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About this Lesson
 Type: Video Tutorial
 Length: 6:57
 Media: Video/mp4
 Use: Watch Online & Download
 Access Period: Unrestricted
 Download: MP4 (iPod compatible)
 Size: 74 MB
 Posted: 07/14/2009
This lesson is part of the following series:
Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Gases (14 lessons, $20.79)
Chemistry: Gases and Gas Laws (6 lessons, $8.91)
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, oxidationreduction 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 electronrich 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 moleculebased 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.
About this Author
 Thinkwell
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You know when you go to recycle plastic bottles and the recycling place asks you to crush them so they don't take up so much space? Did you ever notice that if you leave the lid on, they're not really very easy to crush? In fact, they're impossible to crush. Of course if you take the lid off so that the gas can get out, then that allows you to crush them. But so long as the lid is on, they're pretty tough to crush. In fact, it seems like the harder you squeeze, the harder the bottle is pushing back.
What you're observing qualitatively is that in trying to decrease the volume of the bottle, the pressure on the inside is increasing. Gas is compressible, so you can squeeze it a little bit. If this were concrete, you couldn't even do that much. But by squeezing and decreasing the volume, you're increasing the pressure on the inside of the bottle.
In 1662, Robert Boyle quantified that relationship, discovered it and quantified it. And the way he performed his experiment is he took a utube like we've seen before, put some mercury in it. It's closed on one end, and there's some amount of gas on this side. And that allows him, because he knows the geometry of the tube, he can measure the volume. Then by adding more mercury, what's going to happen is some of the mercury will come up on the left side, but some on the right side, but some will come on the left side as well. By adding more and more mercury what's going to happen is he's going to decrease the volume of his gas over on this side.
Here's an example of some data he might have collected for a sample. At 1 atmosphere, where the two levels are exactly the same, the volume is 0.7 liters. When you go to 2 atmospheres, the mercury on this side is going to be higher still, the volume decreases to 0.35 liters. At 3 atmospheres and 4 atmospheres, the volume goes down a little bit more. You'll note that there's an inverse relationship between pressure and volume. And one manifestation of the inverse relationship is that the product of the pressure and the volume is a constant all of the way through. This is a discovery of nature. We're going to call it Boyle's Law. And Boyle's Law is sort of something that Mother Nature hands us and people just come along and discover.
While keeping the temperature of a gas fixed, if you increase the pressure, then the volume of the gas decreases proportionally. Thank you, God. Another way to make that statement is that pressure times volume is a constant. And we do have to have some restrictions that were sort of implied in the experiment that we did before. Which is for a given amount of gasin other words we can't change the amount of gas that's inside the tube, and at a fixed temperature, so we can't change the temperature of the experiment.
If we plot up Boyle's Law, so this is a plot of the data that I showed you just a second ago. You can see again that there's this inverse relationship that at high pressure, the volumes are small. And as the pressures decrease, the volume gets larger. Mathematically, this curve is something known as a hyperbola. And the adherence to Boyle's Law for a gas is actually pretty good so long as we don't get too far up on the pressure scale. So long as we stay at relatively modest pressures, the fit of the data to PV=C is pretty good.
It turns out that there are a fair number of toys that are based on Boyle's Law. And the one that we're going to look at right now is something called a stomp rocket. This is an example of a stomp rocket. What we have here is a container that's compressible that has some air in it. Everything is at 1 atmosphere right now. And we're going to mount a rocket on the end of this tube that has some volume. Then when we press down on the foot pumpso normally this would be on the floor and a kid would jump on it. Then we decrease the volume of the foot pump, increase the pressure in the system. The response of the rocket to the increased pressure in the system is to go rocketing off. So here we go.
What is the principle behind that toy? We can imagine a problem such as the volume of a stomp rocket pump changes from 1.03 liters, that's its initial volume, to 0.47 liters, that's its final volume after we've jumped on it, when stepped on. But if the initial pressure is 1 atmosphere, so before we do anything, everything is equilibrated at 1 atmosphere. What is the final pressure? What is the pressure going to go to after we've jumped on the pump, and just before the rocket takes off?
We can solve that problem by using PV=C. And another way that we can express that is to say that is to say that if PV is a constant, then the initial pressure times the initial volume, that's P[i]V[i], is going to be exactly equal to the final pressure times the final volume, P[f]V[f]. We have P[f]. We can solve for P[f]. We're interested in finding what is the final pressure after we've stepped on the pump. So we'll solve for P[f], which is equal to P[i] times V[i] divided by V[f]. And we'll plug in the values from the problem. P[i] is 1 atmosphere. V[i] is 1.03 liters, and V[f] is 0.47 liters. We can cancel out the liters in the numerator and the denominator. That's going to leave us with units of atmospheres. That's exactly what we want because we're trying to solve a problem where the question was what is the final pressure? The units have to be atmospheres. And if we plug this in to our calculator and work it out, we get to 2.2 atmospheres.
So what have we learned? We've learned that there is a relationship that was given to us by mother natures called Boyle's Law. It's PV=C, or that there's inverse relationship between pressure and volume. When the pressure goes up, the volume goes down. When the pressure goes down, the volume goes up. And then finally what we did was we showed that there are toys based on this relationship, and by decreasing the volume of the pump, we increased the pressure. And this is exactly the same way a bicycle pump works, for instance. And it's this higher pressure at the end that causes the rocket to go shooting off into outer space.
Gases
Gases and Gas Laws
Boyle's Law Page [1 of 2]
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