 All right, I think this may be the last video I make looking at the views on the YouTube channel Not many at all. So I'm spending a lot of time making videos that I don't think are going to be Making any headway towards improving grades or getting this any progress. So I think this is going to be it So I'm going to make one big video on the gas laws and put it up there and see how it goes There are four primary gas laws and the four primary primary gas laws relate the four major ways that we The variables from the four major ways that we measure gases to one another If you recall those are volume Pressure temperature and amount Those are the four primary ways that we measure gases the four main ways we do and what the primary gas laws do Is they take two of these four variables and examine the relationship between them how they're related how changing one of those variables would change the other The four primary gas laws are boils Charles Gay-Lusax and Avogadro's Boil's law examines the relationship between pressure and volume Charles law examines the relationship between temperature and volume Gay-Lusax law examines the relationship between temperature and pressure Well, Avogadro's law examines the relationship between volume and Amount now the relationship between the two variables that each of the laws examines are either going to be Directly proportional or inversely proportional directly proportional Means the two variables will undergo the same change In other words when one of the variables goes up the other variable will go up Inversely proportional means they undergo the opposite change When one of the variables goes up the other variable goes down The way these four gas laws work out is It for boils law. It's inversely proportional pressure and volume are inversely proportional For all the rest of the laws. They're directly proportional This allows us to make some predictions in as far as behavior of gases are concerned So let's say I have a sample of a gas and I double the volume of that gas and I want to know what happens to pressure Why no is inversely proportional if the volume if the amount and temperature are constant Doubling the volume of the gas should cut the pressure in half Inversely proportional means they have the opposite change if I have a gas And I double the temperature And I want to know what's going to happen to the pressure Provided the volume and amount are constant if I were to double the temperature for gas I would double its pressure because they are directly proportional. They change in the same way Again inversely proportional means they change in the opposite way when pressure goes up volume goes down If volume goes up pressure goes down They change in the opposite way if I double the volume I'd have the pressure If I have the pressure I double the volume they change in the opposite way four times the volume a quarter of the pressure Seven times the pressure one seventh the volume they change in the opposite way inverse Seven times bigger one over seven smaller 12 times smaller one over 12 12 times bigger and again directly proportional same way Three times the amount three times the volume One-sixth the volume one-sixth the temperature In all of these laws, whichever variables are not covered by the law have to be constant So since Avogadro's law is volume and amount the other two variables that we have to deal with Temperature and pressure have to be constant Charles law deals with temperature and volume The other two variables pressure and amount have to stay constant so for all these laws for them to work The other two variables have to be constant They all have equations associated with them and the way that equation looks depends upon the relationship that we're dealing with Whenever you have a directly proportional relationship the relationship is expressed as division So whenever you have a directly proportional relationship the equation will be division Whenever you have an inversely proportional relationship, it's the opposite and the equation will show multiplication Each equation deals with before and after scenarios So while Boyle's law is about pressure and volume with the way the equation sets up You end up with pressure and volume on both sides Starting pressure and starting volume on one side ending pressure and ending volume on the other It's the inversely proportional one, so it's all about the multiplication P1 times V1 starting pressure times the starting volume Equals P2 times V2 The ending pressure times the ending volume Charles law is about temperature and volume So we're going to have a T1 and a V1 on the left side and a T2 and a V2 on the right side But this time since the law is directly proportional, it's all about division So the way we set it up V1 over T1 Equals V2 over T2 Okay, loosex law is about temperature and pressure Again, it's directly proportional. So it's all about division We're gonna have a temperature and pressure on both sides and we set it up very similar to Charles law But instead of Vs on top, we have Ps on top like in division because that directly proportional relationship And then finally Avogadro's Volume and amount Amount is breved with N for number of moles Again, a V and an N on one side a V and an N on the other starting on this side ending on that side So that's what the equations look like now Mathematically working problems with Boyle's law. It's kind of important that you're in a routine You're in a pattern. I mean it should be easier than stoichiometry because it's all single variable algebra stuff But what really worries me a lot Are these variables and the denominators? If you had to do a Charles law problem where you had to solve for the final or the initial temperatures Very common mistake is failing to move the variable out of the denominator and solving for the inverse Not a good thing same thing with Gay-Lew sex law. I Worry about those T's on the bottom And if you have to solve for the initial temperature or the final temperature I worry that you're going to solve for the inverse of the temperature down here at some mouth I worry about you solving for the inverse of a mouth So what I suggest to do when you have a reference sheet and it has these Equations on it. I suggest you take these Three gas laws and you cross multiply them out and make them look like Boyle's law So V1 times T2 Equals V2 times T1 now. There's no variable in the denominator. Now you can't make that mistake P1 times T2 Equals P2 times T1 Again, now there's no variable in the denominator anymore. So you can't make that mistake you 1 times n1 Or in 2 Equals be 2 times n1 Again variable out of the denominator now and you can't make a mistake questions look like this gas has a temperature of 350 Kelvin as I mentioned in a prior video Kelvin is the unit We have to have for gas laws no negative numbers in there. So everything works out like they're supposed to so gas is a temperature of 350 Kelvin and The pressure 3.6 atmospheres It could be any unit for pressure and use millimeters mercury tour any of them. I Just picked atmospheres. I like it So gas has a temperature of 350 Kelvin and a pressure of 3.6 atmospheres So the gas is compressed to 9.8 atmospheres What will the temperature be? Well the first step in solving a problem like this is figuring out what it is We have to work with and sometimes there's context clues like a temperature of of 350 Kelvin I know that's a temperature Pressure of 3.6 atmospheres, I know that's a pressure. What about that one? Doesn't say pressure doesn't say temperature. What is it? The answer is right there atmospheres That's a unit of pressure. So we know we have a second pressure in this one. What we're missing is temperature The second temperature We want to find out what that's going to be Well, what will the temperature be? Now there's got to be ones and twos assigned to this and there's some context clues that you have to look for in order to Figure that out. One of the biggest ones one of the most often overlooked ones is the word two I mean how many times a day do you use that word? Have you ever really thought about what it means? Well the word to to Means where you're going Think about using it in everyday life I'm going to the gym What does that mean? That means you're going to end at the gym. That's where you're gonna end up I'm going to my mom's house Again, what does that mean? I'm going to end up at my mom's house To is where you're gonna end and this question tells us we're going to 9.8 atmospheres That's where we're gonna end. That's the number two Which means this has to be number one that must be P1 Now as far as this temperature is concerned figuring that one out There's the word and and again, how many times a day do we use the word and? Think about what it means And means things are joined together Husband and wife that are joined together. There are a couple and Means things are joined together 350 Kelvin and 3.6 atmospheres these two numbers are joined together and Since this one is a one this one also has to be a one. That's how they're joined They're both the starting ones Now sometimes there will be other context clues like the word initial or original That means starting that means one Or it'll say final Or ending that's two Let's look for those as well Now we have four equations to choose from to solve this problem picking the right one as a matter of doing this Listing things out. I see I have two T's and two P's while there's only one equation With two T's and two P's in it. It's a gay loose ax law problem And again, maybe I don't want to use that this might be the better one to use P1 times T2 equals P2 times T1 Let's see how this works out. I substitute so my P1 is 3.6 atmospheres My T2 that's my variable. That's T1 that I'm looking for T2 Equals P2. That's the 9.8 times T1 350 Now if you do that cross multiplying things all your primary gas law problems end up looking the same way One side of your equation has both numbers on it. The other one only has one You'll solve them the same way. You'll multiply those two numbers together 9.8 times 350. That's 3430 and we multiplied the atmospheres the Kelvin's of the ATM times K That's what we did to them. We multiplied them Nothing happened to this side now ready to solve Since we're multiplying by 3.6. We'll divide both sides by 3.6 here the atmospheres cancel So T2 is some number in Kelvin. That's the only unit left We take 3430 divided by 3.6 and we would get 953 Now I'm not doing significant figures with this I don't do significant figures with this because it's enough for you to learn and keep track of as it is We can look at these numbers and get an idea if we did it right Because we up here We said Gay-Lucic's law says temperature and pressure are directly proportional. I increase the pressure It went from 3.6 to 9.8. I increase the pressure so I should see an increase in temperature 350 to 953 it went up This is almost a three times increase So we should see almost a three times increase here and we do we know we did this right We don't have to worry about it We don't have to think about it anymore when we turn a problem like that in we'd be done with it As long as you do this cross multiplying thing the math for all four gas laws is the same You go through you figure out what variables you have you find the equation that matches those variables and every time with the cross Multiplication one of your side will have two numbers on it. You'll go ahead and simplify and multiply that side out The other side will only have one number on it divide by that one number and you'll have your answer very uniform way to approach it That's why I like doing it that way Now we haven't got to this yet, but I'm sick of said I'm making one big video We have the ideal gas law scientists saw all these four Gas laws and thought wouldn't it be wonderful. We had one equation that did it all And so what they did is they tried to come up with that one equation that did it all And what they came up with is this? PV equals n r T P is pressure V is volume and is amount are we haven't seen before That's something new R is something called the ideal gas constant and T is temperature that ideal gas constant attempts to take all the relationships from those four primary gas laws and Combine them into a single number For us in the way that we're doing this in class The number that we're going to use for our Is going to be so does that look it back up on my paper here? 0.0821 Laters atmosphere per mole Degree Kelvin it's got all four units in it crazy isn't it got all four units in it and again, that's because it's a tempting to Give us the relationship for all four variables in one number Well, here's the thing if you're trying to put the relationship for all four variables in one number It ain't gonna work well, and it doesn't the ideal gas law doesn't mean it's the ideal law It means you need the ideal gas you really need the perfect gas for this lot of work, right? What is the perfect gas? One ideal gas Has a temperature of 273 Kelvin and a pressure of one atmosphere STP standard temperature and pressure The gas has to be at STP for the law to work if you wander too far away from STP Then the predictions aren't very good the further away from STP you go the worse the predictions get So really the only thing you can play around with and this is volume and amount If you're gonna play one volume amount you might as well use our God who's law in the first place because that one really works So it's it's not a great law. It's not a good law It's a law for the perfect gas and if you have a perfect gas that works, okay Now because of this mess over here Pressure has to match this unit. So it has to be in atmospheres and Volume has to match that unit. It has to be in liters And a mountain has to be in moles and Temperature has to be in Kelvin like it usually does for a gas law Now all those things are perfect and all your stars align you can solve a problem like this. I Gas has a pressure That's not one or too far of 1.3 atmospheres a volume. I don't know how about 30.5 liters and A temperature That's not one or too far of 300 Kelvin. What is the amount? We're gonna try to find moles in this one So atmospheres is pressure Volume is V. That's 30.5 liters Kelvin is temperature We're looking for a mount Idol gas constants idol gas constant that never changes Well, it changes if I weren't using liters. It wouldn't be the same number if I weren't using Atmospheres, it wouldn't be the same number It would change That's all we need so we can solve for n again Pv equals n our T Pressures 1.3 Volume is 30.5 That is what we're looking for 0.0 a 21 for our R our R And our temperatures 300 First thing we're gonna do in this is some simplification. I'm gonna go ahead and multiply these two numbers together and that's 39.65 I'm gonna go ahead multiply those two numbers together and that is 24 point six three Now I'm ready to solve divide both sides by the 24 point six three Now I did not put my units in here Most because of time video is almost a half hour long already We don't need to cancel the units we know that our amount has to match whatever our amount unit was in our And that's moles. That's it. We're done There is one more law we have to do and that's Graham's law of effusion and Unfortunately, it's probably the most confusing one and Again, because I've already just gone over 25 minutes on this video and because maybe two people are gonna watch it I'm not gonna take it to 35 40 minutes. We're gonna end it right there I've almost used up a planning period doing this now again probably the last video I don't see enough people watching it to justify spending An hour a day making videos and getting them upload and stuff like that so you can search YouTube for other stuff For this point out. Good luck