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Current time:0:00Total duration:8:57

Video transcript

welcome to a new planet this is actually a planet I'm going to call planet gram and you can already see the blue alien on this planet and the reason I want to call a planet gram I'll be honest is because we're going to talk about Graham's law and I thought it'd be kind of a fun way to remember it and think about it so before I came to this planet I actually brought along with me a giant pot and this pot is like a cooking pot but inside of it and I put a lid on it of course but inside like I've got some molecules of oxygen actually from our home planet Earth I brought some molecules of oxygen and I'm drawing them as Oh to two molecules or two atoms rather of oxygen in one molecule of o2 I've also got some carbon dioxide here and of course carbon dioxide in the name you can already hear it it's got dioxide so it's got two oxygens as well almost looks like a little bowtie right so I've got a few of these molecules and I was very careful I actually made sure that in my pot I had 50% carbon dioxide's and 50% oxygens so I've got equal proportions of both so I have a friend over here an alien friend and I asked my friend to stand some distance away from my pot and you can see I'm actually cooking my pot I've got some you know fire with fire wood underneath it and I say you know please stand ten feet away from my pot sir and this little alien friend is a good friend of mine so he says no problem and the reason I'm asking him to help me with it is because he has a very special nose a very very special nose he's never in his life smelled oxygen or carbon oxide he's you know lived on planet gram his whole life and planet gram has these little green molecules but he has such a special nose that he can actually detect whether he's smelling carbon dioxide oxygen so I'm going to actually take this lid off and I'm going to say hey you know if you detect with your special nose either one of these let's say that these molecules one of them goes over and kind of goes into his nose if you can detect it please let me know which one you're smelling and and that's my test and I want to know which of these molecules oxygen or carbon dioxide is going to reach knows which is 10 feet away first so it's basically a race and you can make a prediction right now as to which molecule you think is going to get to his nose first the oxygen or the carbon dioxide now you might think well it's very easy there's a direct path but actually remember these molecules these green molecules in the planet atmosphere are whizzing around right they're going in all sorts of different directions and as a result they're going to smack into our carbon dioxide or oxygen molecules as they try to make their way over there and kind of a random fact but an interesting one to think about is that in our atmosphere we have a lot of nitrogen right a lot of nitrogen gas now if you took one nitrogen gas molecule which is n2 and let it go and measured its speed and kind of clocked it it'd be going at about a thousand miles an hour but the only reason it doesn't actually go that speed in reality is because the molecules of nitrogen they actually will smack into each other and bounce off of each other millions and millions of times every second and so because they're smacking and colliding constantly they never really reach those those real potential speeds they go much slower so really what we're talking about is when molecules are bouncing and clanging into each other and slowly making progress towards our little aliens nose that is the idea of diffusion they're going to kind of rattle around rattle around and slowly make their way over to his nose and maybe if I came back like let's say ten minutes later maybe this little oxygen would be right here maybe you might have a little carbon dioxide right here you know slowly kind of making progress towards the nose that's kind of what we're trying to figure out which one we'll get over there first so you've had time to think about it and I'm actually going to tell you how I I think we should approach the problem which is thinking back to kinetic energy now we're heating this thing up so we're putting thermal or heat energy into the molecules both types of molecules are getting the same amount I've got the oxygen getting some kinetic energy I'm going to put a little o for oxygen and remember the formula is one-half mass times velocity squared and it's going to equal or should equal the amount of energy that my carbon dioxide is right and I'm going to do that as a little c4 carbon dioxide so these two molecule types should be getting the same amount of energy now remember that's not like it's one molecule we're thinking of we're thinking of many many molecules right so first I'm going to have to change these units a little bit a more mass is going to change to molecular weight molecular weight because again I'm thinking about the individual molecule right so I've got to figure out what these molecules weigh and V is going to change over to rate or diffusion rate and the reason I'm doing that is because again I'm thinking about the overall diffusion of the gas it's not like I'm betting on any one molecule I'm betting on the entire population of carbon dioxide molecules beating out the population of oxygen molecules or vice versa the the oxygen molecules beating out the carbon dioxide molecules but not an individual molecule so I have to think of the average rate that those molecules are moving so let me rewrite this equation right it's going to now be 1/2 times molecular weight to put it in parenthesis times diffusion rate I'm just going to call it rate rate and we'll call it rate one and one will be for the oxygen in fact molecular weight one can be for the oxygen as well and over here I'm going to say it equals one-half times the molecular weight 2 and 2 refers to carbon dioxide and rate 2 refers to carbon oxide as well and I really don't need to keep carrying on with these halves right I can just multiply both sides of the equation by 2 and get rid of them so that makes a little bit easier and I almost forgot I have to square both sides that would have been a mistake right I forgot to square them earlier so now I've squared them and let me actually rearrange it to make it a little bit neater in the new color so let's let's do this so let me write it out nice and neat and this is actually going to be Graham's law so all I'm doing is rearranging the formula I've got rate 1 this is the diffusion rate of one molecule divided by the diffusion rate of a second molecule and then the molecular weight on the other side of the second molecule divided by the molecular weight of the first molecule and you do a square root of this side so that's just a rearrangement of the four but what I've written out for you is now Graham's law it's basically kind of taking you know the kinetic energy rule and kind of rearranging it to make sense for molecules and let me make a little bit of space here and so that an extension of this would be if you're just thinking about one molecule then the rate the diffusion rate when I say rate I mean diffusion rate is going to be proportional to the square root of the molecular weight so let's figure out how to apply this to our little riddle right we wanted to know whether oxygen or carbon dioxide is going to diffuse faster and I can now go back to our periodic table and look up oxygen I know that the molecular weight is 16 here in carbon is 12 and that means that Oh 2 is just 16 times 2 so the molecular weight is 32 and carbon dioxide is going to be you know two oxygens plus 12 more so it's going to be 44 so these are the molecular weights of carbon dioxide and oxygen so basically what I do is I just plug them in and I say ok let's plug them into the formula let's use this one right here and I'm going to call rate 1 my oxygen rate so what's happening with the rate one will say well rate one is rate of oxygen I'm going to write a big oh here equals the square root of let's make sure I stay consistent I said one was oxygen so it's going to be 32 down here and 44 up here right and then that's going to be multiplied by rate of carbon dioxide and I'll put a C for carbon dioxide so what does this work out to be that's one point one seven I just punch it into the calculator so really the diffusion rate of oxygen so the diffusion rate of oxygen is one point one seven times faster this is our answer times faster than the rate of carbon dioxide so that's our answer right the oxygen is going to be the winner so it's going to move faster this is going to move a little bit faster and it's going to get to our alien friends nose first so this is the power of grams law it's basically telling us that hey if you have a small molecular weight you're going to be able to diffuse pretty fast