in this video I'm going to talk about gases and more specifically the relationship between temperature pressure and volume of gases these relationships are expressed as gas loss and we'll talk about four different gas LW but before we discuss gas laws I want to talk about pressure unit conversions which you actually have to memorize here's the common pressure units ATM stands for atmosphere one atmosphere equals to 760 mmhg stands for millimeter mercury this is another pressure another unit for pressure that equals to 760 t t RR which is another unit for pressure which also equals to 14.69% some of these came from let's look here this is in your PowerPoint slides if you have a dish full of mercury and you insert an empty test tube in it the Mercury will go up into the test tube and at one atmosphere the level between the bottom of the dish and the top of the Mercury level will be exactly 760 mm Mercury which is the same as 7.6 CM so a little bit less than 10 cm so that's where the unit came from for millimet mercury and pound per square in PSI came from the following scenario imagine that you are at sea level and there's a column resting on your head that column extends from the top of your head to the top of the atmosphere the base of the column is a square that has dimensions of 1 in and the column is filled up with gas particles gas molecules such as carbon dioxide oxygen argon helium and so on this column exerts a certain amount of mass on your body and that's exactly 14.69% if you move into a valley or in this case a well the column is much larger there's more air particles or air molecules in it and you'll feel a higher Mass exerting exerted on your body Which is higher atmospheric pressure now let's do some examples with pressure conversions of pressure units how many Tor are in 17.3 lound per square in start you can use this uh you can solve this problem using the imal analysis so you'll start with what's given in the problem which is 17.3 PSI and then use the conversions that are given here to 760 T equals to 1469 PSI put PSI on the bottom that way we can cancel PSI and you're left with tour 895 tour and the other thing to keep in mind is whenever you have to do calculations that involve 10 temperature the temperature has to be in kelvin not Celsius not Fahrenheit but Kelvin all right now let's start with the first law boils law boils Law relates pressure and volume of a gas so in all of the laws that we're going to talk about you have a gas at initial conditions and the initial conditions are shown as the number one for example P1 and V1 is the initial pressure and initial volume of the gas and then this gas under go some kinds of uh some types of changes maybe the pressure increases or the volume decreases and P2 V2 show the final conditions of the gas after the changes have taken place Bo's law shows that as the pressure increases the volume decreases this is a reverse relationship between or inverse relationship between pressure and volume and here's a picture from your textbook that shows exactly that imagine that you have a container with a movable piston attached to the top and if the initial volume of the gas is 4 L and the pressure is 1 atmosphere and if I push the Piston down about halfway here in the middle of the container now the volume is only 2 lit so I've decreased the volume by two times and the pressure is increased two times now the pressure is two atmospheres the gas particles are much closer together they Collide a lot more often with the container with the walls of the container and that's why the pressure is increased so let's go back here to the lecture notes Let's do an example a gas occupies 1.5 L at 950 T find the new volume in milliliters if the pressure is reduced to 500 T So if you're not sure what's the volume what's the pressure look at the units the units will tell you whether you have volume or pressure the unit L stands for liter and that's volume and I recommend that you write down before you do any calculations write down what's given in the problem so so what I'll do is I'll write down P1 = to V1 = to P2 and V2 in this problem P1 is 950 T and I know that this is pressure because T is the unit for pressure and that's the initial pressure and P2 is 500 Tor so I write that down and then the initial volume is 1.5 L and the final volume is what we're looking for but we want the final volume in milliliters now remember remember that the units of the initial conditions have to be the same as the units in the final conditions so in pressure we're fine P1 and P2 both have units of Tor no need to convert here but V1 is in liters and V2 has to be in milliliters so here we have to convert L to milliliters and once you've done all your conversions now you can actually uh start solving the problem so first write the equation for Bo's law which is P1 V1 equal to P2 V2 and then solve for v2 V2 to solve for v2 you have to divide both sides of the equation by P2 so now we're isolating we're solving for v2 and V2 equal to P1 V1 / P2 plugging on the numbers for P1 V1 and P2 and you end up with the final answer pay attention to significant figures and this case let's see um if you go back to the problem V1 has three s fix P1 has three s fix and P2 has three s fix so the final answer has three significant figes okay moving on to the next law Charles law Charles law shows the relationship between volume and temperature and this is a direct relationship as the Vol as the temperature increases the temperature of the gas increases the volume also increases make sure that both T1 and two T2 are in kelvin not in Celsius or Fahrenheit they have to be in kelvin uh let's go back to your PowerPoint slides and again we have a container with a movable piston initially the gas in the container is 1 lit that's the volume of the gas and it's at temperature of 200 Kelvin if we Heat this up with a bunson burner and we allow the Piston to move freely the Piston will go up which will increase the volume now the volume will be 2 L and the temperature will be 400k or kelvin so both the temperature and the volume are doubled here's another example if we attach a rubber glove to uh this glass F which is called Florence flask and we heat it up with a buns and burner the air inside the flask heats up it expands and the glove gets filled up with air let's do the following example a gas occupies 3.5 4 microl at 17.3 Cel if the temperature is raised to 3.3 Kelvin find the new volume in kiloliters here you have to do a lot of conversions let's write down what's given V1 where's V1 V1 it's right here microl lers that's the initial volume but we want the new volume in Kil so we have to convert microl to kilol and here's that conversion and then we have T1 T1 is 17.3 celi but remember that the temperature always has to be in kelvin so we'll convert that to Kelvin we have T2 which is already in kelvin no need to convert it and we're looking for v2 in kilol so we've done all our conversions here now we can solve for v2 start by writing the formula for Charles law V1 over t1al to V2 over T2 we're solving for v2 to find V2 you need to multiply both sides of the equation by T2 so here I'm putting one T2 and here's the other T2 I can cross I can cancel T2 on the right hand side of the equation and now V2 equals to T2 V1 / T1 I plug in all the numbers here all the measurements that I get from from my previously uh done conversions so let's see what what do I have T2 is 3.3 V1 is is right here 3.54 * 109 and V1 is yeah there you go and then we have the temperature exactly T1 is 290 significant figures also three significant figures and the final volume is in kilol the third law is gak's Law and that's a relationship between pressure and temperature as the temperature increases the pressure also increases this is another direct relationship there's a picture in your textbook that I can show you um this is a container that has a piston that's actually stationary it cannot move so imagine that you have a tank full of gas a solid tank and the temperature initially is 200 Kelvin at 1 atmosphere if you heat it up the temperature is now 400 and the pressure is two atmospheres so both double another example of guox law a gas at 800 T and 299 Kelvin is cooled to 175 Kelvin Find P2 in PSI so really the only conversion we have to do is the pressure we need to convert Tor to psi and the temperatures are already in kelvin solve for P2 what we need to do is multiply both sides of the equation by T two and then plug in the numbers and you get the pressure in PSI and then the last law that you need to know is the combined gas law so what I recommend is that you memorize just the combined gas law once you memorize this combined gas law you can derive the other three laws By ignoring one of the variables for example if I ignore T1 and T2 imagine the T1 and T2 were not part of this equation then I have boils law if I ignore the pressure P1 and P2 then I have charge law and so on so the combined gas law is really all you need to memorize um notice how in the combined gas law there is total of six measurements or six variables and how do you know that you have a combined gas law versus one of the other three laws if you're given five measurements in the problem and you're looking for the sixth one that's a combined gas law if you problem if you're given only three measurements and you're looking for the fourth one that's one of the other three gas laws okay so here in this problem we have the initial volume and the initial temperature and the initial pressure all these are given the gas expands to a different volume and a different pressure find T2 so we have to do conversions convert P1 from millimet mercury to atmospheres you can do that or you can convert atmospheres to millimeter mercury why do I do that because I want P1 and P2 to have the same units I also have to convert liters to milliliters or milliliters to l it's up to you again because I want V1 and V2 to have the same units and the temperature is already in kelvin and I'm looking for T2 let's start with the combined gas law P1 V1 over T1 = to P2 V2 over T2 now here in this problem T2 is what I'm looking for I need to solve for T2 so whenever yourown is on the bottom of the fraction in the denominator you first need to do something called cross multiplication you've studied that in your algebra classes what does that mean that means that you're going to bring this denominator place it over here so we're going to play take T2 and place it on the left hand side and we'll take T1 put it on the right hand side so the intermediate step that I didn't show is we end up with P1 V1 T2 equals to P2 V2 T1 and now we can actually solve for T2 by dividing both sides of the equation by P1 V1 and that way we can um cross cancel P1 P1 and V1 V1 and the last thing you to do is plug in all the numbers here the final temperature is in kelvin that's 375 Kelvin