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We have a situation here where we have a

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four meter cubed container.

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Let's say that's a balloon of some sort.

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And instead of having just one type of molecule of gas in

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this container, we have three molecules of gas.

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We have some oxygen molecules, some hydrogen molecules, and

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some nitrogen molecules.

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And what the problem tells us is, we have 2.1 total

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kilograms of gas.

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An of that, by math, 30.48% is oxygen, 2.86% is hydrogen

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molecules, and 66.67% is nitrogen.

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So what we need to figure, and it's all at standard

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temperature at least. It's zero degrees Celsius, which we

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know is 273 Kelvin.

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But we need to figure out what is the total pressure in the

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container, or being exerted on the surface of the container?

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And then, this is a new concept, we want to figure out

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the partial pressures of each of these gases.

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Essentially, how much are each of these gases contributing to

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the total pressure?

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And you can imagine, if this is a container and each of

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these are the three types of gases, some of the pressure is

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going to be from the blue, maybe oxygen is the blue gas,

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from the blue gas bumping into the walls.

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Some of the pressure is going to be from the hydrogen

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bumping into the walls, maybe that's this yellow gas, and

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some of the pressure is going to be from the nitrogen

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bumping into the walls.

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Let's say that's the brown gas.

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So the partial pressure due to nitrogen, that's the pressure

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just due to the brown particles bumping into walls.

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Let's see if we can figure this out.

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So the first thing to figuring the total pressure is, we have

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to figure out the total moles of molecules we have. And the

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easiest way I can figure out to figure out the total number

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of moles is to figure out the moles of

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each of these molecules.

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So if we have 2.1 kilograms of gas-- let me write this down--

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If we want to know moles of nitrogen.

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Let me do it in the nitrogen color.

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We know that 66.67% of this, we could say 2.1 kilograms or

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2100 grams, we know that that's nitrogen.

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So let's do it in grams. Because when we talk about

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molecular mass it's always in grams. It doesn't have to be.

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But it makes it a lot simpler to convert between atomic mass

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units and mass in our world.

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So this is 2/3 of 2100, that's 1400 grams of N2.

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Now what's the molar mass of this nitrogen molecule?

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Well we know that the atomic mass of nitrogen is 14.

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So this molecule has two nitrogens.

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So its atomic mass is 28.

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So one of these molecules will have a mass of

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28 atomic mass units.

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Or one mole of N2 would have a mass of 28 grams.

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So one mole is 28 grams. We have 1400 grams-- or we say

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grams per mole, if we want to keep our units right.

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So if we say 1400 total grams so divided by 28 grams per

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mole we should get the number of moles.

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So 1400 divided by 28 is equal to 50.

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That worked out nicely.

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So we have 50 moles of N2.

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We could write that right there.

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All right.

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Let's do oxygen next.

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So we do the same process over again.

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30% is oxygen.

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So let's do oxygen down here, O2.

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So we take 30%.

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Remember, these percentages I gave you, these are the

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percentages of the total mass, not the

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percentage of the moles.

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So we have to figure out what the moles are.

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So 30.48% of 2100 grams is equal to about 640.

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Let's round off.

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So this is equal to 640 grams.

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And then what is the mass of one mole of

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the oxygen gas molecule?

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The atomic mass of one oxygen atom is 16.

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You can look it up on the periodic table, although you

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should probably be pretty familiar with it by now.

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So the atomic mass of this molecule is

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32 atomic mass units.

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So one mole of O2 is going to be 32 grams. We have 640

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grams. So how many moles do we have?

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640 divided by 32 is equal to 20.

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We have 20 moles of oxygen.

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Let me write that down.

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We have 20 moles.

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Now we just have to figure out the hydrogen.

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2.86% of all that is hydrogen.

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So let's see, if we do 2100 grams, remember I want to do

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everything in grams, so I just want to do a

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unit conversion there.

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2100 grams times 2.86% is equal to about 60 grams.

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So hydrogen, this 2% of that 2100 grams is 60 grams. And

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then what's the molar mass of one hydrogen.

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That's H2.

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So we know that the hydrogen atom by itself has a mass of

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1, doesn't have a neutron in most cases.

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So the atomic mass of this is 2.

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Or the molar mass of this is 2 grams.

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So one mole of H2 is equal to two grams. We have 60 grams.

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So we clearly have 60 divided by 2, we have 30 moles.

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So this is interesting, even though hydrogen was a super

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small fraction of the total mass of the gas that we have

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inside of the container, we actually have more actual

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particles, more actual molecules of hydrogen than we

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do of oxygen.

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That's because each molecule of hydrogen only has an atomic

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mass of 2 atomic mass units, while each molecule of oxygen

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has 32 because there's two oxygen atoms. So already we're

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seeing we actually have more particles due to hydrogen than

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due to oxygen.

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And the particles are what matter, not the mass, when we

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talk about part pressure and partial pressure.

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So the first thing we can think about is how many total

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moles of gas, how many total particles do we

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have bouncing around?

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20 moles of oxygen, 30 moles of hydrogen, 50 moles of

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nitrogen gas.

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Add them up.

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We have 100 moles of gas.

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So if we want to figure out the total pressure first, we

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can just apply this 100 moles.

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Let me erase this.

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I want to keep the problem statement

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there the whole time.

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There you go.

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And I can erase some stuff that you're not

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seeing off the screen.

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And now I'm ready.

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So we have 100 moles.

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So we just do our PV is equal to nRT.

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We're trying to solve for P.

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P times 4 meters cubed is equal to n. n is

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the number of moles.

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We have 100 moles.

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Is equal to 100 moles times R.

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I'll put a blank there for R, because we have to figure out

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which R we want to use.

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Times temperature, remember we have to do it in Kelvin.

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So 0 degrees Celsius is 273 Kelvin.

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And then which R do we use?

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I always like to write my R's down here.

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So we're dealing with meters cubed, we're not dealing with

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liters, so let's use this one.

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8.3145 meters cubed pascals per mole Kelvin.

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The units there, I think I should keep, these are in

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meters cubed pascals divided by moles Kelvin.

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And then our temperature was 273 Kelvin.

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Now let's do a little dimensional analysis to make

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sure that we're doing things right.

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These meters cancel out with those meters.

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We divide both sides of the equation by meters.

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These moles cancel with these moles.

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The moles of the numerator, the moles of the denominator.

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Kelvin in the numerator, Kelvin in the denominator.

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And all we're left with is pascals.

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Which is good because that is a unit of pressure.

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So if we divide both sides of this equation by 4.

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I'll just divide the 100 by 4.

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25 times 8.3145 times 273.

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And the only unit that we were left with was pascals.

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Which is nice, because that's a unit of pressure.

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So, let's do the math, 25 times 8.3145 times 273 is

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equal to 56,746 pascals.

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And that might seem like a crazy number.

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But the pascal is actually a very small amount of pressure.

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It actually turns out that 101,325 pascals is equal to

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one atmosphere.

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So if we want to figure out how many atmospheres this is,

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we could just divide that.

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Let me look it up on this table.

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Yes, 101,325.

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So if we wanted to, we could write this in kilopascals.

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That's 56.746 kilopascals.

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Or if we wanted it in atmospheres we just take

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56,746 divided by 101,325.

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It equals 0.56 atmospheres.

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So that's the total pressure being exerted

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from all of the gases.

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I deleted that picture.

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So this is the total pressure.

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So our question is, what's the partial pressure?

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We could use either of these numbers, they're just in

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different units.

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What's the partial pressure of just the oxygen by itself?

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Well, you look at the moles, because we don't care about

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the actual mass.

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Because we're assuming that they're ideal gases.

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We want to look at the number of particles.

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Because remember, we said pressure times volume is

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proportional to the number of particles times temperature.

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And they're all at the same temperature.

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So the number of particles is what matters.

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So oxygen represents 20% of the particles.

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20/100.

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So, the partial pressure of oxygen, let me write that as

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pressure due to oxygen, due to O2.

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00:11:12,370 --> 00:11:15,019
It's going to be 20% of the total pressure.

209
00:11:15,019 --> 00:11:23,069
20% times, let me write 56.746 kilopascals.

210
00:11:23,070 --> 00:11:26,360
I just took this pressure measurement.

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00:11:26,360 --> 00:11:29,930
If I wanted atmospheres, times 0.56 atmospheres.

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00:11:29,929 --> 00:11:32,719
So the partial pressure of oxygen-- well, I already have

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00:11:32,720 --> 00:11:33,840
the 0.56 written there.

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00:11:33,840 --> 00:11:45,879
So times 0.2 is equal to 0.112 atmospheres.

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00:11:45,879 --> 00:11:47,240
It's just 20% of this.

216
00:11:47,240 --> 00:11:50,779
How did I get 20%?

217
00:11:50,779 --> 00:11:55,419
We have a total of 100 mole molecules in our balloon.

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00:11:55,419 --> 00:11:57,319
20 moles of them are oxygen.

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So 20% are oxygen.

220
00:11:58,710 --> 00:12:01,800
So 20% of the pressure is going to be due to oxygen.

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00:12:01,799 --> 00:12:03,639
So it's this many atmospheres.

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00:12:03,639 --> 00:12:06,360
If I took 20% times the 56,000.

223
00:12:06,360 --> 00:12:16,620
0.2 times 56, you get roughly 11.2 kilopascals.

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I'm just multiplying 20% by any of these numbers.

225
00:12:18,669 --> 00:12:20,919
And the numbers are going to change depending on the units.

226
00:12:20,919 --> 00:12:21,929
So you do the same process.

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What is the partial pressure due to nitrogen?

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00:12:26,649 --> 00:12:32,429
Well even though 2/3 of the mass is nitrogen, only 50% of

229
00:12:32,429 --> 00:12:34,359
the actual particles are nitrogen.

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So 50% of the pressures is due to the nitrogen particles.

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00:12:37,470 --> 00:12:38,879
Remember, you have to convert everything to moles.

232
00:12:38,879 --> 00:12:41,529
Because we only care about the number of particles.

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00:12:41,529 --> 00:12:46,049
So if you want to know the partial pressure due to the

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00:12:46,049 --> 00:12:50,389
nitrogen molecules, it's 50% of these.

235
00:12:50,389 --> 00:13:03,399
So it's 28,373 pascals.

236
00:13:03,399 --> 00:13:05,009
That's roughly.

237
00:13:05,009 --> 00:13:08,919
Or if you took half of this, approximately 28.4

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00:13:08,919 --> 00:13:10,519
kilopascals.

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00:13:10,519 --> 00:13:16,590
Or approximately 0.28 atmospheres.

240
00:13:16,590 --> 00:13:18,530
And then finally, if you want to figure out the partial

241
00:13:18,529 --> 00:13:24,600
pressure due to the hydrogen atoms. The partial pressure

242
00:13:24,600 --> 00:13:27,560
due to the hydrogen atoms. Hydrogen, even though it's a

243
00:13:27,559 --> 00:13:30,129
very small part of the mass, it actually represents 30%

244
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percent of the molecules.

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00:13:31,299 --> 00:13:33,279
And it's the molecules that are bumping into things.

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We don't care so much about the mass.

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So 30% of the molecules.

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00:13:40,210 --> 00:13:43,830
And remember, when we talk about kinetic energy, if

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something with a small mass has the same kinetic energy,

250
00:13:45,899 --> 00:13:47,199
it's actually moving faster.

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00:13:47,200 --> 00:13:48,840
So when we talk about temperature, that's average

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kinetic energy.

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00:13:49,799 --> 00:13:52,069
So maybe in this we could imagine that the hydrogen

254
00:13:52,070 --> 00:13:54,750
might be moving faster than the nitrogen or the oxygen.

255
00:13:54,750 --> 00:13:57,019
But we don't have to think about that too much right now.

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00:13:57,019 --> 00:14:01,159
But the partial pressure due to hydrogen is just 30% of any

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of these numbers.

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Pick one.

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Let's do it in atmospheres.

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0.3 times 0.56 is equal to 0.168 atmospheres.

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And so the total pressure should be equal to the

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pressure of each of the partial pressures

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of each of the gases.

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Plus the partial pressure of oxygen, plus the partial

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pressure of hydrogen.

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And so this one, we figured out was 0.28 atmospheres.

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The oxygen was 0.112 atmospheres.

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And this was 0.168.

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And if you add these together, you will see indeed, that they

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add to 0.56 atmospheres.

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Which was the total pressure of our system.

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Anyway, this is a very long and hairy problem.

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But the key takeaway is that every molecule in the system

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contributes to the total pressure in proportion to the

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number of moles it has as a percentage of the total number

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of moles in the system.

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I hope that didn't confuse you too much.

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