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  • - [Instructor] In this video,

  • we're going to introduce ourselves to the idea

  • of partial pressure due to ideal gases.

  • And the way to think about it is

  • imagine some type of a container,

  • and you don't just have one type of gas in that container.

  • You have more than one type of gas.

  • So let's say you have gas one that is in this white color.

  • And obviously, I'm not drawing it to scale,

  • and I'm just drawing those gas molecules moving around.

  • You have gas two in this yellow color.

  • You have gas three in this blue color.

  • It turns out that people have been able to observe

  • that the total pressure in this system

  • and you could imagine that's being exerted

  • on the inside of the wall,

  • or if you put anything in this container,

  • the pressure, the force per area that would be exerted

  • on that thing is equal to the sum

  • of the pressures contributed from each of these gases

  • or the pressure that each gas would exert on its own.

  • So this is going to be equal to

  • the partial pressure due to gas one

  • plus the partial pressure due to gas two

  • plus the partial pressure due to gas three.

  • And this makes sense mathematically

  • from the ideal gas law that we have seen before.

  • Remember, the ideal gas law tells us

  • that pressure times volume is equal to the number of moles

  • times the ideal gas constant times the temperature.

  • And so if you were to solve for pressure here,

  • just divide both sides by volume.

  • You'd get pressure is equal to nR

  • times T over volume.

  • And so we can express both sides of this equation that way.

  • Our total pressure, that would be our total number of moles.

  • So let me write it this way, n total

  • times the ideal gas constant

  • times our temperature in kelvin

  • divided by the volume of our container.

  • And that's going to be equal to,

  • so the pressure due to gas one,

  • that's going to be the number of moles of gas one,

  • times the ideal gas constant times the temperature,

  • the temperature is not going to be different for each gas,

  • we're assuming they're all in the same environment,

  • divided by the volume.

  • And once again, the volume is going to be the same.

  • They're all in the same container in this situation.

  • And then we would add that to the number of moles of gas two

  • times the ideal gas constant, which once again is going

  • to be the same for all of the gases,

  • times the temperature divided by the volume.

  • And then to that,

  • we could add the number of moles of gas three

  • times the ideal gas constant

  • times the temperature divided by the volume.

  • Now, I just happen to have three gases here,

  • but you could clearly keep going

  • and keep adding more gases into this container.

  • But when you look at it mathematically like this,

  • you can see that the right-hand side,

  • we can factor out the RT over V.

  • And if you do that, you are going to get n one

  • plus n two

  • plus n three,

  • let me close those parentheses, times RT,

  • RT over V.

  • And this right over here is the exact same thing

  • as our total number of moles.

  • If you say the number of moles of gas one

  • plus the number of moles of gas two

  • plus the number of moles of gas three,

  • that's going to give you the total number of moles

  • of gas that you have in the container.

  • So this makes sense mathematically and logically.

  • And we can use these mathematical ideas

  • to answer other questions

  • or to come up with other ways of thinking about it.

  • For example, let's say that we knew

  • that the total pressure in our container

  • due to all of the gases

  • is four atmospheres.

  • And let's say we know that the total number of moles

  • in the container is equal to

  • eight moles.

  • And let's say we know

  • that the number of moles of gas three

  • is equal to two moles.

  • Can we use this information to figure out

  • what is going to be the partial pressure due to gas three?

  • Pause this video, and try to think about that.

  • Well, one way you could think about it is

  • the partial pressure due to gas three

  • over the total pressure,

  • over the total pressure is going to be equal to,

  • if we just look at this piece right over here,

  • it's going to be this.

  • It's going to be the number of moles of gas three

  • times the ideal gas constant

  • times the temperature divided by the volume.

  • And then the total pressure,

  • well, that's just going to be this expression.

  • So the total number of moles times the ideal gas constant

  • times that same temperature,

  • 'cause they're all in the same environment,

  • divided by that same volume.

  • They're in the same container.

  • And you can see very clearly that the RT over V is

  • in the numerator and the denominator,

  • so they're going to cancel out.

  • And we get this idea that the,

  • I'll write it down here,

  • the partial pressure due to gas three over

  • the total pressure

  • is equal to

  • the number of moles of gas three

  • divided by the total,

  • total number of moles.

  • And this quantity right over here,

  • this is known as the mole fraction.

  • Let me just write that down.

  • It's a useful concept.

  • And you can see the mole fraction can help you figure out

  • what the partial pressure is going to be.

  • So for this example, if we just substitute the numbers,

  • we know that the total pressure is four.

  • We know that the total number of moles is eight.

  • We know that the moles,

  • the number of moles of gas three is two.

  • And then we can just solve.

  • We get, let me just do it, write it over here,

  • I'll write it in one color,

  • that the partial pressure due to gas three over four

  • is equal to two over eight, is equal to 1/4.

  • And so you can just pattern match this,

  • or you can multiply both sides by four

  • to figure out that the partial pressure due to gas three

  • is going to be one.

  • And since we were dealing with units of atmosphere

  • for the total pressure, this is going to be one atmosphere.

  • And we'd be done.

- [Instructor] In this video,

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B1 中級

分壓介紹 (Introduction to partial pressure)

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    林宜悉 發佈於 2021 年 01 月 14 日
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