is the minimum you will see on the table this tells me that it has six protons and that its atomic mass is 12.011 that means 12.011 amu it also means that 12.011 grams is exactly equal to one mole which i can use as the conversion factor i can say 12.01 grams to one mole or one mole to 12.01 grams that is what you will find on the table though what if i wanted to find it for water water is h2o it's comprised of hydrogen and oxygen cy would look up hydrogen and oxygen on my table so hydrogen and oxygen hydrogen is going to have a 1 for atomic number up here and the um atomic mass 1.008 oxygen will say 8 and will be 15.999 what i see though is water has two hydrogens and one oxygen in it so i need to take the values of 1.008 and multiply that by two and add that to the value of oxygen times one what do i mean by that i mean two times 1.008 grams per mole is how we write it plus 1 times 15.999 grams per mole equals 18 point i didn't actually write it all that far let's see 18.020 grams per mole normally i memorize oxygen at 16.00 and i choose that value um so one mole of water is equal to 18.020 grams per mole or grams sorry i'm so easy as atomic mass grams of water if i looked up for one mole of aluminum phosphate you do not know naming yet i know that you guys are getting naming in the very next chapter but what i see here erase this for some space let me erase the wrong thing what i see here is i have two aluminums so i need two aluminum this three is distributed through so i have three phosphates and i've got four oxygens down here but multiplied by three i've got 12 oxygens so this means two times 26.98 grams per mole for aluminum three times 30.97 grams per mole for phosphorus and 12 times again 16.00 grams per moles how you're most often report oxygen you'll find the table says 15.999 16.00 is fine these are the values i'm going to find off the table though if i look up the value for aluminum i'm going to see it has a mass of 26.98 phosphorus is 30.97 and oxygen is 16.00 i'm going to add all these up so 2 times 26.98 plus 3 times 30.97 plus 12 times 16. when i add all of this up i find the molar mass of aluminum phosphate to be 338.9 grams of aluminum phosphate again what do these things mean this means if i have exactly 12.01 grams of carbon i have exactly one mole of carbon which means i have exactly 6.022 times 10 to the 23rd carbon atoms if i have 18.02 grams of water that means i have one mole of water which means i have 6.022 times 10 to the 23rd water molecules and if i have 338.9 grams of aluminum phosphate that means i have exactly one mole of aluminum phosphate which means i have 6.022 times 10 to the 23rd aluminum phosphate compounds