Section 5.8/9 | Coconote

Welcome to section 5.8 and 5.9. Alright, gentle people, we're going to continue our discussion about effusion and diffusion, and we're going to be talking about collision frequency. So let's go ahead and think about this little thought experiment. Let's say that I have HCl gas and I have ammonia gas. So I'm going to put this on either end of a tube that's filled with air. Now what I'm expecting to happen is that they come and meet, and what I will find is when they meet, a solid is going to form, and I can tell how far each gas has moved. Now if I do the calculation out, what I would expect to happen is that the NH3 would move 1.5 times further than the HCl. Now if I do this in real life, what I get out is that the NH3 just went 1.3 times as far as the HCl. And so the question here is what is happening? Well what's occurring here is that when I look at this tube, this tube is already filled with air molecules and those air molecules are going to impede or slow down the movement of my gas NH3 and HCl and that's because these things are going to collide with each other. So what I can do is I can measure how much they collide with each other and this is called the collision frequency. Now the collision frequency or the number of collisions I have per second are going to be dependent on a couple of factors. Concentration, average speed, and molecular size. So to illustrate this let's think of an analogy. Let's think about a movie theater and the idea is I want to go ahead and empty my movie theater and I want to see how many times people bump into each other. Now what I will see is concentration is going to affect how much people bump into each other. If I have a packed movie theater and I tell everyone to exit, I'm going to have a lot more bumping than if I only had like one or two people inside that theater. The average speed, if I told everyone to run out of the theater versus I tell people to calmly get up and exit the theater, well, the faster they move, the more they're going to run into each other. Lastly, the molecular size. Let's say I film my theater with really swole individuals, like Dave Bautista swole bodybuilders. So I tell these bodybuilders to exit the buildings. Well, the Dave Bautistas are going to bump into each other a lot more than if I had kindergartners. So if I had small toddlers or children, and i tell them to get up and leave the building calmly since they're smaller they're going to bump into each other a lot less now i can put all these factors in to one grand equation and so this is the equation for collision frequency so z is my collision frequency n over v so that's going to be the number of molecules over the volume Well, number of molecules over a volume, that's the same as a concentration. So that concentration term is going to be times 4 times d squared. Now, d squared is going to be the distance between the center of one molecule and the center of another molecule. So this is a measure of the size of each one of these molecules. And the last term that you guys see right here, this is a measure of velocity. You guys see the RT, the square root over the molar mass. So this is a measure of speed. So putting all these things together, what we can do is measure collision frequency. So why don't you guys go ahead and measure how many times an oxygen is colliding inside air. So what I'm going to do is I'm going to give you room temperature conditions. So this is going to describe the oxygen atoms that you guys have right around you right now. All right, gentle people, here's my equation for collision frequency, and I'm going to take this apart one section at a time. So the first thing I want to do is do that concentration term in blue. And so let's start there. I'm going to start with PV equals nRT. So I'm going to go ahead and rearrange this formula. I'm going to put n over V equals P over RT. And so in this case, I'm looking for small n over V. which equals the pressure divided by RT. Now my pressure is 1 atm. The R that I want to use in this case is 0.08206 liter ATMs mole Kelvin. And of course, I want to put my temperature in Kelvin, 298 Kelvin. What I get out of here is 0.041 moles over liter. So I want you guys to be careful here. I solved for small n over volume. And small n is moles. I want big N, which is molecules. So if I take that 0.041 moles per liter, I know that I have 6.022 times 10 to the 23rd molecules per mole. So the moles cancel out. And I also know that 1,000 liters is a cubic meter. If I do this calculation out, I get 2.47 times 10 to the 25th molecules per cubic meter. And this equals capital N over V, so the number of molecules per volume. Now you might be asking why I changed to cubic meters. Well, that's because of the next calculation that I'm going to run. D is the diameter of our molecule. And in this case, we're interested in the oxygen molecule, which is 300 picometers. This is 300 times 10 to the negative 12 meters, or in other words, 3 times 10 to the negative 10 meters. And so that's why I wanted to change the last calculation. into meters cubed. Now for our molar mass, remember like always when we use these types of velocity types of equation, we want to go ahead and make sure we put it in kilograms per mole. So an oxygen is 16.0 times 2 grams per mole, and so I can calculate that out to 0.032 kilograms per mole. Now I can put all of this together into my z equation. So z equals 2.47 times 10 to the 25th molecules per cubic meter. This is times 4. And then I get my diameter, 3 times 10 to the negative 10th meters. And I'm going to square that term. And this is all times my speed term of pi. And this time I want to use 8.3145 joules per mole kelvin. I want to put my temperature as 298 in kelvin. And then lastly, I put my molar mass, 0.032 kilograms per mole. What you guys will see is that I will calculate a z out to 4.4. times 10 to the ninth molecules per second. Now I want you to realize that those molecules are colliding. So instead, what you should write down is that this is collisions per second. What we really calculated was how many times those oxygen molecules are bumping into each other. So right here is the correct answer. And what you guys can see is the oxygen molecules around you are colliding with each other over a billion times per second. And that's why if you have a gas that's moving 300 meters per second, it still takes a while to actually diffuse through because it's going under so many collisions per second. Well, I hope that made sense and remember to stay safe, Ken1.

Now what I'm expecting to happen is that they come and meet, and what I will find is when they meet, a solid is going to form, and I can tell how far each gas has moved. Now if I do the calculation out, what I would expect to happen is that the NH3 would move 1.5 times further than the HCl. Now if I do this in real life, what I get out is that the NH3 just went 1.3 times as far as the HCl. And so the question here is what is happening? Well what's occurring here is that when I look at this tube, this tube is already filled with air molecules and those air molecules are going to impede or slow down the movement of my gas NH3 and HCl and that's because these things are going to collide with each other.

So what I can do is I can measure how much they collide with each other and this is called the collision frequency. Now the collision frequency or the number of collisions I have per second are going to be dependent on a couple of factors. Concentration, average speed, and molecular size. So to illustrate this let's think of an analogy. Let's think about a movie theater and the idea is I want to go ahead and empty my movie theater and I want to see how many times people bump into each other.

Now what I will see is concentration is going to affect how much people bump into each other. If I have a packed movie theater and I tell everyone to exit, I'm going to have a lot more bumping than if I only had like one or two people inside that theater. The average speed, if I told everyone to run out of the theater versus I tell people to calmly get up and exit the theater, well, the faster they move, the more they're going to run into each other. Lastly, the molecular size. Let's say I film my theater with really swole individuals, like Dave Bautista swole bodybuilders.

So I tell these bodybuilders to exit the buildings. Well, the Dave Bautistas are going to bump into each other a lot more than if I had kindergartners. So if I had small toddlers or children, and i tell them to get up and leave the building calmly since they're smaller they're going to bump into each other a lot less now i can put all these factors in to one grand equation and so this is the equation for collision frequency so z is my collision frequency n over v so that's going to be the number of molecules over the volume Well, number of molecules over a volume, that's the same as a concentration. So that concentration term is going to be times 4 times d squared. Now, d squared is going to be the distance between the center of one molecule and the center of another molecule.

So this is a measure of the size of each one of these molecules. And the last term that you guys see right here, this is a measure of velocity. You guys see the RT, the square root over the molar mass.

So this is a measure of speed. So putting all these things together, what we can do is measure collision frequency. So why don't you guys go ahead and measure how many times an oxygen is colliding inside air. So what I'm going to do is I'm going to give you room temperature conditions. So this is going to describe the oxygen atoms that you guys have right around you right now.

All right, gentle people, here's my equation for collision frequency, and I'm going to take this apart one section at a time. So the first thing I want to do is do that concentration term in blue. And so let's start there. I'm going to start with PV equals nRT. So I'm going to go ahead and rearrange this formula.

I'm going to put n over V equals P over RT. And so in this case, I'm looking for small n over V. which equals the pressure divided by RT. Now my pressure is 1 atm.

The R that I want to use in this case is 0.08206 liter ATMs mole Kelvin. And of course, I want to put my temperature in Kelvin, 298 Kelvin. What I get out of here is 0.041 moles over liter. So I want you guys to be careful here.

I solved for small n over volume. And small n is moles. I want big N, which is molecules. So if I take that 0.041 moles per liter, I know that I have 6.022 times 10 to the 23rd molecules per mole.

So the moles cancel out. And I also know that 1,000 liters is a cubic meter. If I do this calculation out, I get 2.47 times 10 to the 25th molecules per cubic meter. And this equals capital N over V, so the number of molecules per volume.

Now you might be asking why I changed to cubic meters. Well, that's because of the next calculation that I'm going to run. D is the diameter of our molecule. And in this case, we're interested in the oxygen molecule, which is 300 picometers. This is 300 times 10 to the negative 12 meters, or in other words, 3 times 10 to the negative 10 meters.

And so that's why I wanted to change the last calculation. into meters cubed. Now for our molar mass, remember like always when we use these types of velocity types of equation, we want to go ahead and make sure we put it in kilograms per mole.

So an oxygen is 16.0 times 2 grams per mole, and so I can calculate that out to 0.032 kilograms per mole. Now I can put all of this together into my z equation. So z equals 2.47 times 10 to the 25th molecules per cubic meter. This is times 4. And then I get my diameter, 3 times 10 to the negative 10th meters.

And I'm going to square that term. And this is all times my speed term of pi. And this time I want to use 8.3145 joules per mole kelvin. I want to put my temperature as 298 in kelvin. And then lastly, I put my molar mass, 0.032 kilograms per mole.

What you guys will see is that I will calculate a z out to 4.4. times 10 to the ninth molecules per second. Now I want you to realize that those molecules are colliding. So instead, what you should write down is that this is collisions per second. What we really calculated was how many times those oxygen molecules are bumping into each other.

So right here is the correct answer. And what you guys can see is the oxygen molecules around you are colliding with each other over a billion times per second. And that's why if you have a gas that's moving 300 meters per second, it still takes a while to actually diffuse through because it's going under so many collisions per second. Well, I hope that made sense and remember to stay safe, Ken1.

Transcript for:Section 5.8/9

Transcript for:
Section 5.8/9