this video is on Charles Bo's and Gayu saaks law so in all the different gas laws that we are going to look at they all involve in one way or another pressure volume temperature and moles and we're going to look at the different mathematical relationships between these four variables sometimes they will be directly proportional meaning as one goes up the other will go up and sometimes they will be inversely proportional which means means as one goes up the other will go down as you can see here Bo's law has to do with pressure and volume and it says that they are inversely proportional so again that means that as you apply pressure to something the volume will decrease you can think of a syringe when you're thinking of this as when you're pressing the syringe down the volume inside the syringe is decreasing Charles law talks about volume and temperature and it says that they are directly proportional this means that as the temperature goes up the volume will go up you can think of a hot air balloon as your example for this that as you increase the flame in the hot air balloon as you increase the temperature the balloon expands and gets bigger and that is Charles law and the third law here Gayu saak law talks about pressure and temperature being directly proportional similar to Charles law being directly proportional um with pressure and temperature you can think of any aerosol can that as a temperature if the temperature increased in that can the pressure would be increasing too and that would lead to it blowing up um important here is that your temperature has to be in Kelvin and that is the same thing for Charles law anytime you are given temperature you must convert it to Kelvin and as a refresher to do that you take your Celsius and add 273.15 so boils law here is the formula you need to know and that is P1 V1 equal P2 V2 P stands for pressure and v stand for volume the ones and the twos stand for initial and final so sometime you will see this formula written for p initial volume initial equals P final volume final or the ones and twos mean the same thing it does not matter what we're doing with these formulas we will be given three of the four variables notice we have four unknowns here so we'll be given three and we're just going to plug them in and solve for the fourth one using algebra so the first example here says a helium balloon with a volume of 1.1 l and a pressure of .91 atmospheres expands to 3.1 L after being taken into the mountains what is the new pressure assuming no change in temperature and no gas has escaped so I like seeing what we have right now so it says we have a volume of 1.1 so that is a V1 I see I have a pressure here of 0.91 that is a P1 and it says it expands to this volume that is my V2 and it's asking for the new pressure so that's P2 so we know this is Bo's law because it's the notes and it's right after the slide but when all these laws are mixed you want to label everything and see okay I have two PS and two v's that means I'm using Bo's law so I'm just going to rewrite the law here and now I'm just going to plug stuff in so my P1 is 0.91 1 atm my V1 is 1.1 L my P2 is like my X in my algebra equation I don't know what that is and my V2 is 3.1 L and now just with math I'm going to multiply the left side together get those and what I'll do is I'll end up dividing both sides by 3.1 L and you can do this ahead of time do it as one big step that'll work too just watch your significant figures the other thing you want to make sure of is that your units are the same so like volume here we have lader lader so we're left with atmospheres so that's just something else if you had different units you'd have to convert them to make sure that this they're the same so when I do this in my calculator I get 0.32 ATM here you can see the human body with the lungs expanding and Contracting so when the air is inhaled here coming through here your lungs are getting bigger and then when you're when you're exhaling here they're Contracting the pressure gauge on a patient's full .7 L oxygen cylinder reads 8.5 ATMs at constant temperature how many liters of oxygen can the patient's tank deliver at a pressure of 092 ATM so again I'm just going to go through and start labeling stuff so this is my V1 and I know that because my unit liters 8.5 ATM is my P1 the question is asking how many liters so that is my V2 I don't know that and then this is my P2 so it looks like I'm using boils law again so I'm going to rewrite my equation and start plugging stuff in notice my pressure is an ATM both times so I don't have to worry about converting anything there and I'm just dividing both sides by 092 M my V2 equals 84 L another check you can have here we know that boils law is inversely proportional so look what's happening to the pressure the pressure is going from 8.5 to .92 so the pressure is going down which means the volume should go up and look what happened with the volume we started with 10.7 and we ended with 84 and you can always check that in these problems if we go back to the other one look what happened to the volume the volume went up so the pressure should go down and it went from 0.91 to 32 so that's a nice check that we have the next law is called Charles law here is your formula for Charles law so we have two fractions here looks like a proportion and we have V1 over T1 equal V2 over T2 the ones and the twos mean the same thing for final and initial the v's are your volume still and your t's are your temperatures so again we want to be very careful here that our temperature is in kelvin that is key we're really going to set this problem up the same way we're going to label what we have and then go from there so it says a 19.5 ler sample of Neon right there is my volume is cooled from 76 to 38° C so 76 would be my T1 and I know I need to change that to Kelvin I would do that right away so you do not forget 349 Kelvin and my T2 is 38° C and that's 31 Kelvin what is the volume so it's asking for my V2 so I know I'm working with Charles law and and then you're going to plug stuff in carefully now algebraically here with boila we divided both sides by a number here we are going to multiply both sides by 311 and when we do that our V2 will be 17.4 lers the nice check that we have here Charles law volume and temperature are directly proportional so what happens to one happens to the other our temperature went down our volume should also go down which it did Gayo sax law your formula for Gayo sax law is P1 over t1al P2 over V over T2 P stands for pressure here everything else is the same remember to put your temperature in Kelvin this is treated exactly the same as Charles law algebraically the only difference is you have pressure instead of volume before leaving your tire pressure is 35.2 PSI that is my by P1 the temperature is 25° C so I'm going to change that right away and I get 298 Kelvin I have to watch my significant figures here I should have one decimal point to the right since I'm adding so 298 point that' be two 298.15 so 298.2 yep after driving the tire pressure is 36.5 PSI so that is my P2 what is the new temperature so T1 we are looking for T2 and again we're going to be multiplying both sides by the denominator and our T2 equals 30916 Kelvin or 36° C so that is gay X law