Ideal Gas Law Practice Problems

Alright, let's do some

practice

problems

with the

ideal

gas law. PV is equal to NRT. Here is our first one, two point three moles of helium gas that 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 we are going to do is clarify our variables. Here I'm going to use R, which is a constant, so it has nothing to do with this problem. It's always here, maybe your teacher or your textbook gave it to you. another value for R other than 0.0821 if that's the case, still watch this video but then watch the other video called what if R is not point zero eight two one and that should make everything clear, okay?

Anyway, R is here, which one is it? The volume of the gas V is going to be the value that I am solving for now, let's connect the others well so that 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 add 273 to it, so the temperature will be 273 plus 41, so we end up with 314 Calvin.

Now is a good time to look at these variables up here and compare their units with the units in our. We want them to be equal. Well, then, 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 from ours, we would have to convert them so that they were the same, for example, if the pressure was one point seven zero kPa and we have ATMs down here, we would have to convert kPa to atmosphere to make it the same as the units in our okay, keep that in mind for the future, okay, so we know we're solving for V, let's move on.

Now and we rearrange the equation, we want V to be on one side by itself, so all I have to do is divide both sides by P and in that case I have P up here and P down here, so they're just I'm going to cancel and I'm going to let us be left with V equal to n R T divided by P there's the equation, okay now R let's talk about R for a second r is a pain in the ass because it has two parts, right? a top and has a bottom, how do we connect this thing that has both a top and a bottom to the top of a fraction?

Okay, there's no good way to do this. Some people do it and form a three-story fraction. which I hate, I think it's too ugly and too confusing. I'm going to show you a way I like to deal with us, which may be different from how your teacher or textbook tells you to do it, but be patient. I think it's actually a really good way to do it and I think it certainly makes the unit clearer and how we set everything up, so I'll show you what I do there just to make room. I'm going to move this here and now.

I'm going to take these variables and I'm going to plug them in, so I'm going to make V equal to n 2.3 moles and like I said, when we get to our, I'm going to leave our until it's okay. I'm going to do n, then I'm going to do T multiplied by T 314 Kelvin divided by P 1.70 atm. Now I said I was going to leave it until the end, okay, so let's go back to our times, our Kelvin ATM moles of 0.0821 liters. Alright, the reason I left it until the end is so we can put it up to here and we don't have to worry about putting it on top of this fraction.

Okay, but since all of these multiply, it doesn't matter. what order we put the NRT in, so I put the last one, no big deal, now I have all my units set up here. It's very satisfying to go through them and cancel them, okay, moles here, moles down there, ATM down here, ATM up. there those cancel Kelvin up here Kelvin down there is fine, which means I only have liters left 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 I'm going to get is thirty-four point eight seven eight zero one all right, how many digits do I round this to?

Well, I look for the number up. here the one with the fewest significant figures is two point three moles, which means that my final answer has to have two significant figures, so I take the three, I keep the four and I look at the next store to the eight to see if I round this up or keep it the same, it's an eight, so I'm going to increase it, so thirty-four points, blah, blah, Allah will become 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 cancels out, so 35 liters is the volume of the gas below these.

Well, let's take a look now at what happens when R is at 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'm going to do is I'm going to go ahead and fill in these variables as we go, at a given 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 occupy a volume of thirty-five point two eight liters.

What is this temperature in degrees Celsius? Okay, so T is going to be the variable that we're going to solve for before we go ahead and rearrange this, let's look again at the units of all the variables that we're going to plug into the equation, do the units up here match the units of our ATM? ATM liters liters moles moles okay, We're set up just one more time, if the unit here doesn't match the units in our, we would have to convert them to match. In this case, we will solve for T to get T by itself.

We'll divide both sides by n times R, the NR up here and the NR down here will cancel, so we're left with PV divided by NR T equals l equals T I know some people don't like it when the variable we're solving is on the right side so we can rearrange it so that T is equal to PV divided by n R, let's go ahead and plug these variables in now, here r is at the bottom. I'm going to show you what to do with that, but we're going to let it last like we did before, okay, so T is equal to the pressure 2.15 atm times the volume thirty-five point two eight liters divided by n, which is three point two four moles, and what I do when R is at the bottom, I take R and I turn it around, so what is normally in the lower Kelvin moles will be at the top and what is normally in the upper atmospheres of 0.0821 liters will end up at the bottom. down, okay, so again I leave it for last, all I do is flip it if R is at the bottom, I take the normal value of R and flip it upside down, okay, again, I love this, it's very satisfying, okay, I'll keep going here and Cancel my units ATM up here ATM down here oh man, doesn't it feel good? moles down here moles up here cancel liters up here liters down there I'll stick with Kelvin, which makes sense because I'm solving for temperature, so my final answer will obviously have the units of Kelvin, but cancel out all these other units and be left alone. with the unit I'm looking for it also lets me know that I went ahead and set up the equation correctly, so I connect. all these numbers and the final answer that I will get is two eight five point one five three six Kelvin how many digits do I round to accept three significant figures for most of these four significant figures here, but I always have to go. with less so I'm going to round this to three significant figures I keep the to keep the eight I keep the five and look next to the one I round it keep it the same I keep it the same so it's going to be 285 Kelvin, but we're not done yet because, yeah Do you remember the question, what is this temperature not in Kelvin but in Celsius?

So the last thing I have to do is take this Kelvin temperature that I had and I converted it back to Celsius according to this equation to get the temperature in Celsius, take the temperature in Kelvin and subtract 273, so here's my temperature. 285 is my temperature in Kelvin minus 273 and that will give me 12 degrees Celsius and that is my final answer.