you are so incredibly lucky today is the day your life changes forever because today is the day you meet the mole the secrets of the entire universe are about to be [Music] unblocked what is the mole well the mole provides a conversion factor between number of atoms and mass up till now we've had a really awkward unit that we've used to discuss the mass of atoms for example if I wanted to talk about the mass of one atom of carbon I would have to say that I had a mass of 12.011 01 1 am a mu are atomic mass units well you won't walk into the lab and find any atomic mass units anywhere what we need is we need a way of relating a number of atoms to grams and that's what the mole provides us now there is in reality a big issue with what I'm telling you and a quick performing of the math um by you if you if you go to Google you'll discover that there is a a couple um a small error in the statements I'm about to make but not one important enough for us to worry about conceptually so now that I've gotten the disclaimer out of the way let's take a look approximately 6.022 * 10 the 23rd protons has a mass of 1 g approximately 6.022 * 10 23rd protons has a mass of 1 g well protons and neutrons have the same mass so 6.022 022 * 10 23rd neutrons would also have a mass of approximately 1 g well the carbon 12 isotope has a mass of 12 amu we're talking about the specific isotope here well the carbon 12 isotope would have six protons and six neutrons how did I get my six protons i went to my periodic table remember carbon is element number six it's block on the periodic table looks like that how many g of protons does 6.022 * 10 23rd carbon 12 atoms have well 6.022 22 * 10 23rd carbon 12 atoms would have 6 * 6.022 * 10 23rd protons and if every time we have this many protons it's 1 g then we would have six g of protons my carbon 12 atom if I have 6.022 * 10 23rd carbon 12 atoms then I would have 6.022 * 10 23rd neutrons* 6 neutrons for an atom and we said that whenever I have this many neutrons I have 1 g so I would have 6 g of neutrons well if protons and neutrons are the only source of mass in my atom then 6 + 6 is 12 g so 6.022 * 10 23rd carbon 12 atoms would have a mass of 12 g so that means if I have a mass of 1 atom of carbon of 12 amu and if I have 6.022 * 10 23rd carbon atoms it's 12 g then 6.022 * 10 23rd is my conversion factor between a number of particles and its mass in grams now 6.022 * 10 the 23rd is a huge mouthful to say all the time we say it too much we begin to sound like Moleman everybody write down Moleman the Fantastic Four villain we're all familiar with named numbers we all know that if I tell you you have a dozen then you know that I have 12 well rather than have to say 6.022 022 * 10 23rd we gave it a cute adorable name we called it a mole m O L E just like that small animal that has been wreaking havoc in my garden a mole of carbon atoms would contain 6.022* 022 * 10 23rd carbon atoms a dozen carbon atoms would be 12 carbon atoms right so a mole of carbon atoms is 6.022 * 10 23rd carbon atoms if I told you you had a If I told you you had a dozen hammers you would tell me that you had 12 hammers everybody write down Thor i said hammer after all all right if I had a dozen hammers I'd have 12 hammers well if I had a mole of hammers I would have 6.022 * 10 23rd hammers a mole is simply a named number and that number is 6.022 * 10 23rd what makes it special is that anytime I have a mole of atoms I can read the mass off the periodic table in grams if I look at that periodic table block for carbon it's matter of fact I'll scroll down to my periodic chart here i hope I'm not making people seasick as we scroll through to the very last page periodic chart right there's carbon what the mole lets me do is it lets me read the atomic mass in units of grams i have one mole of carbon so its mass is 12.01 g of carbon up till now all I've been able to use my periodic table to say is one atom of carbon is 12.01 01 amu so by having a mole I can read my masses off my periodic table in grams for example one atom of magnesium has a mass of 24.31 amu one mole of magnesium however would have 24.31 gram of magnesium and how many atoms of magnesium would be in that one mole of magnesium that one mole of magnesium would contain 6.022* 10 23rd atoms of magnesium i want to make sure this horse is thoroughly dead because this is super important it provides we have learned a conversion factor now between a number of atoms and moles right because I just said that one mole of magnesium is 24.3 g and 6.02 * 10 23rd atoms let's choose another element let's go with cadmium right there cadmium if I have If I have That's not going to show up just a second if I have one Oh that's not helping any If I have one atom of cadmium I have a mass of 112.4 amu however if I have one mole of cadmium I have 112.4 g of cadmium and 6.022 * 10 23rd atoms of cadmium this conversion factor given to me by my periodic chart is now going to let me solve all sorts of problems whoa what did I do here i'm apparently trying really hard to crash my computer know who likes to crash things the Fantastic Four villains the Frightful Four everybody write down the frightful four so a mole of carbon atoms would have a mass of 12.011 g of carbon that's given to me by periodic table if I have two moles of carbon how many carbon atoms would I have we treat moles like a conversion factor we know that 12.011 g of carbon is one mole of carbon we also know that one mole of carbon is always by definition of a mole 6.022 022 * 10 23rd atoms of carbon so if I have two moles of carbon I'm going to place moles where they cancel out and I know that 1 mole of carbon is 6.022 * 10 23rd atoms of carbon i now have canceled out my units of moles multiply everything on top divide through by everything on the bottom and I wind up with 1.20 or* 10 24th atoms of carbon now my two moles of carbon would have what mass of carbon well we know thanks to our periodic table that one mole of carbon is 12.011 g of carbon so if I have 2 moles of carbon I'm going to place moles where they cancel out place my grams on top and that gives me 24.022 g of carbon we can go the other direction with it right conversion factors are always a two-way street so if I have 36 g of carbon how many moles of carbon do I have well I'm going to place my 36 g of carbon in my starting position i'm going to place grams where they cancel out i know that one mole of carbon has a mass of 12.011 g of carbon so I'm going to place moles where I'll have them one mole 12.01 011 g my grams have canceled out i'm left with units of moles multiply everything on top divide through by everything on the bottom and I wind up with 3.0 moles of carbon i can take it a step further how many atoms of carbon would be in that 36 g of carbon so I'm going to start off with 36 g of carbon don't want grams of carbon so I'm going to place my grams of carbon down here where they cancel out the only thing I know about grams ever from this point forward whenever you see grams in chemistry class your first gut instinct should be to convert to moles i always know the relationship between moles and grams thanks to my periodic table one mole of carbon is 12.011 g of carbon so place my grams where they cancel out i'm left with moles so I've got 12.0 111 g of carbon per one mole of carbon now I've gone from units of grams of carbons to units of moles of carbon but that's not what my problem is asking for it wants a number of carbon atoms so I'm going to place my moles down here where they cancel out and I know the relationship between moles and anything by definition one mole of anything is 6.022 * 10 23rd so one mole of carbon atoms is 6.022 * 10 23rd carbon atoms hey atoms of carbon is what I'm looking for so I'm going to multiply everything on top divide through by everything on the bottom and I wind up with 1.8 * 10 24th atoms of carbon chemistry is easy life is hard after all you're not trying to fight the Beyonder everybody write down the Beyonder the molar mass of a substance is the mass of one mole of the substance so I've thrown out a new term for you here molar mass molar mass is the mass of one mole of a substance so the molar mass of carbon would be 12.011 g what would the molar mass of sodium be h come on answer it i know you guys are saying "Nah I don't want to answer it." Sodium nah yeah okay make sure you try the salad bar i'll be here all week so we come back down we find sodium there's sodium on our periodic chart one mole of sodium has that number right there in grams as its mass so the molar mass of sodium would be 22.99 g of sodium let's keep on going here now what we've already established is that the mole is a conversion factor essentially if we look at what we used on our examples we use the ratio of moles to mass we also use the relationship of moles to number in other words we use the very definition of a mole as a conversion factor and we can use these conversion factors to answer all sorts of questions for example how many moles of lithium in 14.2 two grams of lithium the first thing I'm going to have to do is I'm going to have to run to my periodic table and find the molar mass of lithium so I run to my periodic table here i find lithium there's lithium and I discover that one mole of lithium has a mass of 6.94 g 6.94 g so I come back up here and I know that one mole of lithium is 6.94 g of lithium according to my periodic table how many moles of lithium in 14.2 g of lithium so I'm going to treat these problems just like I did the unit conversions that we were doing the other day so I've got 14.2 g of lithium to start my ratio chain with whatever unit I have here I'm going to place down there since I'm starting with grams of lithium I'm going to have grams of lithium down here where they cancel out well the only thing you ever know about grams going forward is the relationship to moles we know that one mole of lithium according to our periodic table has a mass of 6.94 g so now I've gone from grams of lithium to moles of lithium which is what I'm being asked to do so multiply everything on top divide through by everything on the bottom and you get 2.046 moles of lithium how many atoms of lithium would be in that 14.2 g of lithium same process start our line 14.2 g of lithium whatever unit you start with you need to get rid of so since I'm starting with grams of lithium I'm going to get rid of grams of lithium the only thing I know about grams ever is the relationship to moles one mole of lithium is 6.94 g so I've canceled out my grams so I've gone from grams of lithium to moles of lithium i don't want moles of lithium so I'm going to have to get rid of them so whatever unit I have here I cancel it out by placing it down here so moles of lithium down here where they'll cancel out do I know a relationship between moles and atoms yes by definition of the mole one mole of anything is 6.022 222 * 10 23rd of it so 1 mole of lithium atoms would be 6.022 * 10 23rd atoms of lithium hey I now have atoms of lithium which is the unit I'm looking for so I'm going to multiply everything on top divide through everything on the bottom and I discover that this whole stuff of working with moles is as easy as one two three that's right i worked really hard to manipulate my numbers there for you