 # Ideal Gas Law Practice Problems all right let's do some

with the

## ideal

gas law PV equals NRT here's our first one two point three moles of helium gas are at a pressure of one point seven atm and the temperature is 41 degrees Celsius what is the volume of the gas the first thing that let's do is get our variables straight now here I'm going to be using R which is a constant so it doesn't have anything to do with this problem it's just always here now maybe your teacher or your textbook has given you another value for R that isn't 0.0821 if that's the case still watch this video but then watch the other video that's called what if R isn't point zero eight two one and that should make everything clear okay so anyway R is right here what's the volume of the gas V is going to be the value that I'm solving for now let's plug the other ones all right so we have a pressure of one point seven zero atm we have the amount of gas is two point three moles and the temperature is 41 degrees Celsius which you probably already know we're going to have to end up converting to Calvin okay so let's go ahead and do that right now to get to Calvin we take our degrees Celsius which here is 41 and we add 273 to them so temperature will be 273 plus 41 so we're going to end up with 314 Calvin now is a good time to look at these variables up here and compare their units with the units on our we want them to be the same okay so ATMs up here ATMs down... here that's good moles here moles there Calvin there Calvin there right if any of the units were different than what they are in our we would have to convert them so that they were equal so for example if pressure were one point seven zero kPa and we have ATMs down here we'd have to convert kPa into atmosphere so that it would be the same as the units on our alright keep that in mind for the future all right so we know we're solving for V let's go ahead now and rearrange the equation we want V to be on one side all by itself so all I've got to do is divide both sides by P and in that case I have P up here and I have P down here so they're just going to cancel out and I'm going to let be left with V equals n R T divided by P there's the equation alright now R let's talk about R for a sec r is such a pain in the neck because it has two parts right it has a top and it has a bottom how do we plug this thing that has both the top and a bottom into the top of a fraction okay there's there's no really good way to do this some people do it and they make like a triple-decker fraction which I hate I think that's so ugly and it's far too confusing I'm going to show you a way that I like to deal with our that may be different from how your teacher or textbook tells you to do it but but bear with me I think it's actually a pretty good way to do it and I think it certainly makes the unit's clearer and how we set everything up... so I'll show you what I do there just to make space I'm going to move this up here and now I'm going to take these variables and I'm going to plug them in okay so I'm going to do V equals n 2.3 moles and as I said when we get to our I'm going to leave our until the okay so I'm going to do n then I'm going to do T times T 314 Kelvin divided by P 1.70 atm now I said I was going to leave our till the end okay so let's go back to our times our 0.0821 liters ATM Kelvin moles all right the reason why I left it till the end is then we can put it all the way here and we don't have to worry about putting it on top of this fraction okay but since these are all multiplied together it doesn't matter what order we put the NRT and so I just put our last it's no big deal all right now I have all my units set up here this is so satisfying to go through and cancel them okay moles up here moles down there ATM down here ATM up there those cancel out Kelvin up here Kelvin down there all right which means that I'm left with only liters and that makes sense because I'm solving for volume okay now it's time to put all this math into my calculator I'm going to 2.3 times 3 14 times 0.0821 all of that divided by one point seven zero the answer that I'm going to get is thirty four point eight seven eight zero one all right how many digits do I round this to okay I look for the number up here that has the fewest significant figures... that's here two point three moles which means that my final answer has to have two significant figures so I keep the three I keep the four and I look next store to the eight to see whether I round this up or keep it the same it's an eight so I'm going to bump it up so thirty-four point blah blah Allah is going to turn into 35 rounded to two significant figures and what are my units I know what my units are my units are leaders because everything else here cancelled out so 35 liters is the volume of the gas under these okay let's take a look now at what happens when R is on the bottom of the fraction so we'll do a similar problem but I'll show you how to deal with R in this situation okay and what I'll do is I'll just go ahead and fill in these variables as we go all right at a certain temperature three point two four moles of co2 so that's our n how much how much gas three point two four moles of gas are at a pressure of two point one five ATM and they take up a volume of thirty five point two eight liters what is this temperature in Celsius okay so T is going to be the variable that we're going to be solving for before we go ahead and rearrange this let's again look at the units of all the variables that we're going to plug into the equation do the unit's up here match the units on our ATM ATM liters liters moles moles okay we're set just once again if the unit's here didn't match the units on our we would have...
to convert them so that they did match okay in this case we're going to be solving for T so to get T by itself we'll divide both sides by n times R the NR up here and the NR down here both going to cancel out so we're going to be left with PV divided by NR T equals to l equals T I know that some people don't like it when the variable we're solving for is on the right side so we can rearrange this to T equals PV divided by n R let's go ahead and plug these variables in now here r is on the bottom I'm going to show you what I do with that but we're we're going to leave it to last just like we did before okay so T equals pressure 2.15 atm times volume thirty five point two eight liters divided by n which is three point two four moles and what I do when R is on the bottom is I take R and I flip it upside down okay so what is normally on the bottom Kelvin moles is going to be on the top and what is normally on the top 0.0821 liters atmospheres is going to end up on the bottom okay so again I leave our till last all I do is I flip it if R is on the bottom I take the normal value of R and I flip it upside down okay again I love this it's so satisfying all right I go through here and I cancel my units ATM up here ATM down here oh man doesn't that feel good moles down here moles up here cancels out liters up here liters down there I'm left with Kelvin which makes sense because I'm solving for temperature so my final answer is...
obviously going to have the units of Kelvin but cancelling out all these other units and being left with just the unit's I'm looking for also lets me know that I went ahead and I set up the equation correctly okay so I plug through all these numbers and the final answer that I'm going to get is two eight five point one five three six Kelvin how many digits do I round this to okay three significant figures for most of these four significant figures here but I always have to go with a fewest so I'm going to round this to three significant figures keep the to keep the eight keep the five and look next door to the one do I round it up keep it the same I keep it the same so it's going to be 285 Kelvin but we're not quite done yet because if you remember the question asked what is this temperature not in Kelvin but in Celsius so the last thing that I've got to do is I've got to take this Kelvin temperature that I had and convert it back to Celsius according to this equation to get Celsius temperature take the Kelvin temperature and I subtract 273 so here's my temperature 285 is my Kelvin temperature minus 273 and that is going to give me 12 degrees Celsius and that is my final answer