The Combined Gas Law - Explained"},"lengthSeconds":"842","ownerProfileUrl":"http://www.youtube.com/c

Hello guys, this is mr. millings and in this video we are going to learn about the

combined

gas law, so what is the

combined

gas law and how does it work? It says right here that the combined gas law is a gas law that combines Boyle's law, Charles's law, and Gay Lussac's law. law in a simple formula in which three variables of gas pressure, volume and temperature are taken into consideration, so in a previous video we learned about Boyle's law and Boyle's law states that if it remains constant the temperature of a gas and the pressure and the volume of that gas will be inversely proportional as one increases the other will decrease and then we learned about Charles's law and Charles's law states that the volume and temperature of a gas are directly proportional if the volume of a gas doubles then that is because the temperature of the gas doubles, etc, etc. and then we learned about Gay Lussac's law and he remains at a constant volume, the pressure and temperature of a gas are going to be directly proportional, right, if the pressure increases it is because the temperature also increases if the pressure is reduced to the half, then that is because the temperature is also reduced by half, so we learned about Boyle's law, Charles's law and Gay Lussac's law in other videos and we learn how to solve problems using the formulas you see here , but wouldn't it be great if there was some kind of formula that somehow combined all three gas laws into one easy-to-use formula?

Do you think there is a formula that combines the three formulas into one well, if you think so, you are absolutely right and that is the combined gas law and that is what we are going to talk about in this video, so let's take a look at the combined gas law and let's see how it works and then apply the combined gas law to several different types of problems, so what we're looking at is the combined gas line. The combined gas law tells us that p1 v1 over t1 is equal to p2 v2 over t2, so when we work with the combined gas law.

We are observing three different Toros of that gas. We are looking at the pressure, volume and temperature of that gas. What will happen to that gas is pressure, volume and temperature if we start manipulating some of those variables. and here it says that when we work with the combined gas law formula, all units of pressure and volume must be equal and last but not least, the temperature must be in Kelvin. Okay, when we work with the combined gas law, all Kelvin. all temperature units should be in Kelvin, if we are working with milliliters of gas here then we should work with milliliters of gas here, if the pressure here is in atmospheres then we should make sure that the pressure here is also in atmospheres okay , so here's your combined gas lab: the original pressure of the gas multiplied by the original volume divided by the original temperature will be equal to the final pressure of the gas multiplied by the final volume divided by the final temperature of the gas, so let's go .

Go ahead and use this combined gas law formula now to solve different problems where we have some changes in one of these variables that we see in front of us in this first example, it says that a gas occupies 40 liters to 1 atmosphere and 200 will exert the gas. If the temperature increases to 400 K and its volume decreases to 20 liters, then when we run into these word problems, what I like to do is go ahead and label everything, so let's take a look at what gas is. about the beginning, if we take a look, the gas is occupying 40 liters at the beginning, so that will be its v1, it tells us that the pressure of this gas at the beginning is one atmosphere that will be p1 and the temperature of this gas at the beginning will be to be 200k, so there's your t1.

The question here is how much pressure will the gas exert if the temperature is to change and increase to 400k, so this will be t2. Its volume will decrease to 20 liters, so here. is its V 2 and we are asked to solve for ptoo so here is our formula, but let's go ahead and list everything we have P 1 V 1 and T 1 and if we take a look here, the original pressure of this gas is going to be 1 atmosphere if we take a look the original volume of this gas is going to be 40 liters and if we take a look this is already in Kelvin remember that when we work with this temperature it always has to be in Kelvin if it is in degrees Celsius We need to make that conversion Sorry, the pressure is what we are trying to find, we are trying to calculate the new pressure of this gas when the volume decreases to 20 liters, so the volume here will be 20 liters if we take a look at t2 it looks like the temperature is increasing at 400k, so now that we have all this set up, the formula we're going to use to solve this problem is p1 v1 over t1 is equal to p2 v2 over t2 and it looks like we're trying to solve for p2 so what I like to do is get rid of of the fractions here and what we can do is we can cross multiply to get rid of our fractions, we can cross multiply to get rid of our fractions. of these fractions and if we do that we are going to end up with p1 v1 t2 is equal to p2 v2 multiplied by t1 and then this problem that they ask us to solve for p2 we want to get p2 only on one side of the equal sign so we are going to divide both sides by V 2 and T 1 so it looks like the formula we're going to use to solve this problem is going to be p2 equally P 1 V 1 T 2 over all v2 multiplied by t1, so now that we've done all this work, we've done all this algebra To isolate our variable, we can simply replace these numbers into p1, which will be one atmosphere times v1, which is 40 liters times t2, which is 400 K, and then we're going to finish by dividing this by V 2, which is 20 liters times t1, which is 200k, so when we put this into our calculator, we'll end up with an answer of 4, but let's take a look.

Kelvin cancels the liters cancels leaving us with atmospheres so the new pressure of this gas will be 4 atmospheres, let's look at another example in this second example it says that the pressure of a gas increases from 500 turns to 800 turns and its temperature decreases from 75 degrees Celsius at 50 degrees Celsius if the final volume of the gas is this here, then calculate its original volume, so if we take a look, we are asked to first calculate the original volume, the original mean, so we are asked to let's find v1 in this issue. and so if we take a look, let's set everything up, let's find out what p1 is, let's find out what v1 is at t1, let's find out what p2 is, let's find out what v2 is, let's find out what t2 is and then we can plug it in. in our formula, so the pressure goes from this to this, so here is our p1 500 runs, p2 will be 800 runs, if we take a look, we are asked to find the original volume, so that is what we are trying to find.

The final volume it tells us is 125 milliliters. T1 if we take a look it will be 75 degrees Celsius however we have to convert this to Kelvin correctly so to get our t1 here we take 75 plus 273 and we will end up with 348. K we have to convert this to Kelvin before we can insert it into our formula to get t2, we have to take 50 degrees Celsius plus 273 and we'll end up with 323 K, so now that we have all these numbers we can plug them in. our formula so let's take a look here is our combined gas law formula and what we can end up doing is we can cross multiply to get rid of our fractions here no one likes fractions so we can cross multiply and if we cross multiply we will end up with P 1 times V 1 times T 2 equals p2 times v2 times t1, we are asked to find out what V 1 is, so we have to divide both sides by P 1 and T 2, these will cancel on both sides, so the formula we're going to use to solve this problem is V 1 equals p2 times v2 times t1 in all p1 times t2 so here we go, let's plug these numbers in here Q: It looks like it's 800 times the Tour times v2, which is going to be 125 milliliters times t1, which is going to be 348 K, we're going to divide this by p1, which is 500 Tour times t2, which is going to be 323 K, and when we put all this into our calculator, we're going to end up with 215, which is going to cancel out Calvin va to cancel leaving us with milliliters, so the new volume.

Sorry, the original volume of our gas will be 215 milliliters. Let's take a look at another example in this third example, it says if it is 50 liters of gas. exerts a pressure of 1 point 5 atmospheres at 25 degrees Celsius, so what will be its new temperature if its volume decreases to 20 liters while its pressure triples? So if we take a look here, let's figure out what's going on and let's go ahead and tag. all these little variables here that are in this little problem here and then we can continue from there so here we go let's take a look at what's happening in this little problem it tells us that we have 50 liters of gas starting so that es is going to be v1, it's exerting a pressure of 1.5 atmospheres, so it's going to be our p1 and its temperature is 25 degrees Celsius, so the temperature needs to be converted to Kelvin, it's going to take 273 plus 25 and we'll end up with 298 K since our t1 then T 1 will be 298 K let's continue reading they ask us to find out its new temperature we want to calculate t2 apparently it seems that its volume is decreasing to 20 liters and what is happening with its pressure, the pressure here is triple the pressure here it triples, so if this is the initial pressure and this is tripled here, then 3 times 1.5 is 4.5 atmospheres, so here we go, we're asked to solve for t2 now, so if we take a look we can multiply to get rid of it. of these fractions nobody likes fractions so we are going to cross multiply and what we are going to end up with is p1 v1 times t2 equals p2 times v2 times t1 and now they ask us to solve for t2 so we are going to divide both sides of p1 and v1, p1 and v1 will cancel from the left side, so t2 will be equal to p2 times v2 times t1 throughout p1 times v1, so now we can start plugging these numbers into the units of pressure.

The same there and the atmospheres, the volume is the same there and the liters and we have our temperature in Kelvin, so let's plug this into p2, which will be four point five atmospheres times v2, which is 20 liters times t1, which is 298 K , and we are. We'll end up dividing this by p1, which is 1 point 5 atmospheres times v1, which will be 50 liters, so when we put all of this into our calculator, we'll end up with 358. Okay, as we see here, the leaders will cancel out atmospheres. will cancel out leaving us with Kelvin, so what will be the new temperature of this gas?

It looks like the new temperature will end up being 358K, so if you like what you see, go ahead and click on that little bomb at the bottom right. corner of the hand and that will subscribe you to my YouTube channel and feel free to leave any comments or questions in the comments section below and I really hope you found it helpful.