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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

• 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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# 分壓介紹 (Introduction to partial pressure)

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林宜悉 發佈於 2021 年 01 月 14 日