the ideal gas law there's actually many gas laws we're going to focus on the ideal gas law and we're going to talk about some of the other ones and how they're derived from the ideal gas law um but the one that you're going to use for most of your calculations is ideal gas law this is the ideal gas law pv equals nrt you'll hear it referred to a lot as pevnert basically if you just you know pronounce all the letters pevner pv equals nrt um but it is it's the law we use for gases that behave ideally now ideal is not like a it's it's sort of like most gases don't behave ideally really no gas behaves ideally but a lot of cases get very close to behaving ideally so it's our ideal gas law and again we use it for all gases the only time we couldn't use it is at um high extremely high pressures or extremely low temperatures then the ideal gas law starts to break down we won't experience these in regular chem you should just know that that's when the ideal gas loss starts to break down so p is pressure v is volume n is the number of moles those are all the variables r is the ideal gas law constant and then t is temperature so what is the value of r well we know that at stp at standard temperature and pressure that one mole of gas equals 22.4 liters um so if you rearrange the ideal gas law equation to solve for r this is what we get r equals pv over nt so again that was just rearranging this law if i solve for r i'm going to divide both sides by nt that gives me pv over nt so that's what you see here so if um i did r at stp like i calculated at stp i would put in my one atm for the pressure by 22.4 liters because that's what one mole of gas is at stp again that's one mole of gas so for in the denominator we do the one mole and then 273 kelvin that's zero degrees celsius which is standard temperature but converted to kelvin is 273. so this is our ideal gas law constant we are going to use this so much that you should memorize it so 0.08206 atms times liters over moles times kelvin all of your units need to be converted to atms liters moles and kelvin so if i gave you a different pressure we learned all the pressure units so let's say i gave you kpa instead of atm you would have to convert to atm before doing your ideal gas law conver your ideal gas law equation if i gave you milliliters you would have to convert to liters if i gave you something other than moles for example grams that will happen a lot where you're given grams instead of moles and you first have to convert to moles you are almost exclusively always given temperature in degrees celsius and you have to convert to kelvin by adding 273. so here's an example equation how many grams of methanol can be produced from 3.50 liters so i'm not going to have to convert that i'm just going to be able to plug it in of hydrogen gas at 575 psi i know i can't convert in psi so i have to use my conversion which is here the one atm equals 14.7 psi and 55 degrees celsius again i know i'm not going to be able to use celsius i'm going to have to convert to kelvin by adding 273. so here's my equation down below it says how many grams well grams isn't part of our pv equals nrt but we know that we can convert moles to grams so rearranging the equation um pv equals nrt if i just go back here to solve for n right that means i'm going to divide both sides by rt so pv over rt will equal n so that's what you see here n equals pv over rt and then i plugged in everything so pv gets plugged in with the um the conversion that we did for the the pressure so we had the 575 we converted it to 39.12 atm and that's what gets plugged in is the atm the 3.50 liters we didn't have to do anything from that that just came straight from the problem our constant which again was on that last slide but we memorized it and then we converted our celsius to kelvin by adding 273 so a way to check that you make sure you've done this correctly is everything should cancel with those r units so i have a liter in the numerator and in the denominator so they cancel atm is in the numerator and in the denominator so they cancel and then here in this bottom part i have um kelvin in like the numerator of my denominator and in the denominator of my denominator so those two will cancel leaving moles at the very bottom but because this is a fraction that actually swings moles up to the numerator so that would give us our answer in moles and then we would have to do a moles to gram conversion using molar mass to find the actual mass from the ideal gas law we can derive avogadro's law boyle's charles gelusak and combined gas law so these are the individual laws so for boyle's law we would start with the ideal gas law and then boyle's law keeps temperature and moles constant so here's the pv equals nrt if moles which is n and temperature which is t is constant r is already a constant so that means pv is the only thing changing then our formula is p p1 v1 equals p2 v2 um showing that those are two different gases so charles law kind of operates the same way um v and t are the only ones changing because pressure and moles are constant so rearranging the equation that's v over t equals v2 over t2 again with two different gases galoo socks is pressure and temperature are the only things that are changing so p1 over t1 again putting them on the same side of the equation avogadro is just volume and moles and then combined is pressure volume and temperature again these are all derived from the ideal gas law equation if you just um like the ones that the variables that are constant if you like take those out of the equation and then rearrange to put everything on the same side of the equal sign that you can get to all of these five uh people i guess combined is not really a people but all of those laws all those five laws so this is just a little picture that i found that i thought was helpful so pv equals nrt so if i was going to do boyle's law which is up here in the corner this p1 v1 equals p2v2 so nr and t are all constant which means pv equals a constant some constant k let's just say so if i have one gas that equals constant k and i have a second gas that equals constant k i can therefore say that that first gas equals that second gas since they equal the same thing um and that's where i get the law p1 v1 so that's the first gas equals p2v2 that's that's it's not really actually a second gas it's just the gas at a second um second like second values so it's like it's like if i had oxygen gas and the first pressure was one atm and one liter and then mice equals my second pressure it would still be that oxygen gas but we would now be at like maybe two atms and then looking for a new volume um so that's what these mean one and two it's it's more like it's not it's not actually a different gas it's the same gas but at a different in different circumstances there we go um i actually found this picture really helpful too because it includes like which ones are constant i really liked that but it only shows boyle's charles and gabe and combined it doesn't show you gala soccer in uh and avogadro but um you do need to know all five you uh more likely won't be ex like asked to do calculations for all five i just really would like you guys to know um the name of the law what the law is which variable variables are being held constant um in order to make that law possible