Partial pressure

- [Voiceover] We have a situation here where we have a four meter cubed container, let's see that's a balloon of some sort, and instead of having just one type of molecule of gas in this container we have three molecules of gas, we have some oxygen molecule, some hydrogen molecule and some nitrogen molecule. And what the problem tells us is we have 2.1 total kilograms of gas, and of that by mass 30.48% is oxygen, 2.86% is hydrogen molecules, and 66.67% is nitrogen. Now we need to figure out-- And it's all at standard temperature at least, 0° Celsius which we know is 273° Kelvin. But we need to figure out what is the total pressure in the container, or being exerted on the surface of the container, and then, this is the new concept, we wanna figure out the partial pressures of each of these gases, essentially how much are each these of these gases contributing to the total pressure. And you can imagine, if this is the container and each these are the three types of gases some of the pressure is going to be from the blue, maybe the oxygen is the blue gas, from the blue gas bumping into the walls, some of the pressure is going to be from the hydrogen bumping into the wall, maybe that's these yellow gases, and some of the pressure is going to be from the nitrogen bumping into the walls, let's say that's the brown gas. So the partial pressure is a partial, you see the partial pressure due to nitrogen, that's the pressure just due to the brown particles bumping into the walls. So let's see if we can figure this out. So the first thing to figure out, the total pressure, we have to figure out the total moles of molecules we have, and the easiest way I can figure out the total number of moles is figure out the moles of each of these molecules. So we have 2.1 kilograms of gas, let me write this down, if we have 2.1, so if we're just dealing with, if we wanna know moles of nitrogen, we have two-- Let me do it in the nitrogen color. Moles of nitrogen. We know that 66.67% of these 2.1 kilograms or 2,100 grams, we know that that's nitrogen, so let's do it in grams because when we talk about molecular mass it's always in grams, it doesn't have to be but it makes it a lot simpler to convert between atomic mass units and mass in our world. So this is 2/3, so 2/3 of 2,100 that's 1,400 grams of N2. Now, what's the molar mass of this nitrogen molecule? Well, we know that the atomic mass of nitrogen is 14, so this molecule has two nitrogens so its atomic mass is 28, so one of these molecules will have a mass of 28 atomic mass units, or one mole of N2 would have a mass of 28 grams. So one mole is 28 grams, we have 1,4000 grams, so we have... Or we say grams per mole, so if we wanna keep our units right. So if we say 1,400 total grams divided by 28 grams per mole, so we have 50 moles of N2. So we write that right there, 50 moles. Alright, let's figure out, let's do oxygen next. So we do the same process over again, 30% is oxygen so we take, so it's oxygen down here, O2, so we take 30%... And remember, these percentages I gave you these are the percentages of the total mass not the percentage of the moles so we have to figure out what the moles are. So 30.48% of 2,100 grams is equal to 640 grams. And then, what is the mass of one mole of gas, of the oxygen gas molecule? The atomic mass of one oxygen atom is 16, you can look it up in the periodic table although you should probably be pretty familiar with it by now. So the atomic mass of this molecule is 32 atomic mass units, so one mole of O2 is going to be 32 grams. We have 640 grams, how many moles do we have? 640 divided by 32 is equal to 20, we have 20 moles of oxygen. We write that down, we have 20 moles. Now we just have to figure out the hydrogen. This 2% of that 2,100 grams is 60 grams, and then, what's the molecular, what's the molar mass of one hydrogen, of H2? So we know that the hydrogen atom by itself has a mass of one, doesn't have a neutron in most cases, so the atomic mass of this is two, or the molar mass of this is two grams. so one mole of H2 is equal to two grams. So one mole is two grams, we have 60 grams, so we clearly have 60 divided by two, we have 30 moles. 30 moles. So this is interesting, even though hydrogen was a super small fraction of the total mass of the gas that we have inside of the container we actually have more actual particles, more actual molecules of hydrogen than we do of oxygen. That's because each molecule of hydrogen only has an atomic mass of two atomic mass units while each molecule of oxygen is 32 'cause there's two oxygen atoms. So already we're seeing we actually have more particles due to hydrogen than due to oxygen, and the particles are what matter not the mass when we talk about pressure and partial pressure. So the first thing we think about is how many total moles of gas, how many total particles do we have bouncing around? 20 moles of oxygen, 30 moles of hydrogen, 50 moles of nitrogen gas, add them up, we have 100 moles, 100 moles of gas. So if we wanna figure out the total pressure first we can just apply these 100 moles-- Let me erase this 'cause I wanna keep the problem statement there the whole time, let me erase this. There you go, there you go, and I can erase some stuff you're not seeing off the screen. And now I'm ready. So we have 100 moles, so we just do our PV is equal to nRT. We're trying to solve for "P", "P" times four meters cubed, is equal to "n", "n" is the number of moles, we have 100 moles, is equal to 100 moles, times "r", I'll put a blank there for "r" 'cause we have to figure out which "r" we wanna use, times temperature. Remember, we have to do it in Kelvin, so if it's 0° Celsius it's 273° Kelvin. And then which "r" do we use? I always like to write my "r"s down here. So we're dealing with meters cubed, we're not dealing with liters, so let's use this one: 8.3145 meters cubed Pascals per mole Kelvin. So this is 8.3145, and the units there-- Actually maybe I should, let me do this. Oh, I didn't want to do that in yellow. The units there think I should keep, these are in meters cubed Pascals divided by moles Kelvin, and then our temperature was 273 Kelvin. Now, let's do a little dimensional analysis to make sure that we're doing things right. These meters cancel out with those meters, we divide both sides of the equation by meters. These moles cancel with these moles, moles in the numerator, moles in the denominator. Kelvin in the numerator, Kelvin in the denominator. And all we're left with is Pascals, which is good because that is a unit of pressure. So we get four-- So if we divide both sides of this equation by four we get "P" is equal to, I'll just dive 100 by four, 25 times 8.3145 times 273, and the only unit we were left with was Pascals, which is nice 'cause that's a unit of pressure. So let's do the math, 25 times 8.3145 times 273 is equal to 56,746 Pascals. And that might seem like a crazy number but the Pascal is actually a very small amount of pressure, it actually turns out that, I think it's 101,325 Pascals is equal to, or 101,325 is equal to one atmosphere. So if we wanna figure out how many atmospheres this is we can just divide that by 101... That large number, I think that's right, let me look it up on this table, it says 101... Yeah, 101,325. So if we wanted to put this in, we could write this in Kilopascals, that's 56.746 Kilopascals, or if we wanted it in atmospheres we just take 56,746 divided by 101,325 equals .56 atmospheres. So that's the total pressure being exerted from all of the gases. I deleted that picture. So this is the total pressure. So our question is, what's the partial pressure? We could use either of these numbers, there's in different units. What's the partial pressure of, say, nitrogen? Well even though 2/3 of the mass is nitrogen only 50% of the actual particles are nitrogen, so 50% of the pressure is due to the nitrogen particles. Remember, you have to convert everything to moles 'cause we only care about the number of particles. So if you wanna know the partial pressure due to the nitrogen molecules it's 50% of this, so it's, you know, it's 28,300... Ah, let's just say it's roughly 28,373 Pascals, that's a roughly, or if you took half of this approximately 28.4 Kilopascals, or approximately .28 atmospheres. And then finally if you wanna figure out the partial pressure due to, let me do a different color, the pressure due to the hydrogen atoms, the partial pressure due to the hydrogen atoms, hydrogen even though it's a very small part of the mass it actually represents 30% of the molecules, and it's the molecules that are bumping into things, we don't care so much about the mass. So 30% of the molecules, 30% of the molecules... And remember, when we talk about kinetic energy something with a small mass has the same kinetic energy, it's actually moving faster, so when we talk about temperature that's average kinetic energy, so maybe in this we can imagine that the hydrogen might be moving faster than say the nitrogen or the oxygen, but we don't have to think about that too much right now. But the partial pressure due to hydrogen is just 30% of any of these numbers, pick one, let's do it in atmospheres, times .56 is equal to, .3 times .56 is equal to .168 atmospheres. And so the total pressure should be equal to the pressure of each of the partial pressures of each of the gases, plus the partial pressure of oxygen plus the partial pressure of hydrogen. And so this one we figured out was .28 atmospheres, the oxygen was .112 atmospheres, and this one's .168, and if you add these together you will see indeed that they add .56 atmospheres.