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Chemistry: The Ideal Gas Law

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  • Type: Video Tutorial
  • Length: 8:39
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 93 MB
  • Posted: 07/14/2009

This lesson is part of the following series:

Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Final Exam Test Prep and Review (49 lessons, $64.35)
Chemistry: Gases (14 lessons, $20.79)
Chemistry: Ideal Gas Law, Kinetic-Molecular Theory (5 lessons, $7.92)

This lesson was selected from a broader, comprehensive course, Chemistry, taught by Professor Harman, Professor Yee, and Professor Sammakia. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/chemistry. The full course covers atoms, molecules and ions, stoichiometry, reactions in aqueous solutions, gases, thermochemistry, Modern Atomic Theory, electron configurations, periodicity, chemical bonding, molecular geometry, bonding theory, oxidation-reduction reactions, condensed phases, solution properties, kinetics, acids and bases, organic reactions, thermodynamics, nuclear chemistry, metals, nonmetals, biochemistry, organic chemistry, and more.

Dean Harman is a professor of chemistry at the University of Virginia, where he has been honored with several teaching awards. He heads Harman Research Group, which specializes in the novel organic transformations made possible by electron-rich metal centers such as Os(II), RE(I), AND W(0). He holds a Ph.D. from Stanford University.

Gordon Yee is an associate professor of chemistry at Virginia Tech in Blacksburg, VA. He received his Ph.D. from Stanford University and completed postdoctoral work at DuPont. A widely published author, Professor Yee studies molecule-based magnetism.

Tarek Sammakia is a Professor of Chemistry at the University of Colorado at Boulder where he teaches organic chemistry to undergraduate and graduate students. He received his Ph.D. from Yale University and carried out postdoctoral research at Harvard University. He has received several national awards for his work in synthetic and mechanistic organic chemistry.

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2854 - The Ideal Gas Law
And now the moment you've all been waiting for. We've introduced Boyle's Law, Charles's Law, Avogadro's Law, and now we're going to combine all of those observations into a single expression. And that single expression called the Ideal Gas Law might very well be the only thing you even remember about chemistry when you're 50. Pressure times volume is equal to the number of moles times the constant, which we'll talk about in a bit, times the temperature in Kelvins, . And this expression embodies all of those other laws. You can see that there's still an inverse relationship between and . That's Boyle's Law. There's still a linear relationship between and . That's Charles's Law. And there's a linear relationship between and . That's Avogadro's Law.
Now empirically you determine the value of . So you take a sample of gas. You measure its pressure. You measure its volume. You know how many moles. You measure the temperature. And from that, is uniquely determined. And turns out to be approximately with these units: liter-atmospheres per mole-Kelvin, which seem really strange. But if you think about the algebra, it's necessary to have units on that allow you to cancel things out as you need to in order for this expression to be true.
Now one of the questions you might have is what's an ideal gas? And the simple answer is that an ideal gas is just something that obeys the Ideal Gas Law. And it turns out that lots of gases, at modest pressures, around room temperature obey the Ideal Gas Law just fine. And that's why it's worth talking about it. But at a deeper lever, what we're going to see is that the assumptions about the Ideal Gas Law involve things like the fact that the particles of gas don't really occupy very much volume compared to the size of the container. A way to simplify that is to say that the particles are assumed to be point particles. You may have heard the expression how many angels can dance on the head of a pin? Well in this case it's how many ideal gas particles can fit into a container? And the answer is infinitely many, because each individual particle doesn't occupy any space.
And then the second thing that we assume--and we're going to talk about this later on some more--is that there aren't any interactions between the gas particles. They're neither attractive nor repulsive. So they basically don't even know that they're there, that each individual particle doesn't know that the collection of other particles is there. And those are the kinds of assumptions that we need in order to observe that the Ideal Gas Law holds. In particular, when we have a real gas like a sample of hydrogen, it's going to obey the Ideal Gas Law when the assumptions about the Ideal Gas Law make some sense.
So how can we use the Ideal Gas Law? And one of the things that we can do is we can calculate the volume of 1 mole of gas. And let's say let's calculate it at 0.00 degrees C and 1.00 atmosphere. Now the reason why I chose 0.00 degrees C and 1.00 atmosphere is because chemists have decided to give these two conditions a special name. And we call that special set of conditions STP for standard temperature and pressure. And standard temperature and pressure is just 1.00 atmospheres and 0.00 degrees C. Now remember this thing in Kelvins is something entirely different. But it's the temperature at which ice melts that we use when we define STP.
So we're going to calculate the volume of 1 mole. One thing to remember is, when we calculate the volume of 1 mole here, it doesn't matter what kind of gas we're talking about. So any kind of gas, assuming it's obeying the Ideal Gas Law, is going to occupy a volume given by this expression. So how do we use the Ideal Gas Law ? We can rearrange that to solve for volume. , and let's plug in the values that we had on the previous page. Remember temperature has to be in Kelvins, and this corresponds to 0 degrees Celsius. Plug this all in - 22.4 liters. Now to give you some idea of how big 22.4 liters is it's about the volume of a toilet tank, the thing in the back of the toilet. That's about 22.4 liters. And that's the volume of a mole of gas at standard temperature and pressure.
Let's look at another problem now. And the next problem we're going to look at is going to involve this. And what this is, it's basically a party canister full of helium. And helium is an interesting gas, because it has an interesting property. Don't try this at home, but... How many moles of helium gas are contained in a 10-liter cylinder at 25 degrees C and 120 atmospheres? The effect doesn't last very long because I'm inhaling oxygen and displacing the helium. And we'll talk about why the helium should be displaced quickly later on. But let's go ahead now and solve this problem.
Okay. Again we're going to use the Ideal Gas Law. We're interested in the number of moles contained in this cylinder. To remind you, the cylinder is this big. And we're going to have to make some approximations, because we don't know exactly what the size of the cylinder is. So let's say that it's 10 liters. That's probably pretty close. And it turns out that there's a gage on the front, so we can read off the pressure on the inside of the cylinder. And converting the pressure units here to our metric units, it's about 120 atmospheres. So we'll use those pieces of information. . That's an approximation. . And we have to make an assumption about the temperature too. We'll assume it's at room temperature. In other words, the inside of the cylinder is the same as the temperature in the room. We'll rearrange the Ideal Gas Law to solve for the number of moles, which looks like that: . Then we'll just plug in these values and solve for . We have that , never changes, and then we need to convert the temperature to Kelvins. And you've seen this a lot now, that room temperature is 298 Kelvins. We work all of this out and we find out that there are 49 moles. We've made some approximations here because we were just guessing what the volume was. But this tells us that there are roughly 49 moles if our assumptions are valid.
So the Ideal Gas Law allows us to bring together all of the stuff that we've learned up until now. And it allows us to quantitatively solve problems. Where before we were always looking at changes, now we can actually look at how different values of these numbers together with this new constant give us answers about the real world.
Gases
The Ideal Gas Law and Kinetic-Molecular Theory of Gases
The Ideal Gas Law Page [1 of 2]

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