Hi everybody. This lecture is going to be about the gas laws. Now I mentioned when I was going over the chapter objectives that the gas laws individually aren't so important and I also want to say that I put a lot of extra stuff in this presentation for extra explanation. So I'm going to go through a lot of it pretty quickly because it's not super important.
So let's just go through this and see how we do okay so the individual gas laws have each have a name and a relationship you don't need to know the names of each gas laws and you don't really even need to know the individual gas laws because they'll all be contained in our ideal gas equation coming up so the variables we'll deal with when we're working with our gases are pressure and temperature, volume and number of moles. Those four things are going to be in a relationship proportional to each other and we'll describe that when we get to the ideal gas law in the next lecture. The individual gas laws are Boyle's law which is the relationship between pressure and volume, Amatins law which is also called Gay-Lussac's law which is the relationship between pressure and temperature, Charles law, which is the relationship between volume and temperature and Avogadro's law, which is the relationship between volume and number of moles. And all of these are keeping the other two things constant as we do those. OK, so let's take a look at the individual gas laws and see what they tell us about nature.
OK, if you go to this link, which you can click on or this link. which you can click on from the PowerPoint slide itself, not from this presentation. It'll take you to a video of me collecting these data. So these data are a measurement of the pressure of a gas versus volume. And you can see it's got this inverse proportionality curve.
It's measuring relative pressure. This is relative to the atmospheric pressure. So if we go back and we change these units, I'm sorry, so if we go and we change the volume units instead of plotting this is pressure versus volume. Let's plot this as pressure versus one over volume and now all of a sudden we have a straight line. That's how inverse proportionalities look when we plot them on a different axis.
Now let's change this axis which is in millimeters of mercury and its relative. Let's change it to absolute pressure and will leave it in millimeters of mercury and now we can see we've got this. Nice straight line.
The line I've drawn here is a data fit to a straight line. But the data points themselves are the actual data that I collected. So, and you can see this is a pretty good fit. The slope of this line is given by this number. And if we extend this line, it will go through to zero.
So, we have this proportionality where... When we go to an infinitely large volume, right, when v goes to infinity, then 1 divided by v goes to 0, the pressure goes to 0. So this is the relationship that Boyle's law tells us about, that there's this inverse proportionality between pressure and volume, and it goes all the way down to 0 pressure if we extrapolate. this line. So here's what the textbook shows for these two graphs showing that if you go from two liters to four liters the pressure goes from 0.6 to 0.3 right we cut it in half by doubling the volume that is how inverse proportionality works.
Okay that's Boyle's law which gives us an indication of how volume and pressure are related. So now we're going to go on to the next gas law, Amatans law, and this one we're looking at a similar measurement. We're looking at the pressure.
This time we're measuring absolute pressure, but we're doing it versus temperature. And again if you follow these links you'll see me collect these five data points and we can fit them with a straight line. This fits pretty well.
I am forcing this line on a certain slope and I'll show you why. So again we are seeing An inverse. i'm sorry we're seeing a direct proportionality this time pressure is directly proportional to temperature i didn't do anything fancy with the temperature units here that's just what the thermometer said now i want to re-plot this on a different axis a different scale so let's squish this up and here's the data points all squished up so here's zero degrees celsius and here's going up to 60. and now i have a lot of room going all the way down here uh to this point which is supposed to be hidden at this point but it'll come up in a second all right so this straight line that i fit these with if i extrapolate that line it will go all the way down and reach this point when we get to zero pressure so this is again we're extrapolating our data to the point point at which we would expect to see zero pressure if everything behaved like it did up here and what we see is when we get to this point down here where there's no pressure the temperature is minus 273.15 degrees Celsius this is where we get the connection between the Kelvin temperature scale and the Celsius temperature scale this point is what we call absolute zero this is the absence of energy the absence of motion we've taken out all of the the energy available and because there's no energy for these molecules to do anything they can't bounce off of each other and if they can't bounce off each other and bounce off the walls of their container then they've got no pressure and the pressure drops to zero so that's um where we get this value from it is zero that's a zero not not no zero Kelvin on the absolute temperature scale and we choose the absolute temperature scale sorry I click too fast we choose the absolute temperature scale to have the same size of individual degrees so one degree Celsius is equal to one degree Kelvin but the scale just starts at minus 273 so that's why we have our 273.15 is the conversion factor between celsius and kelvin all right um charles law is very similar to what we just saw but instead of measuring pressure we measure volume and we get the same kind of extrapolation here if we measure it on the celsius scale they all meet at minus 273.15 that's where the volume of our sample will go to zero no matter what pressure we start at right so the slope of these lines that all end up at this point are dependent on what the pressure of the gas is but they all meet at absolute zero okay and then the last one we're not going to use very much That's just Avogadro's law that says the pressure is proportional to the number of moles, which we'll see when we get to the to the ideal gas law. If we have twice the number of gas molecules in the same volume at the same temperature, we're gonna have double the pressure. We just have twice as many things bouncing off of each other.
So that's Avogadro's law. And like I said, you don't need to know these by name. You don't even need to know these individual relationships, they're all contained in the ideal gas law.