Tips on How to Manipulate the Ideal Gas Law
So we are working with Gas Laws. And we're going to be come across the Ideal Gas Law. We want to manipulate that ideal gas law to find us molar mass of the gas, or density of the gas.
First, let me reiterate that the Ideal Gas Law will always be used when you're dealing with the amount of the gas. So if you're given the amount of the gas, or you have to find the amount of the gas, it's the only gas law that has the amount of gas in it. So whenever you're asked or you're given the amount of gas, think in your head, Ideal Gas Law. I need to go there.
So speaking of Ideal Gas Law, what the heck is it? So it is PV=nRT. Pressure times volume equals the number of moles, times gas law constant, times temperature in Kelvin. Don't ever put it in Celsius, just a reminder. You can find all these variables, but what else can you find using this? You can find the Molar mass of a gas. Yes, so the molar mass of the gas, molar gas we know is grams per mole. If you're given the mass of gas in our problem, we need that in order to solve our problem. So we have to be given the mass of it. We're going to say mass is gram. So this is Molar mass right here, grams per mole. I'm going to short hand it by saying big M. I know it stands for Molarity, but in my case it stands for molar mass of a gas.
There's g for the mass of the gas. I'm going to make it little m. So we're going to say if these are two variables, we're not going to introduce the Ideal Gas Law. So we're given, if we manipulate this, we have grams over grams per mole. If we divide this actually, put some moles up top, so it's grams times mole over grams. If we cross out our units, we're left with moles.
So how did I get that? Grams over grams per mole which is little m over big M. Grams, the mass over molar mass equals if we do that and those units cross out, equals n. So now, I can substitute that into my Ideal Gas Law. Instead of writing n, I can write little m over big M. So I'm going to rewrite my gas law to say PV=mRT over big M. Here is n. So instead of n, I just substitute little m over big Mm.
Here is my new Ideal Gas Law that can help us solve the mole gas of the gas.
What if we're asked about density of a gas? Density of the gas don't forget is grams per liter. Which in other words using the variables from our Ideal Gas Law, we're going to say little m over big V, mass over volume.
So we want to manipulate our equation to get this in there. I'm going to use this one that we derived PV equals little mRT over big M. I want to get rid of this M on the bottom. I want to put v there. So I'm going to multiply by m over v. Multiply this side. If I multiply one side, I have to multiply the other, and then these cross out and these cross out. So I'm left with MP equals mRT over V. M over v is our density. I'm going to make this actually capital d.
So then I'm going to substitute that and say MP=DRT. This is the Ideal Gas Law. So there's three Ideal Gas Laws. You can find lots of different fun thing using it and manipulating things with it.
So hopefully this helps you solve a little harder problems by using the Ideal Gas Law. Don't forget you're going to always use the Ideal Gas Law, not any other Gas Law when you're asking for what you're trying to find the amount of a gas. None of the other gas laws have that as part of their variable. So hopefully this helps you solving more difficult problems.