Lecture 21. Kinetic Molecular Theory
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Title 
Lecture 21. Kinetic Molecular Theory

Title of Series  
Part Number 
21

Number of Parts 
23

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CC Attribution  ShareAlike 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license. 
DOI  
Publisher 
University of California Irvine (UCI)

Release Date 
2013

Language 
English

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Subject Area  
Abstract 
UCI Chem 1A is the first quarter of General Chemistry and covers the following topics: Atomic structure; general properties of the elements; covalent, ionic, and metallic bonding; intermolecular forces; mass relationships. Index of Topics: 0:00:28 Gas Stoichiometry 0:08:51 Kinetic Molecular Theory of Gases 0:12:20 Average Kinetic Energy 0:15:32 Kinetic Molecular Theory and Pressure 0:19:52 Speed Distributions 0:24:27 Root Mean Square Speed 0:35:43 Diffusion and Effusion 0:37:30 Effusion Application 0:40:26 Diffusion and Effusion 0:44:00 Gas Effusion

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Computer animation
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so we have sort of 1 last thing to finish up that really belongs last classes material and then remove and the kinetic montage here gasses so before we can actually move onto that I wanted to the 1 last example this 1 so we're going to start there seeming noticed that the format of the solid similiar to you as well ,comma area have hydrazine course that something I would expect a name like that you could just it Dynegy in touch Idaho In the beginning of this reaction and they tell you how much Of the hydrazine reacts to reduce how much of the nitrogen and they want to know what's the 1st thing he also so 1st of all what is virtually all with flulike formula that no 1 remembers close there's an actual under the theoretical isn't mine it's over again but I think it so good actual point that Governor of undermining the actual minus the radical over theoretical What is that there is something Percent area so we don't have to do a lot in this class just because you know we give you problems and so there's not really a person but it's a good thing to remember for lab but so did you know that so what we have to figure out missing Arizona these right visiting at the actual yield which is how much we need and want to figure the theoretical yield which is how much we could have made it every little bit of reacted and there is no loss there is no side reactions know anything so we had to remain in there so for theoretical and a slowing of the rate cut we do that when we started we started down the reacted to theoretical early we start from the the pole reacted very well what happened in every little bit of those reactants react to that or a source starting on the 2 . 4 5 grams of hydrazine and we want to know the person feels so we know how much nitrogen we have sold at the I'm sorry and to 190 can we just go from GM to GM not usually years has in we need to do and not easily so what we need to go through mall so we need to do that conversion factor every needed another conversion factor to go from most malls and then do we need to convert 2 grams of controversially Leavitt malls doesn't matter in universe so if actually matter because what's going to happen is that if you converted it on grounds it would just ended being both the top and bottom multiplied by the same so doesn't actually matter so let's leave animals because it's a little bit easier as 1 less conversion factor do and if we look at this when we say what's this going to come out with me have a volume of temperature air pressure so a Republican is over there most likely plans and it's a step in the need to do so where do we get the summer In would we get this summer from now is balanced take a quick look at history and yet it's balance so we're OK they're so worried the numbers that go here nearly 1 in 1 day so we have that OK so now about 1 part now we have to go through into actual suffers permanent straight demonstrators which were saying Well let's say we have we use all this out and there's nothing goes wrong with the reaction the 100 per cent yield some of them now we get to find out how much we actually made so what are we going to do to figure that out would quit areas on the other side and wearing a well what we have a volume temperatures in the air pressure and we want so were selling for it's now celebrating where are we going .period which addresses the at 8 . 3 1 and no 1 has a unit of tools and and we had . 0 8 0 0 8 2 1 and now it has leaders atmospheres animals which are new ideas and for temperatures 295 K and we didn't up to now I do it if we have . 0 3 1 0 malls until so now we just go ahead and kill instances the percentage of forget 1 thing whatever yeah and the percentage of trader person granted the question here is he had previously at 40 45 per cent so this was not absolutely horrible event Oh you mean rather than just just putting in more "quotation mark I solving either year you're solving for when the actual reactants of someone actually matter in this case if you used end because both of them would just be doubles breaking have doubled this 1 and you'd have to double this 1 but really when you're talking about the same yield you 1 person of an actual ,comma like an actual species that you have that you can kind of isolating users on this is another have so many have commentariat so which will have no theoretical was actual this is a question that comes up a lot of people makes up 1 example I actually sold you want to think about what you actually have as opposed to what you could possibly have so
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the idea here is we start with actual being what we actually obtained at the very end What if we were doing this problem we could isolate and we could use and so when we look at this and that's going to be this amount because it produces so it actually makes that much where as opposed to the theoretical that's what we figure out using strictly amateur if were given it's kind of a figure when you 1st look learning spectrometry right we tell you Hey here's a reaction when we say we give you a certain amount of these and we ask you to sulfur in say full how much product anemic week I'm alive a little bit when we ask you that because we're saying it's 100 per cent yield we give you that so that's the theoretical moving on some sort of poverty rate and now we can move on the kinetic model but it still weak start started with the ball properties like came the gasses we said Hey if we take assume a goodsized amount of this and we can measure it's pressure as volume as leaders and the we can measure all of this and we need some explaining just sort of kind of a on a little bit of what we're doing knew about what these properties were right so if we raise the temperature for instance what happened to the body raises temperatures in the air mattress tire example against bigger and is so that know the reverse of that if we call them down they got smaller for what we had in actual like a container that couldn't move what happened to the pressure that if we if we raise the temperature would happen to the pressure increases cannot bigger like the balloon did remember when we shot the balloon it can actually get bigger and smaller to size so instead of actually going change in the pressure would go up if we made a Gullfaks there if we need it get hiring would go down media all and we walked through all of those but we never really gave the real reasons for it started explaining a little bit in the sense when I told you about that you know what we took all of the terror that appeared headed as wander around has actually touching on management theory when he did that now and I have a little bit deeper into that sold the what we need to start with nominal kinetic energy actually it's right there in that brief little section the fundamentals there about that but this is going to kind of touch on that idea that still with not experience gas is a lot of is what we have to assume about the gasses the exact thing is for the ideal gas loss because the idea that follows side explaining that the ball properly the kinetic marking the theory goes a little more into what's actually going on the molecules sold just like before 1 AM that the molecules are .period masses and what that means is that all of the masses in this infinitesimally small amount of bodies there is no volume the volume is 0 but they're still you constant rain emotions Siemens before right we see the gas at any particular area of direct that is moving around randomly and all collisions were last what called elastic collision collision means what happens to the energy and a collect in elastic collision he had you don't lose any rights they might bounce off each other and maybe 1 has a different energy than used to but the overall energy between those 2 are the same so that's elastic collisions so energy is transferred the portal energy remains the same so once again just like the idea that the gas molecules are neither attractive nor repulsed so is no interaction right you have to gas molecules in the coming year each other they're not attract each other they're not going to repel each other forward for this theory no cost of all this is true for real gasses now also courses in the news in the Times breaks down will talk about that at the end of this chapter average kinetic energy is proportional to temperature so that means as you increase the temperature what happens to the kinetic energy it increases no notice I say average does that mean that every single particle increases when you increase the temperature yet most of them are going to in order to shift but it doesn't mean that they all have 1 exact temperature knew that there's a range of temperatures and we're just looking at the average so alone all these and more detailed now that was the domestic average kinetic energy is your soul at 2 different temperatures of gas molecules that could have the exact same energy so what what we wanna look at here is with the masses so we need to look at this equation 1 more time and we need to look at this so I see exact same kinetic energy now if they have the same kinetic energy but they have different masses what else has to be different velocity will explain his new and secondary assisting here the source just colony for so 1 onehalf in the square that's that's the kinetic energy you're used to seeing so if the kinetic energy of 2 classes at the exact same temperature we say clearly take nitrogen would come at the same temperature I'm telling you the kinetic energy is going to be the same yet the masses are that means the speed Hassan different right some inversely related so if what that means is the number of helium and nitrogen 2 things at different answers they're going to have the same kinetic energy as if they're in the same temperature so nature's masses bigger so what is it about the velocity it's going to be smaller pay so the higher the masses the smaller the velocity is going to be as some given temperature so that's what I mean by inversely related now they're not directly enormously related because that's where rights of his enemies square roots and there when we actually subculture so let's quickly go back to the simulation this website that I like so much of it is that all about as planned before class so let's look at this before we had done this would only looked at 1 sort of particle I just showing you the blue ones but this scenario which probably if you went and played on like asks you to use saw that you could also put a couple of different types of gasses into it so you can put a lighter species and you could put a heavier sentence so I put a lot of room here were going to be doing a couple different things of this today so if I had this will really like species is shown making smaller which we have to assume they have no volume can't see something has no volume so you have to do that we can heavy species this doesn't job of showing you the Handbook is the speed difference here definitely we can see that so that helps you remember you know you have certain visual picture of it to now if we call it down things that happened to the average speed both still slowdown right now noticed a slowdown but the ball still going to be slower than the rather than 1 still the smaller 1 that welcome back and forth to the
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city dance but it soon exEngland talk about pressure so while I haven't really discussed with 1 actually called pressure so
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if you think about this container and was a what's causing the pressure here 1st of of all what happened by and see what's going to happen to the pressure to go out and asserted measure what's happened this view the molecules it's kind out of it what I causes pressure if we want to think about like a balloon for instance because you can change the volume without changing the pressure was it's a balloon expands a single simple terms hardware maker will expand however think how vital answers questions the area OK so why would that make it expand is more particles most particles and pushing against the rubber on the balloon right so all my breath going into the balloon is pushing the balloon out so the air molecules are pushing on the balloon its analysis put it originated here believes that we can increase the pressure so if I raise the temperature isn't going faster they're hitting the side of the wall faster if I add more water molecules and now the hitting the walls at the same speed but there's more of the hitting the walls so both of those will raise the pressure so that's what this slide as in words so our culture is created by the collisions on the container fact so it's the molecules hitting the edges of the current container that's causing the pressure the faster the molecules hit the more pressure there's going to be right it's the new hitting it with more force and so there's going more pressure now by that same token so this would be like I'm raising the temperature so this this Baldwin is what I did when I increase the temperature now this bullet point is what I did when I said How can you make a more frequent well you put more molecules and there's 1 way also just by raising the temperature it increases the frequency right another going faster and so they're hitting it more often so now let's think about how each of these relate to the idea of gas what do we know happens to pressure as temperatures rose it goes up to write and now we can see what its temperature goes up what happens to the speed it increases so does the hit the wall hard or soft good so temperature increases at the pressure increases as temperature increases because of that but now the more frequent wanted that relate more molecules rate and temperature actually since the so works because this works would be the more walls of the pressure if you add more animals what happens to the pressure increases and that's because you're from making them the molecules hit the ledger the continuum so this is definitely regulates ideal graphite explains why the ideal that work I'm in your book and has a pretty intense derivation of don't worry about it that's right edges but that there reading Houston's the it's interesting but don't memorize it now consider this a great again so I hand waved away the you the Union Square right I do exercise that was just call before now back talk about that and if so what is this thing that I put in there instead of the wall that average molecular species so it's like glossy but now I'm saying is the average velocity over all the molecules because now we can't just pinpoint 1 molecule and say OK you had that speed is so let me and everybody else around the house sp that's not how gasses work there's always going to be a distribution to it so this is the average molecular speed so and history a graph of this adjustment but that this is always what you is using the same way as you use velocity for the most part you be given it I would tell you that you are sports have you calculate it with a different equation of underlined here in a minute 1 of the 2 so you use it just like velocity we need to know a little bit more about in the back of your hankies asking questions was the writing a little bits fewer seconds so we're going to this next flight and I know it's going to be a graph of all but at twoyear 2 different but let's start with this 1 so and that's what we're looking at nitrogen in just nitrogen what's the difference between the 3 back temperature and having so it grass ,comma like this before where we had something down here I think lacks and we thought it might even wavelength and number of photons over here and now we have as molecular speed so this is a particular speed that any given molecule could have and this is the number of molecules so this is like a cow it saying how many molecules have the speed so sold think this is college agreed distributions right you if you going great distribution online and Tripoli initiated this many people this this new people that it's the same idea only now it's a constant instead of art so if I were a point here you could say Well this many molecules have as much speed now do we don't really have to have a number here the right because all of this is just in relation to each other so just like in the distribution you don't care how many people died you know 75 per cent you just care whether that was the average the same thing here we care about the approximate number here as opposed to here as opposed to the count but it said now was to look at what's happening and badgered temperature is increasing what would you expect what happened to your speed increased to without having so this is good that I get people sometimes your ship is going down right but the people in Dallas just because the distribution is being spread out it's being stretched so where is this average speed at about I want 250 so if you're inferior averages somewhere around the peak this is actually a gutsy and so it's not right at the peak but it's close to the figure averages somewhere around here it's about 250 what's your average above 300 you know just started 408 yet selected the backup that is 400 bigger than 250 that so deftly that know what others thought about where that new approximately a 750 something like that so that a bigger soldier peak is getting smaller but that's just because you're stretching the distribution of your making it wider in so the number of molecules with any particular speed is going get smaller because you're giving them a wider distribution speeds now it's not just that the molecules can be from 0 to like 758 there's hardly any about it for 300 K knocking from 0 all winter to like you know about 1200 before it gets really really small 700 can go 0 to like 1700 before it gets really small so make sure you realize that effect and this shows you that as your temperature increases so does your speed it's just that now you have a wider distribution of molecules molecular speed the half of it so that takes care of temperature and speed now let's look it over here if you get this
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1 shows all at the same temperature estimates that 300 :colon but now what's the difference the masses the masses that if so what you told you masses what happened as something gets bigger it gets smaller and something gets smaller it gets past soul of chlorine nitrogen and helium which 1 would you expect in the past helium and that's exactly what we see right because what the average speed 300 will receive 250 someone that average speed here 500 inch average speed here 11 inch something like that so we can see that that's how it's getting faster as we go along this is a really small distribution is at a low temperature at a low speed this gets a little bit faster and a little bit faster that so that we I wanted to I could expect you to replicate the sort of that's not beyond you the ability levels stand in for the final exam I can also give you the graph and then ask you to label it for instance I could do this to leave off 100 300 700 and ask you put those on the graph for me I could you give you this and leave these asking to put it on there for me those are all sorts of things like that I had actually questions about that just don't nature square speed still going is still kind of getting into that remains wary but according kinetic theory of gasses the total kinetic energy per mole history has you don't necessarily have to realize why if you're actually dying to know on command office hours allotted to the derivation of the book but for the examiner needlework comes from just able the use it so everyone is the kinetic energy of 1 Adam is that so if you're thinking this is kinetic 1 out right now such a the for talking 1 now if we want a seat and Adams this is going to be 10 times that so this is getting in the way this comes from what the mall while at 6 . 0 to transcend the 20 3rd arms race so a final that the kinetic energy of 1 Adams equal this I know that the kinetic energy at 10 Adams is equal to 10 times that in order to get a new 1 mold is equal to 1 mole times on is Moeller Mass this is essentially so this gets into another equation that we have and this what I do want you to know how we arrived at this how we were able to get this equation so I give you this result then I think that this is the kinetic energy of a more about once its derided different way and I tell you that now we can derive the kinetic energy of a mobile left Kansas way too we can Well if we know the kinetic energy of 1 adamantly know that that's what happened the squared we multiply that by alQaida's number and know the kinetic energy of a mole so that the mole times onehalf in the square earlier conveying unnecessary what is it really average speed we can think of it as the so did animal and we multiplied by the kinetic energy equation that we've known since either school come 1 fewer fundamentals depending on when you and I and we set equal to those of the other equation that now giving you and told you about now is very different the average speed so we're going to solve the great and this is the Algebra II I. taken this and we divide everything across now we have 3 happened 3 RT divided by an which is your Moellemann squaring it so that we can fall for this but 1 resembles what I told you that I said this is true for mold Adams it comes kinetic molecular fearing we've now solids for kinetic molecular theory and said OK well let's set this result that we get from the clouds molecular theory and send people to the kinetic energy that we know and love that we know a lot of great love us and her grown like that now we solve the you us and now we have this equation for you on that that so this is another equation that we have that we can use so we won't solve the average speed we can go ahead and we can fell into 3 RT over and yes the 0 remains squared so she are announced stands for this that the answer square in question I now must go ahead so 1st actually analysts look in the summertime make sure that it agrees with what we know what we know about the average speed of molecules as mass increases as matter increases what happens in the United States In the the operate mass increases the speed decreases in that happened here if mass increases with Annapolis speech industries so that it goes along with what we've already seen yet all governor's number yet so don't forget any enlightened use Robert Abbas number sort of a shorthand notation it's easier than 6 . 0 2 times in the 20 3rd but it's still a similar amount and you'll see it in your book beer likes call fancy light but and we just talk about that and I never enough yeah all question why are using 2 years so you have to have a look at what you're dealing with here what temperature do we have heard we have held and we have math did they are and that we had before have anymore where the masculinity had leaders atmosphere :colon and Moll no mass you'd already what what did we know does have massive hidden inside jewels so marijuana use that the jewels 1 the 8 . 3 1 on the question yet the yeah on this so if you could double the malls you would have double the amount of kinetic energy but not average speed because it would be divided by the number of malls right so if I double the point value on test does that change Europe average will not really because you have doubled over .period right it's the same idea
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here if you don't change in average by doubling the number you change the total that you don't change the actor anything else that's a good questions so what's your example only then the chances a computer spoiler but that's OK to calculate the Hamas of helium and nitrogen molecules so this time I was trying to calculate the ruling squared speed so we have this equation now we can use this equation elderly derided remember I don't care if you know where the 3 have 30 comes from but I would like you to be able to explain how we got this equation like we did last flight I'm it sold helium 1st so we just basically fell have all I ask is for the remains where all you do is filling your numbers now I say all you have to do with a little bit of hesitation now because you do have to watch your units and watch all of that you need to make sure that there it is up to the is an 8 . 3 4 3 1 4 so the jewels for propelled animal and then there's 1 other thing you need to make sure you do that so many people forget what he's embarrassed this is kilograms rate so if the Moeller announced that it has to be in telegrams and wider latitude telegrams because this is Jules and Jewels has kilograms and don't get control the FIU for energy but it's the 1 compound units were made up of different things and so you have to go ahead and you have to be taken realize this other telegrams that in this has to be converted kg arrested have problems I'm so if you make sure you do all that I mean you can just go ahead and solved so on and it's just going into the equation but making sure you use the right are and that you convert the all mass down 2 kilograms from and if you do all that you want units careful enough you'll see that meters per 2nd which is what you would want for speed yes the it's it's the other constant for are so I give you 2 values are of you knew that .period is the 0 . 0 8 to 1 which is the leaders atmosphere 1 and then I'll give you this 1 which is the jewels for couple so what both of those will be given you will have to get America between them Of the nitrogen seems think again remembering you have to convert 2 kilograms so killing and promote that a little easier than some of the other instances we are kind of your final exam review time remember when we were in water we're not chapter and we had to make sure we can from from the periodic table mats wearing converted into Adams right where converting into kg per head this is easier than that because it's just kilogram from all so don't know when you start studying for quantum don't forget about that don't forget a lot of times in that case when you're solving for things like that the parolee whaling during kilograms for Adams don't do that here this is kilograms per mole so make sure you recognize the difference Algerian you cram sessions that everything is getting combined the different this one's kilograms from so you can bring 2 kilograms per mole say with me India and this is 1 things that comes up on the example of inquiry on most the time when we were going to roll wavelength we wanted kg per up units are more and yes he said a lot louder yeah that's the nascent into in kilograms from also it's just that 28 grams from all divided by House and so we get back I on next so this kind of this kind comes with yeah yeah I identified as such is the reality is that have the island at got temperature anything else then again so next question and that kind of office so he leaves that right we can we look at this and we can see that we can see it on the after and also expected because it's it weighs less so sold to skate gravity a molecule must have a certain velocity which is more likely to escape Earth's gravity the will the phosphorus along with some more likely to have the velocity that facet of 60 per yet so and about the composition of the atmosphere is more likely to be having a shouldn't been helium yeah so the actually summertime helium the Knicks gates so what's left later barrier of and so only 1 of the places where I got this 1 question from had had asked about how does this relate to the composition of the atmosphere and kind interesting I don't normally think about where the atmosphere comes from comes from a lot of places but the idea that helium would state more often than we would lose a lot more that to you know how it away from the atmosphere there from gravity and what we would like to switching gears a bit still cannot molecular theory but a different part diffusion indices so did it intends to Newark gets talked about was the time because the little it's not exactly normal in life to be letting something into an empty container right normally 1 of the container there of some sorry to surrender mixture of air and sold what actually is lower this actually diffusion if I had a helium tank here and squirted helium out into their would letting the helium diffuse into the air it would be mixing with the gas that's already around now there's something else called each year in the fears of the big difference that's where instead of taking a gas and putting it into another gas of you're taking gas and putting it into an empty containers in my antiunion there's nowhere in the area at the back of the so it would call for a small containers of difference to news talking about fusion normally have a very small area that gas is allowed to flow from 1 to the other and you could let it you go back and forth or maybe you you want to go flowing for a different purpose where top honors Salinas certain 2 definitions for you if you don't you probably already heard of but now we defined a little bit better it's mix the 2 2 gasses mixing in the fusion which is going from a container into an empty containers back now before we start talking about the massive diffusion effusions there's there's an interesting applications of fusion that I heart worth talking about "quotation mark more pictures of surrogacy of explains Irish talking about and that's element
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uranium enrichment this is 1 of the ways that they do it there's different ways that they do it but are so why would we care about you rich agreement we won enriched uranium we need to see a deal here on this news that that at the time of enrichment facilities things like that and they start worrying about when people make enrichment facilities because the idea is that you can't do anything with nuclear anything whether that be weapons or power wind just uranium straight out of uranium sale the ground is a mixture of 2 different what is called I should have stepped to isotopes remember what's different bicycles the review transcripts of 2 different so to memorize In order to actually do much with the nuclear things that were used to talking about you need to have a enriched to 235 it needs to be about 94 cents uranium 235 and so you have to be able to do this now there's actually there's lots of different kinds of the need particular isotopes enriched as well as the 1 here and is also slot about sold well aware that the do this is the taken in making U.S. 6 out city what would that be called uranium that's a flaw in the area and when they put on a really high pressure and they put it there container and then they put a membrane here so of membrane that permeable to U.S. 6 but what he thinks the nation's fast something smaller something this big that's something that's not so which you think What if used this membrane faster something 235 or to 13 8 235 so the 235 of comes here and then it basically just separates lecture not not perfect right some of 238 available to refuse into that top container to in some of the EU's 235 isn't going to actually managed to refuse but it gets them closer to give them some of this is enriched used 235 this you can think of either enriched 238 or depleted 235 which every year :colon now that's not really probably quite 90 per cent yet so then they do it again the film this into another container just like this and the separated more and listen into to another here just like that the separator morning got that extra 235 at stuff in here and so like if we called it will call this a stage this facility 4 thousand stages so that's what it takes to Urich Iranian London Tennessee is a version of the Tennessee suddenly go about enriching isotope elegance and there are other ways Iceland was my graduate of career working with on carbon special carbon and nitrogen isotopes of so there's lots of different kinds that we need certain isotopes and someone other ways that they can go about doing it but it doesn't want us to tell it's collected in which is also find sold in this equation again right so let's do a little bit of derivation begins erudition is is good for you so I know How would relate to different gasses so you for example you
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have with this being 238 this thing 235 help primarily those 2 popular really
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fusion of 1 to the fusion of the other so we basically wanted taken will say Well how are the masses related to the rate to the speed of the future so let's do a little better rearranging 1st of all if we had a situation like
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this is the temperature different is the temperature 238 in different images to 35 now right is therefore is the difference in temperature between the nitrogen in the air and oxygen in the air and the not with all of temperature of
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selectivity is going to sing so loud great checks of driving equations to solve for the things that are the same we did this with people Menotti to write what it was all for so far ,comma we sent equal to each other but some great checkered variations on the same thing here we're going to solve a temperature Brazil the temperature is the same so it doesn't really matter so philosophically now for if we have 2 different samples but there at the same temperature and those are going to be equal to each other so we're not learning and that's when people there at the results for all our enemies unable to each other where is the same thing yeah we solve knowledge from people to each other what's going to be the same year is the number 3 in change from 1 side agrees the other because number it is already emerging from the equation that now so what we do with us he went on now I need some rearranging here to so you cross out the 3 and I saw the speeds Over top of the masses so that we can relate this speed be the Manassas together now 1 more set of rearranging and we're going rename 1 thing as well so the rates that the are this you are mosque infusion turns out there their proportional to each other so the rate of is proportional to which means that we can just change in the R 1 and R 2 because the rates can be proportional to the speed an analysis wearable sites because in general will be selling for the rates not amasses theoretically would know what matters we have always found amusing examples Oregon but usually see the their thing right and left so we can say the speed is proportional to the right and so we changed the rate at which changes speed to rate and we solved that's so this is a very useful equation the have still because we can take the rates in can relating to the masses now it will want to read them
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so it will finish up reeled off the next time I guess that in the Mostar during that time as well firsttimers get through much of this is the kind of on it and that uses 1 . 5 5 times faster than probing at the same temperature and traffic in the gaps in the heavier lighter if users fast the that what's the molar so if you want to know the molar Marsalis this the racial like we did over there and we say well the rate of 1 over the right and the other is equal to the mass and that no careful with this money back slide in a notice that whatever the wherever those below the rate was here that goes on the boss right the mass increases the rate goes down so make sure you recognize that the press now we don't have the rated a in the rate of speed but we do know that we have that we have this 1 . 5 5 which is that Riccio sold out us already and so we can just put the 1 . 5 5 is not the part that we have to be careful of is not exactly a but it is it is tricky we have to figure out which number goes where which 1 resolving for so 125 firefighters have bigger and more smaller than 1 figure than 1 so that means that a the industry show that bigger 1 was on top of the smaller 1 was on but let me rephrase that faster was on top of the school rooms and after 1 right because the rates fast and so is the faster 1 was on top here where is the faster going over here .period and that's the 1 we're solving for the have to be careful about the 44 . 0 do I have to Canada's this 1 2 kilograms In after this 1 works the same way that when we did that he won the 1 over on and T1 equals to the detour entity do we have to worry about is the same reason here it's a racially so whatever Anderson people this one's going to come out hasn't doesn't really matter what you and so now we just have to square this and do that algebra for at which all trust you to be able to the algebra partner any at 19 . 6 grams per month so the thing to be careful of fear the thing that's tricky here is making sure you know which mass following for now but also that we knew that it needed to be lighter right so it was like yet what would the wrong it would not be heavier a that only I did something wrong and afflict the ends and gone back and fixed going so the
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merits for a