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Lec 2. Partial Pressures & The Kinetic Theory

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Lec 2. Partial Pressures & The Kinetic Theory
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UCI Chem 1B General Chemistry (Spring 2012) Lec 02. General Chemistry Intermolecular Forces -- Gases, Partial Pressures and Kinetic Theory Instructor: A.J. Shaka. Ph.D. Description: UCI Chem 1B is the second quarter of General Chemistry and covers the following topics: properties of gases, liquids, solids; changes of state; properties of solutions; stoichiometry; thermochemistry; and thermodynamics.
fall stretch Computer animation Primärer Sektor polymer level source
fall probe Microscopy chloride carbon Kohlenstoff-14 charge temperatures molecule water Van der Waals Interactions Thylakoid rust Computer animation temperatures Ideal Dipole Moment Ideal
conformation Chloroform Chloroform hydrogen bonding Electronegativity oxygen chlorine water molecule Wasserstoff Computer animation electron molecule Dipole Moment Perm (hairstyle)
Schwefelwasserstoff density complications container chloride case molecule lead electron temperatures Kakao Butcher Dipole Moment River mouth chemical formulae Selenium germanium balance Gases BET theory sulfur carbon complexes man chemical firm water conditions Computer animation molecule Dipole Moment selective
density Gases density Gases solutions Cubic Computer animation conditions molar Molmassenbestimmung parents Stoffmenge Molecular orbital theory Lymphangiomyomatosis
Cubic mixture Computer animation Elektronen-Lokalisierungs-Funktion density molar stone molar mixture oxygen chemical chemist
chemical formulae Computer animation conversions Mergel Stoffmenge Molecular orbital theory
oxygen nitrogen composition properties Inertgas Verstümmelung chemische Reaktion oxygen chemical orbitals Computer animation compounds molar Erholung
mixture nitrogen Gases Gases bind oxygen chemical molecule Computer animation temperatures molecule Stoffmenge mixture
oxygen Computer animation composition nitrogen capacities temperatures standards molar oxygen chemical
Index samples samples oxygen Computer animation Gases container molar Stoffmenge Mole Fractions oxygen
Methyliodid Gasflasche rates burning Octane chemical Ham Song of Songs conditions combustion Computer animation age Octane report Ideal mixture
solid-phase extraction composition balance Carbon Monoxide carbon nitrogen oxides man oxygen Spectinomycin molecule Wasserstoff combustion Computer animation age Carbon dioxide Octane Stoffmenge Ideal hydrocarbons
Gasflasche mixture oxygen nitrogen balance balance burnings gold oxygen man chemical Computer animation Gasoline Octane Stoffmenge storage mixture Mole Fractions stoichiometry
Zuge Gasflasche power mixture Gasflasche Gases chemical firm Computer animation Magnetometer mixture Mole Fractions Detonation Detonation stuff
molecule accelerator chip Computer animation magnetic Gases molecule firm
DNA recombinant molecule Computer animation model magnetic Gases molecule Stöße chemische Reaktion chemical chemical
Gases Spring container additional Stöße chemical Stöße molecule lead synthetic Computer animation temperatures coordination molecule Spring
Klebeeffekt Computer animation Sieden temperatures nanoparticle man chemical
Stop molecule Klebeeffekt Temp Computer animation function molecule nanoparticle History chemical period beweglicher
Eisfläche molecule power Computer animation temperatures container derivatives chemical form
chemical formulae grade factors growth flat chemical systems molecule Computer animation coupling stone Molmassenbestimmung History period core stuff
chemical formulae molecule Computer animation properties function nanoparticle History case form
Computer animation cake temperatures derivatives
Perfumer container Adamantane case chemical temperatures molecule Computer animation function molecule chemical structures xenon Helium Helium
chemical formulae Tafelschokolade oxygen Bromide Bromide carbon Kohlenstoff-14 oxygen chemical firm Computer animation molecule stone tetra Beer
power Computer animation Bromide stone media carbon gold oxygen chemical
Fusion concentration glass Opium abundant chemical Stöße water molecule flow Drops flow Computer animation temperatures molecule pollution Aroma compound
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Meeting/Interview plant Nitrosoethylharnstoff
OK but let's get back to to where we were if
they find that idea you know before you go for a run in the stretch interior don't get hurt let's do a little neuralgia let's stretch our minds a little bit on my count were gonna start at 150 subtract 7 visualize each number and stopped at the smallest positive number ready go but the 3 you go on .period a many of the thing there are several levels of that game and they're very important to understand the lowest level your lips are moving 150 143 136 wait a 2nd where was the 2nd level Is your hearing that source you have 150 143 136 and 29 . 2 15 section that's faster but that's still slow the next level is yours just seeing the answer it's dead quiet you see it come up just like that a lap In the 4th level of forest is that you never actually do what you're told the 1st thing you always do in scientific problem or a mathematical problem is you try to make it into an easier problem subtracting 7 is difficult so I didn't do that has attracted tens and added 3 1 51 41 43 133 136 but pretty soon I can see that the last digit is just going to these kids sometimes 12 separate sector and then I can see all the numbers like 1 long chain like a snake almost seem all at once on the ball almost every problem that he encounters like that in some way you can get very good at it and if you do you practice you will get that and if you don't you'll be hopeless there's a lot of difference between somebody who can do a cartwheel and the rest of us when we try to do a cartwheel and the real differences not innate ability but the person who is practiced can do it the person who hasn't practiced this fall you got a practice whenever you feel your mind feeling a bit of frustration you're getting smarter then when you pressures of thinking that's a good feeling just don't make it to like them OK let's get on with the work at hand we're going to talk about partial pressures and kinetic theory and I got some of the top
topical people think 1st of all there's a challenge from if you're interested find the pressures we remember we did carbon that chloride we got 30 . 6 2 meters there the volume refined the pressure for the previous problems so that the Vander Wal gas has the same volume of the ideal that's kind of a unique situation that's interesting and then the 2nd part is fine temperatures where the volume of the vendor walls dancers John there's a smaller the ideal that whole of the pressures the center and the and then the final thing is to look up the boiling point of carbon capture chloride and seeing if you can think of any reason why you got the answers she did based on how far away we are from the boiling point of the material yet this year near the boiling point the gas is not necessarily going to be behave that ideally because it's about ready to condensed into a liquid OK intermolecular forces we talked about granted what we talked about the Persian forces this fall my new charge fluctuations momentarily charge fluctuations leading to the appearance of 2 died polls which then cracked but some molecules actually have a permanent dipole
for example water
and chloroform because of
the difference in the electoral negativity of the oxygen and hydrogen Water has a dipole moment beside a slightly negative in the side a slightly positive and chloroform for the same reason the three-day chlorine are the hearts for electrons to make full of the electrons down this way and this becomes slightly negatively charged and this become slightly positively charged in both these molecules have relatively high boiling point they persist in the liquid water in addition conform hydrogen bonds which is a very strong force compared to the other 1 that's a special but if we have a molecule that has a dipole moment then we expect that it will
have a big value of a vendor walls formula because it should have a big attractive force because it's a permanent dipole and so they can definitely lineup and attracting each other under those circumstances if compare the role of more electrons which
leads to more fluctuations versus a small dipole moment and it turns out that it's a little bit tricky there if you just say well and I told this is a bigger for the a moment and this version for and I expect this molecule of the dipole they have a bigger value of and carbon that chloride than to get disappointed because this 1 that has more electrons actually has the slightly bigger value of a and this is just the usual place science the simple cut through which leaves out all the complexity and then there the real case which is usually more complex and requires a lot more studies to figure out why it is that this is bigger than that but that's smaller than this and so and that just means that there different players like an onion that you have to to peel off before you can get very close to reality is you compare water the water has a smaller value of but at least in the liquid water would have much higher intermolecular forces than any of the other 1 if you compare H 2 S which isn't quite as polar as water H 2 westerns is rotten egg gas very poisonous we also find reached U.S. extremely unpleasant smell these melodies to less even a little bit you wrinkle your knowledge and you take off the the other way why is that it's very poisonous the humans who didn't wrinkle their noses and take off the other way are think about volcano erupts in music boy that smells like hot chocolate and you awarded you're gone so anything that appears in nature that's dangerous like flying for each or you name it you will have an aversion to but if it doesn't appear in nature all bets are off you won't find around that's very poisonous just like to us but his mouth and the reason why is nobody ever smelled so we don't have any kind of selection against that type that if we go down 1 from sulfur to selenium we can see that as we add more electrons gets bigger that's comforting there we could try going down from Harvard I went all the way to germanium we go germanium Texas chloride and we get this this figure value as well so it there are some trends but it's always more complicated Tennessee gasses are very dense if they were dance they'd be liquid the story about the nature of the gas it's is not very dense under normal laboratory conditions and we can measure the density we can evacuate container and then we comply with the absence with an accurate balance which measure the difference in mass that's not really that big a deal it's more than you might think too so if we know the density as the mass volume and we know the pressure and temperature and we assume the ideal gas exporter that we know how much man for example ,comma mold but that tells us the molar map With just
measuring the density of the gas and you're thinking what the gas which 1 not necessarily without some ambiguity because some gasses may have and have the same Moeller that life and to and the old we would be able to distinguish them so we
start with equals an and we divide both sides by the and we divide both sides by party and then we write the right-hand side 1st we have the number of moles per volume is equal to the pressure of and the number of malls is the number of GM divided by the molar mass in grams per mole but can put that in and then I can solve for the molar mass and the molar is the grants Artie over PB now fine that's a nice mathematical solution and I do not advise you to use it because the problem with that the unit the unit's you're going to have you we are going to be very funny like cubic meters per volume effects of you convert everything MKS units you're gonna get the answer in kilograms per mole which is not how parents usually followed they usually called Mullah amassing grams per mole and
that he is funny and cubic meters are as injurious etc so
here in the mall amasses given in kilograms were mall and then only at bars and jewels the volumes in cubic meters and the pressure is in these would be units Haskell means meters where the whole thing is awkward I don't advise doing I'll give you an example problem and I'll show you how I always do it if the gas is a mixture then the ball amassed will come out to be the weighted mean and that might not correspond any particular dances you look up anew you table of data and you may have to do there and do some more experiments to figure out what's in there that's exactly what chemists did to figure out what was in let's burn out all the oxygen what's left let's make this thing react let's what's left they finally had some left the room react with anything that's the discovered OK let's try practice problem so let's suppose the density of the air it is 1 . 2 grams per liter at 1 atmosphere and 25 degrees Celsius what is the apparent molar mask of air well OK the 1st thing we always do when we look at these things this look units especially if the unit given in any kind of funny unit I see degrees C I right away thinking no no no where is Lord Kelvin rolling over in his grave if you use that unit we have December and when I Isenberg or when I use a constant I try to write down as many digits as I can if I'm given 7 digits on a constant on an exam baseline 3 1 4 4 so I use all those digits it doesn't take me that long to to write them down people killed themselves and get these constants that
accuracy it's really a crime to round something off too aggressively and then get the wrong hands then go ahead and use 273 . 1 5 as the conversion from Celsius OK the way
I like to do it then because I like using foreign leader atmosphere leader of gas said GM and I have an atmosphere and so I just go ahead and write down here to 98 . 1 5 Kelvin 1 atmosphere 1 leader tried soften the as a harmony number of moles would that be and I plugged in the numbers and I find out that I get 4 . 0 8 7 times 10 to the minus the mall but it said that that was 1 . 2 gram the 1 . 2 grams is 4 . 0 7 0 8 7 times and my mole many grants from all of the 1 . 2 and divided by them and you end up with 29 . 3 6 GM per mole that's the way I prefer to do it because I find that these years than just using the formula and then having messy unit all over the place failure
Fredo any way you want the only thing that matters Is that the orbiter doesn't crash you have to get the right answer you get the right answer nobody cares how you got it if you don't get the right answer nobody cares what great intentions you have
OK if you check on your own you can verify this squares pretty well with the composition of that's about 80 per cent nitrogen about 20 per cent oxygen and about 1 per cent of around the mosque I say others are much smaller but it turns out C O 2 is creeping up in 4th place and as I mentioned the inert gas argon was in fact discovered by comparing oxygen from the air With oxygen from a chemical reaction where certain compounds but when you keep them they produce oxygen and you prepare their peers compound and heated and you generate a bunch of oxygen gets and then you compare the properties of that with oxygen gas that you've isolated from there and you find out that there is a difference but there's something in the air that's not oxygen but doesn't appear to react to anything they could get react they could find out what it was they call are gone Krekar lazy ones this doesn't want to react with anything
In the early days they call these inert gasses because they thought it would never react that's the 60's they got seen on to react with something and so they called the noble gasses because they would react not very strongly to collect royalties focus so why even though Oregon was honored him news of notes was in they just didn't know what it was if we have
mixtures of gasses yes what they don't care the albeit but they all just banging against the sides and they they behave exactly like the same number of moles of 1 and this assumes of course that the molecules don't chemically react or do anything to bind to each other in that's what we're talking about that we have a mixture of nitrogen and oxygen and argon that behaves very similarly to the same number of moles of just 9 not much different and and therefore we have this concept of partial pressure the partial pressure of a gas is the pressure due to just the that gas along just throw away the other guys they have only moles of this gas do I have what the temperature in volume whatever that pressures
that's the partial pressure Of again but the simple idea throw away the other guy and there you go and here's a practice problem was the
partial pressure of oxygen In that St St Kitts and abbreviation for standard temperature and pressure the STP His 273 . 1 5 tell them and 1 atmosphere and if you actually take the time to look up the detailed composition of their 78 . 0 8 4 per cent nitrogen 20 . 9 4 6 per cent oxygen . 94 per cent are gone and . 0 3 9 per cent CO Due to outstanding 2 it wasn't quite that high before
these are all by volume but by by volume as long as we treat them as ideal gasses the volume fraction in the mole fractions are the same we don't have to worry the mole
fraction is just the malls of 0 2 in the sample divided by the total number of moles of gas in the sample and it's usually given as Greek symbol Ky the mole fraction of oxygen in the number of most of oxygen divided by the total and then while the partial pressures just the mole fraction times the atmosphere pressure the mole fraction is 20 per cent the partial pressures 20 per cent of 1 atmosphere or showing 2 0 9 5 atmosphere that's the partial pressure of oxygen and more general eh if we have a time different kinds of gasses please partial pressure of any particular gas is the number of most of that gas divided by the total number of moles in the container times the total pressures to which of the containers not rigid is just the external pressure and we can ride the just an area over and the times two-year we can write this is the mole fraction this divided by that and fraction the let's
call concept pressure and that is a mathematical statement of Dalton's law of partial pressure and in English we just say
the partial pressure of the gas in the mixture is equal to its small fraction multiplied by the total pressure it's good to be able to understand it both ways just as the Compaq equation and then as a center for you can explain to someone else OK please drive a car said a car running under light duty proves what is that that means I'm driving very conservatively 5 miles under the speed limit and never accelerating unnecessarily and watching the cars go around you as if there's some great hurry to get home and watched the because you are going exactly the the speed limit speed limits lender that not a suggested rate of travel it's the dilemma if conditions are perfect you don't go necessarily at Pacolet let's forget that from let's assume our engine is burning ISO octane which is CAD age 18 using intake air at atmospheric pressure I still walking In took this into a cylinder compressors and detonated make an explosion and then convert them into mechanical energy very inefficient but there you go let's assume ideal combustion the question is what should the partial pressure of the fuel vapor B In the song well I think we
know the composition of the air about 20 .
9 4 6 4 7 0 2 and let's assume it behaves ideally as an ideal gas what we need to know then is how much oxygen it takes to burn the ISO acting assuming ideal combustion is kind of a code for balance it alters C O 2 and age to complete or ideal combustion hydrocarbon goes the C O 2 and H 2 0 those actually do that in a real car I usually produces some carbon monoxide very poisonous and nitrogen oxides of not which believe the brown haze over Los Angeles but let's ignore that for now we have I ISO octane CA shh plus some number of moles of 0 2 give some number of moles of C O 2 unknown plus some number of moles of H 2 0 on while the way you do this kind of thing is you 1st work with the ones that have the man there's only 2 molecules with carbon this 1 and this 1 this 1 has a carbon this 1 has 1 province so why is that's the 1st thing you do then you look at the hydrogen there's only 2 molecules with hydrogen there's this 1 with 18 and there's this 1 with and therefore
is not once you have y and z you put a man and I figure out how much oxygen breaks the balance the oxygen because oxygen within both the other guy we don't start with oxygen you go around in a circle we bouncy oxygen last and it comes out of the
25 over to 16 and 19 and and this is molecular oxygen which is to instead 25 it's 25 overs to or 12 and a half 1 thing to notice is that for every mall of ISO octane in gasoline that we burn we get 8 miles of which is quite quite a lot 0 if we want to burn as at the start metric mixture for every mole of ISO we're going to have to have 12 and a half moles of oxygen but we are burning the ISO octane with oxygen were burning and with it and so we got intake a ton of nitrogen and all those other things began enough oxygen in the cylinder and make it work 1 thing you might ask yourself after looking at this is why don't we just burn the fuel with pure oxygen now would have a lot of great effect we wouldn't get any Knox because we wouldn't have any nitrogen in the cylinder it would burn hotter for Ashura oxygen pure oxygen things weren't really hot but then we'd be in a tank of oxygen to carry around and we have isolated oxygen from the air which would be energy-intensive and so the short answer is the reason we don't do that is the reason we don't pay the streets with gold it's just too expensive it looks nice work but it's too expensive To do this not practical but if we burned in their let's figure out how much we need well we've got to have 12 and a half bowls of oxygen but oxygen is only 20 . 9 4 6 per cent in the air and so instead of 12 and a half malls of oxygen we need 59 . 6 8 bowls of air from all of you so the total number of moles in and in there yes 59 . 6 8 plus 1 mall a few also the mole fraction of fuel is . 0 1 6 4 8 a little more than 1 and a half per cent vol per cent fuels when
we detonated it's mostly fair and there's a little fuel that kind of squares with how you imagine it might be In an internal combustion engine if you think about you don't think that's going to be the fuel or anything like that and if we
assume before the compression and detonation but we're bringing stuff in an atmosphere pressure another word we don't have a supercharger foreign turbochargers on but we are actually compressing the gas before we put it in which would give us more power perhaps but maybe shorter engine life defending how drive but then I think the early signs have a lot of problems but then the total pressures 1 atmosphere the mole fraction of fuel is 1 . 6 times the 1 . 6 times their and so its 1 . 6 times 10 months to that atmosphere is the the partial pressure of fuel final answer when you tromp on it the computer controlling the fuel-air mixture doesn't look at me the exhaust gas the same way when you drive conservatively it tries to assume prices adjusted so that there is no 0 2 left over but no extra fuel that being the most efficient way to go but if you want more power you just say Forget efficiency I wanna go then you put fuel rich mixture and the reason why you do that is so that you have some fuel on the way out to make sure that the cylinder doesn't over the and just blow up a mail and then efficiency goes way down it would be very illustrative for all of you to ride 1 time With the guy who drive the car the the estimated fuel mileage from the for city and highway driving those numbers that you never make 36 and 22 whatever they are miles per gallon they drive the car extremely conservatively obviously the drive car very
aggressively the manufacture of those crazy this bloody doing driving my car very aggressively and making me look bad on my own so the guy drives a car very very conservatively more conservatively than most of you have ever thought of Drive you hardly feel a chip that modern very very gently never push on the accelerator will need only you and then you actually do get that mileage if you drive aggressively you also give us worse air quality to the Quran exterior coming out and anybody who runs in the morning and tell whether Carter's been driving by in the last 2 minutes right away I can tell no cars on the street somebody go buy a little while ago even if they're gone this is a difference in their problem OK
let's talk about the kinetic theory we had these empirical laws Aliza generalization of observation To the theory is that of a rationale to explain White added and this is a kinetic theory which is designed to to explain those law we make some assumptions in any theories the assumptions were going to make 4 1st molecules are separated in space and the gas by many diameter so it is against the snow or nothing like a liquid number to the gas molecules collide and move randomly that's pretty much fine after all gas molecules don't brain so they can plan what they're going to do interestingly no molecules have brain and yes big assemblages of molecules do have different or harboring number 3 there are no attractive or repulsive forces what that unilateral on from behind a wall the number for the average kinetic energy of gas molecules is proportional to the camps that was actually pretty good In fact and would fall from number 3 no these assumptions
it's always important to know what the assumptions of a theory are because if any of the assumptions are violated then the conclusions may not fall it's very important that people want their assumptions on when they forecast an economic model what they assuming and how plausible is that some working you verify that there would actually have to have assumption 1
well assumption 1 is essentially that the molecules that no volume themselves and that's not going to be true at very high pressure but this series for the theory of gasses in Milan not guesses at very high pressure assumption number 2 is fairly accurate there should be no chemistry occurring no chemical reactions they just move randomly they don't collide and recombine stick assumption number 3 as I mentioned is clearly wrong because we know that all gasses can liquefy and all gasses have repulsive forces 2 from the hydraulic jack but it's mostly located traditional dances because we don't try violate the car with compressed gas we use of fluid a liquid to lift the car and we're going to talk
about gasses and assumptions 3 leads to Dolphins loss in that
assumption forestry if there are no forces if there are no forces there and basically the temperature the kinetic energy it is the only kind of energy and proportional to the temperature potential energy is the energy due to opposition Due to some coordinator synthetic additives energy dude emotions a potential energy is the energy like a spring being compressed but this spring has a 4 it's finding if the molecules have no forces between them there's no Springs we can be threatening otherwise and so there is no potential energy at all and therefore the only energy this is the unity of slamming around kinetic energy and that will be proportional to the temperature the pressure arises from collisions between gas molecules and the container wall gas molecule hits ricochets here it's going to go on the Brown around those and that tends to push the thing out there which is the pressure of gasses trying to escape it would like to keep going in a straight line if you want selected you have to put pressure on thank you change direction if we half the volume and these are moving randomly then the number density number per unit volume doubled same number that the volume so we have twice the the collision With the container but then we're going to get twice the
pressure but we have the volume we get twice the pressure placed on this little theory and that was boils lost so this year he explains the empirical observation in the world in generalize the Boyle's law and means this theory is on the right track because of the Greenwood experiment if we
increase the temperature we increased the average kinetic energy in proportion and with a little bit a man which I won't go through we can show that the pressure increases in proportion but we increase the temperature the double the absolute temperature we will double the pressure but we know that if we keep the pressure constant that is the volume would have to double instead and so if we double the temperature and keep the pressure constant we will double the volume that means the volume increases linearly With temperature and that's Charles was long 0 we derive Charles law from this simple theory as well and we can also derive other goggles from these assumptions as well the pressure depends on the number of particles but not the kind of particle but that the it's preferred proportional to the number of molds but
not the kind of material just the number of particles the number of
moles in there OK suppose now we ask more detailed questions because our proposing this period kinetic very weary of motion the question what does it look like in I against molecules well and plan to ricochet off we will do that and but had to suffer very long history and his freight train from behind know and I'm off again and I by 2 other guys and then I'm going really fast and so the question really years if we could take a snapshot In stop look at mall and say OK you how fast you going how many meters per 2nd you you you and we make this the what is it look like clearly the on going all at exactly the same speed that's very unlikely and they can all be stopped the there'd be a solid and they can all be going really fast for the gas would be hotter but there has to be some magic distribution which is the most likely like curve for a class the most likely outcome and Maxwell figured out how To make this histogram and arrives the functions so very few molecules are moving slowly you just can't move slowly in aghast because you get hit by somebody and then you just have to speed up and you can't be going too fast of too many of them are going to fast the gas would be hotter than the actual
observation temperatures the imagine suddenly the gas molecules start moving faster and faster and faster and faster where did all that energy comes from the that he but we are dealing with the thing my constant that thank you well known what I'm saying is that can happen if we did it would have we get more in the High Trail Persia but if we just sit there with a container at constant temperature pressure serve-and-volley and just a lot let's take a snapshot let's look at what happened and we would expect to have to many going too
fast so there is a magic distribution that Maxwell worked out the only live to be 49 I don't know when this picture with but I think I'm doing better than the he lied during questioning I don't know that think you with this early demise or not but he was 1 of the smartest guy so far no question about that and he figured out that it would be best form the histogram the number of molecules moving at a speed the Is this spinach under this radical times the squared times an exponential function which looks like the kinetic energy and the square 1 half in the square divided times t maybe Faribault Minn feinstein which is a measure of the thermal energy so we divide the kinetic energy by the thermal energy we get dimension list than anything an exponential have unit because enactment of power series right now because there was little to L'Oreal and we can things with different unit and here again is the massive article 10 kb is Bolton's constant and is the absolute temperature health we never use any other temperature this derivation is really beautiful
and until you see beautiful thoughts you may appreciate beautiful but you may not yet appreciate beautiful thought because many you haven't seen much but this really is beautiful but it's a little difficult so it's beyond the scope of our core this is Whitaker the forces the can get to the bottom of certain things like that it turns out that there is
a relationship between the gas consonant and Bolton's constant and they're just related by spokesman's Costas per molecule in the gas customers per mole so they're related by all the gods those numbers very big 6 times 10 . 3 and we can we can then rewrite Maxwell instead of using OK we can use our and the other .period rose number stuff cancels out here and then we get a more useful thing where we can have this factor here which is unfortunately again kilograms or more the square and then kilograms from all these growth Touati R has to be in Jewell said this is again a slightly tricky formula units wise and I'll go through a couple of problems to make sure that you I understand how to handle the unit so here the molar masses in kilograms and are must be in jewels and then you get meters per 2nd for the velocity well with this system RAM whenever you have a history fired her for the class I can say what is the the highest grade with lowest grade with the average grade will be medium rare where packed flats about how well the value was the most probable most people that think the cannot and the mean and median and the most probable or or the root-mean square these are statistical measures that tell you about the shape of
this year these are used in statistics for any kind of distribution the let's talk about the meeting the root mean square and the most probable those are the ones that we have formulas for the recent rise 1st of all the property
that this distribution has to have is that the probability of a student having some school or as the be 1 and that means that the integral Of this function has to be unit there all those numbers in the history and have add up to the total number of people in the class otherwise as the person and it obviously can be more now we take the speed here up to infinity but of course particles can go faster than the speed of light as far as we know but our gas particles are nowhere near the speed of light so that earned them the kind since there are no particles of the anyway we can figure out the average speed the average of anything it he's some Over the histogram of the thing so in the case of a school where you just take the score time summoning people got that score that's all we're doing here were taken the velocity times how many molecules have been philosophy out what fraction adding mall and that integral which it is easy to do but I won't do it it turns out to be the square root of a party over 5 Emison kilograms mole I guess so that's a simple form for the average velocity
or the average speed Excuse me In a gas of the temperature key we can get the
root-mean square speed literally I mean square take the square cake the mean of the square at the square root Of the mean of the square and you get the root mean square and that's a different integral to do but it turns out you can do that and you get square artistry RT upon no provided some the other at the time and you can yet the most probable speed that's where the slope of the histogram is 0 I'll show you on a plot where that is and that's easy to do that requires little algebra again and you get the
squared Touati over and that gives us all our distribution and here is
a picture of what the distributions might look like in 10 meters per 2nd if I have a heavy molecule what I seen on then I have a much much slower but more peak near low speed and if I have a very light Adam Excuse me not molecules like helium I find that I get very wide distribution of values and that the means speed is much higher this is the most probable speed in each case for each of these guys and you can see but it's not quite symmetrical there more guys going fast and there are going slow what kind of structures on the way out that's the the squares Of that function these are very fast speeds thousand meters per 2nd and that's it kilometers per 2nd you would that we get pushed aside the but means there would seem very violent and it doesn't factored that into anything the reason why doesn't really do anything as because it's like a traffic jam on the 405 only the cards are actually crashing into each other and that's why they're going nowhere but I'm going thousand meters per 2nd but I'm not going in the same denied directions for very long before I hit something I love this way but I'm going that way and on average I'm going absolutely nowhere unless there's a when unless there is an actual macroscopic pressure difference someone on the other hand I do spread out we do know that if we when a container here that has perfume and eventually start smelling In fact he cut a road like most of Lincoln would be a good 1 and you just put it in a vase in the living room on the way out of the door in the morning when you come
back and open the door the whole house this is the thing beautiful rich smell of that wonderful flowers those diffuse during that time throughout the whole Place and you can change the kind of flower of data Holland field have 1 little more citrusy worsening little chocolate
etc. OK let's let's calculate some relative speed here let's compare the most probable speedy for molecular oxygen notes and carbon Tetra bromide CPR for at 100 degrees Celsius 2 Celsius never use Celsius let's have a look the most probable speeds the top we had a formula for it the most probable speed as the squares to over an and here I just rode out all the units for a molecular oxygen 32 grams per I don't want grants because I don't have any brands of beer the licensee converted kilograms are jewels from all 4 Calvin Calvin go away jewels small go away and then I just leave it will work out the numbers and I get 440 Julesburg per-kilogram to the square root one-half that should be on the
presumably but well maybe not that it isn't the but I like go through this so that I can show you how to convert it to a speedy story but you
is a new media of the jewel of Workers Force times distance and for years math and kg times meter per 2nd for angered by the meter is a kilogram on the meter square 2nd but we had a jewel per kilogram the one-half hour so we had meter square the 2nd floor the kilogrammes gold where do swear that I will newspapers that the accident that foreign foreign needed for that the jewels overkill on the 1 hand powers and that means that on the other hand for carbon capture bromide we in and carbon 12 . 0 1 grants from all bromine 79 . 9 grams Verkerk kg again we're going to get you will still have the one-half and get on with city of molecular oxygen is moving a lot faster than carbon Tetra bromide because it's a lot lighter and the speech go like the inverse square the molecular masses obvious since there it is inverse
square root temperatures the same that's how it works and this dependence on the inverse square
root explains both diffusion and guess fusion both of which can be important the gas molecules move at high speed but they don't go anywhere because they keep changing direction the like somebody's switches majors 3 times at No . president selected direction and then tho at a moderate rate than go like crazy and then change in birds here therefore the net flow of one-time gas through another 1 is much much slower than the individuals and this is called diffusion profusion is the random spreading out of molecules until the concentration everywhere is the same whatever molecule is responsible for the fragrance and Mister Lincoln and actually there's more than 1 they have a certain Bolton Mass and they refuse out of the of the flowers each and then they spread around the room some concentration which is quite small but your nose and pick it up easily since noses of greater effect In liquids if I put a drop of the dime and leave it in a glass of water and come back the next day the whole water opium Dailey :colon but I would just randomly spread around and if I take a pollutant and I dumped it in the back pay it'll randomly spread around everywhere and then it'll be a million times more expensive to clean it up than if I caught it early
and to screw it up and down once you let them spread out you're in trouble it takes a lot of work To put the genie back in the land you don't want to do that firstly with pollutants and control on right away that fusion is
similar but it's it's the escape of a gas from a container With can hold into an area of low pressure like a back like this who that guy went out that 1 that 1 he went out and the big heavy silver guys didn't do it they're moving too slowly they just don't hit the side is often so they are going to get out as easily where is moving faster than analysts the 5 10 home where is moving slowly States forever to get out but then chemists found they could use this as a way seperate then if you have a series of 10 holes you
eventually get all the fast guys gone through In the process what you want you know a process to prepare pure fast and the most important aspect of good news in the nuclear fuel cycle effusion can used for isotope separation we can't
separating uranium 235 from
uranium 238 by chemistry because they have the same chemistry chemistry is about electron the isotopes that different numbers of neutrons nuclear but in the same electron configuration and so they react pretty much the same we are going to be able to separate the FBI chemist but they have different Moeller Mass 1 has to 35 1 238 and therefore they are at different rates of fusion therefore if I can prepare Garcia uranium compounds and put it through a town of 10 holes the U 235 compound of cultural panels 1st and I can get and make a bomb which was the purpose of doing it natural uranium is just . 7 per cent you 235 if we we have 4 stages of the fusion using the hexafluoride U F 6 which turns out to be a gas what kind of enrichment would we get OK the rate of escape through the 10 "quotation mark like the speed and that's the inverse square root of the masses so what we need the masses not just the bare uranium atoms of the hexafluoride which of the gasses so we
take the we learned to be put in that this is diffusion apparatus and we find that 1 of 349 grant from all once 352 grants from
all therefore the rate of effusion the 235 isomer versus 238 is the inverse of the 238 on top To the advice on the bottom squaring of 352 over 349 1 . 0 0 4 3 that is a miserable number because that didn't change things much well if you do it 4 times you get a factor 1 . 0 0 4 3 each time so you multiply them and so therefore stages of fusion you now get an enrichment but by a factor of 1 . 0 1 7 3 well if you start with natural or which is . 7 per cent when you get this factor now I enrichment . 7 1 2 per cent it was a little higher In order to make fuel for a reactor like sentinels fresh you have to get uranium content up to about 2 to 3 per cent States per cent uranium 235 that's enough In order to make a bomb you need more than 90 per cent of the conceded that enriched uranium to make a bomb you're going to have to have a lot of stages of fusion or something In order to do that and that's usually a big thing that Google Earth and identify and say what's that thing there that wasn't there before I want to make what's called weapons-grade uranium we need 19 per cent this year have 90 per cent and you have a kilogram you have a very dangerous thing 8 what you figure out how many stages of fusion it would take to make a bomb the it's going be a loss and just make a note that centrifuges which is what the Iranians are using right now are much more efficient then passive diffusion and perfusion technology with a centrifuge I've put the gasses in the air and I just didn't like crazy and EU 238 goes out more toward the edge and the 235 more toward the middle and I set up a column out of the middle and then I hunkered over to another centrifuge then the
238 out some of the 235 feet going to keep going and going and at the end of the pier and converted yeah what because you
have to make it into a gaps if its uranium metallurgist will sit there like a lump you could make it and any gaps but most metals don't make gasses it's very hard to make most metals make any kind of again you can make nickel tachycardia meal you can make uranium hexafluoride there a few examples but but usually it's hard to get a medal Adam to go going the gas phase they like the solids From solid is nothing moves and so it doesn't you just sits there and you can't separate and if you melted into a liquid again and you can't really separate anything you need to get the gas In order separate that's why you you make but without a 3 per cent Richmond you just can't produce power the uranium 235 is the 1 that produces the powered by nuclear fission you 238 to sits there like wet newspaper the view online campfire you gotta have some feeling the masses and stuff burns and then if you have some players suffered the words units and newspaper hanging around it will go without if you have too much stuff that burned like a giant family gasoline and lighter than blows up that's why we bring it up to about 3 per cent to generate power following reactor here because we don't want to have so much uranium we make a higher percentage 20 per cent is called low-enriched uranium and LEU low-enriched uranium is not considered a hazard for anybody making of long because it's still too far away from 90 per cent no worse than before yeah your country and you're only interested in power and our research reactors then you can obtain fuel "quotation mark cellular fuel that we offered to sell the fuel to Iraq and they refuse to no we want to enrich and make our
own fuel the problem with building an enrichment plant is that you can keep going and that's why we're a little bit suspicious about was the inventor my focus will continue on the next