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# Thermodynamics part 4: Moles and the ideal gas law

## Video transcript

before I continue I want to introduce you to what might be an unfamiliar concept although if you've taken chemistry you might know a little bit about it it's called a mole and this isn't the thing that grows on on your face with a hair in it or the animal that dig did in your backyard although those are also called moles but we're talking about the SI unit called a mole and a mole is just a number it's like saying you know mole of something means a certain number of something just like a dozen or a well I don't know what other things are there in our numbers but it's like saying you know a dozen eggs is 12 eggs right a dozen equals 12 well just like that a mole a mole of eggs would be six I always forget the exact number it's six point oh two three I think something of that of that nature six point you can look it up I I think it's six point oh two three times ten to the twenty the right the exact number just because I think I'm at that 23 M I miss misremembering let's see this it the mole I'm on Wikipedia now and I'm I just looked up the mole okay there you go on Wikipedia see it's very easy oh yeah I was close its 6.022 6.022 times 10 to 23 of something so it's a very it's a very large number of something so normally we don't deal in moles of eggs I don't think there have been a mole of eggs ever produced in the history of universe 10 to the 23 is a very very very large number so where is it useful well a mole is useful for counting atoms and and so what what is a mole of atoms well it's that it's that or molecules what's that many molecules it's six followed by roughly 23 zeroes of molecules very very big number but what's interesting about a mole is that when I have a mole of something its mass so let's say it's its mass in grams so let's say a mole mole of carbon it's mass and grams is going to be equal to so mass and so mole of carbon if I have a mole so if I have this many carbon molecules its mass and grams it'll have X grams it'll it'll have a mass of X grams where X is the atomic mass number atomic mass of of a atom of carbon although if I was saying about a mole of them all molecule I would figure out the atomic mass of the entire molecule so what's an atomic mass number let me see if I can if I can do a web search on a on a periodic table so yeah I'm showing you what I do here I don't know it's not fancy so let me do let me go to Google Google com and let's look up periodic table let's see if we can find a good one periodic table this one looks good let's see what I can do is sometimes it up oh no looks like everything is freezing up - oh there you go so periodic table of elements good let's see what we can do so if we go to carbon which is right here we see that it's it's atomic number 6 and that's the number of protons it has but let's see if I can zoom in on carbon what happens periodic table oh there you go that's pretty neat so the atomic mass number it's the mass of the entire atom and just so you know I mean we're kind of delving into a little bit of chemistry here but most of the mass of an atom is the protons and the neutrons and the neutrons and the protons weigh roughly the same thing and then the electrons are much much much smaller so if you if you pretty much factor in the mass of the protons and the neutrons you pretty much have the mass of the particle and then just another a little more chemistry here is that although on average most of the most of the atoms have roughly the same number the neutrons some don't some you know you could have a carbon atom that has you know seven neutrons you could have another one that has five another one with six so and those are actually all called isotopes and I won't go into all of that but they're just the same atom with different numbers of neutrons but in general the atomic mass number just if you had a kind of a broad rule of thumb is is equal to sorry the atomic mass is equal to the mass of the protons and the neutrons and they tend to be equal so if the atomic number is six the mass 10 the atomic mass tends to be 12 so why is this useful so we can say if we have I don't know what is this gallium if I have a mole of gallium right I mean actually let me you can let's say niobium let's say I have a mole of niobium if we look here on this on the periodic table it has an atomic mass number of 41 and then it's average atomic mass if we were to average all of the isotopes or kind of how you know based on the weighting of how they exist in nature it's 92.9 so roughly 93 so it's actually a little bit more than double its atomic number but let's say it's a 92 point let's let's say 93 so if we had a mole of niobium if we had 6.022 times 10 to the 23 of niobium we it would weigh it would not weigh it would have a mass of 92 grams so that's pretty easy and you look at any element molybdenum the matte you know we see here oh whoops let's say chromium we see it's atomic mass number is roughly 52 we see that there so if I have a mole of it if I have 6 times 10 roughly 6 times 10 to the 23 of it that much will have a mass of 52 grams so that's how we think about a mole so if I tell you I have a mole of something I'm also telling you how many of that a molecule I have on the and I'm also telling you how what the mass of that mole of that mold that quantity will be if assuming that you have a periodic table in front of you so with that said with that out of the way let's do some let's make some more progress with our thermodynamics invert colors so we said in the last several videos let me see when I'm running out of time now I have plenty of time that pressure times volume pressure times volume is somehow proportional it's somehow proportional I'm you know let's call that K and this is an arbitrary number it's not some special constant to the total kinetic energy kinetic energy total of a system total and we also said that that is equal that that is roughly proportional you know that's some constant that's another constant times the number of objects or we've you this kinetic energy per molecule right so in general we could also say that you know this is proportional of this which is proportional this that pressure times volume is equal to is proportional and we'll use our because you'll see where that's that's coming from in a second it's it's proportional it's equal to some constant times the number of molecules N and when I write small n here see here I just saying the absolute numbers I've had five molecules I've put a five here but now this n I'm counting in moles right so if I say I have if this n is 1 that means I have six 6.022 times 10 to the 23 molecules so let me see 1 mole equals 6.022 times 10 to the 23 right so I'm just saying so this is just another way to write the number of molecules and then that's times temperature and then if we rearrange it PV equals NRT we have a relationship that if I know the pressure and the volume and the number of molecules I can figure out the temperature or if I know the number of molecules the temperature and the pressure I can figure out the volume assuming assuming I know what R is and I'm about to tell you what that is R is called the universal gas constant and it is R is 8.31 fools joules per joules per mole Kelvin and that kind of tells you what you need in this in this in this formula this should end up being joules right so if you have this if you have pressure in Pascal's and you have volume in meters cubed you'll end up with joules there this should be in moles moles this is eight point three one joules per mole Kelvin and then this as we always said should be in Kelvin and honestly if you if you just memorize two things in all of thermodynamics you'll probably be able to do 95% of problems but you actually should have the intuition of how they work but just remember that P over P V over T is equal to a constant or that if you change them they relate to each other that you know they all equal a constants of p1 times v1 divided by t1 is equal to p2 times v2 divided by t2 and then you and then you also just need to memorize PV is equal to n RT where R is equal to 8.31 joules per mole Kelvin and I know you might not have a lot of intuition of this formula yet because I haven't used it but I'm going to do that in the next video but these are these are literally the two most important things you should know in thermodynamics and hopefully you have a little intuition at this point of what they mean see you soon