 Lecture today is the last gasp and condensed phases. Recall we were talking about gases and we were talking about purifying uranium for various uses. And this is a much more efficient way. Chemists love this. Very energy efficient. Boy, you shine a laser light at these gases and the uranium 235 absorbs the light and the uranium 238 doesn't. And so you ricochet them off. Usually you ionize them or you do something and then you sweep everything aside and then you have what you want. Separated the material. Unfortunately there was a collision between science and policy here because these kind of plants can be made very, very tiny. And so you could hide them anywhere. And the government decided maybe we don't really want to do this and popularize this technology because it'll be very hard to keep track of who's doing what. And science and technology always has this tension. They made a new kind of bird flu to see how it worked. It's very contagious. There's a lot of controversy about whether they should publish how they made it so that somebody not quite as bright can copy that and make it. Of course scientists would like to publish everything. We believe in freedom of information but you have to be a little cautious sometimes. So here's the summary of gases. They're the simplest form of matter to understand. That's why we have these simple dimple equations that model gases fairly well. And an ideal gas is like a mathematical circle. It's something we invent to stretch out the behavior of real gases to all possible temperatures and pressures from zero to infinity and can't possibly be true in all circumstances for a real gas. And separating gases from one another is hard work because the atoms or molecules just move around randomly and you're trying to impose order on them and they don't have any brains so you have to do all the controlling. If you decide that after you read the NOAA report that recently came out that said that it's six degrees Fahrenheit warmer this spring than average and that lots of migratory birds appear to be confused coming back too soon and then there's no food for them to eat and then they stand around moving to the wrong areas and normally go because it's too hot where they used to go, that type of thing and you say, I got an idea let's try to put the genie back in the bottle and capture all that CO2. That is going to be a lot of work and work in chemistry is synonymous with using energy and the question is where are you going to get that energy that you're going to try to do something like that? You can't get it by burning more coal. We have the kinetic theory of gases starts from four assumptions know the four assumptions whenever you have a theory you have to know what the assumptions of the theory are if any. Helium gas because of the Maxwell Boltzmann distribution helium atoms go much much faster than argon, krypton or xenon in fact they go so fast that they escape velocity and so every helium atom you let into the atmosphere eventually leaves the Earth's gravitational field and we leave a streamer of them behind in space but helium is ever so important to have around it's a non-renewable resource and it's extremely important you wouldn't have any MRI without liquid helium and so we should not be filling balloons and letting them go up as if there's no tomorrow we should be conserving it like we should be conserving a lot of things that we're using up too quickly the atmosphere when you look up and you see the waning gibbets and it looks like it goes on forever because you're looking through it it doesn't go on forever it basically goes nowhere this part here is the atmosphere this little thin layer it's not as big as people think and you can change its composition by belching all kinds of things into it and then you're going to be standing around saying why do we do that well the answer in the early days was nobody knew it was a problem that's not the case now what's happening now is a case of colossal inertia and the prisoner's dilemma problem being played out okay let's talk about condensed phases first of all never ever write pv equals nrt unless you're talking about an ideal gas or trying to approximate a real gas as an ideal gas this equation of state is only for gases there are no simple equations of state for liquids or solids because liquids or solids have some order and they change a lot depending on what the material is in fact intermolecular forces play a big role in the behavior of liquids and solids because the atoms are close together they're bumping into each other constantly or they're locked in place in a solid lattice and they're locked in place by forces the only forces that matter for atoms and molecules are electrical forces gravity in particular has no role to play on the atomic scale because the atoms don't have much mass so if you think that a liquid condenses because the atoms see each other and attract each other like the earth attracts the moon that's not even remotely applicable yes it's extremely difficult to compress a liquid you can always compress anything even a solid if you squeeze on it enough you can crush it sometimes you get a different behavior if you take solid hydrogen hydrogen is in the first column above lithium, sodium and all the others all those other ones are metallic but solid hydrogen is not metallic but if you really, really, really squeeze on it it collapses, it goes down and then it actually conducts electricity so it becomes a different material entirely and that's true as we'll see when we talk about phases different, the same molecule or same group of atoms can behave differently depending on the phase solid CO2 is completely different than liquid CO2 or gaseous CO2 same with ice, water and steam they have different properties and this is what I said the strongest electrical force is a charge and then a dipole and then those fluctuating dipoles that I described to you when we talked about the van der Waals A term for attraction we said the chance that all the electrons would be perfectly symmetrical at all times is very tiny and so there have to be fluctuation and once there's a fluctuation then anybody around the electrons can move toward the positive side and there's a momentary attraction they attract momentarily I knew I was paying attention to language too closely when I came back on a transatlantic flight from England that was landing in San Francisco and the pilot said we will be landing momentarily in San Francisco and my heart started beating and I started to get up because I thought if we're landing momentarily I might not have time to get off the plane because landing momentarily means it doesn't mean landing in a moment it means landing for a moment but it's been misused so much I think if you look it up now they accept either usage but when I talk about momentarily having charge I mean momentarily okay liquids can flow although sometimes they flow very slowly you may have to be extremely patient to figure out that something is a liquid you may have to watch it very very closely over a long time and eventually liquids assume the shape of the container and we have a measure of resistance to flow called viscosity I think you all know qualitatively what it is something like gasoline is not very viscous so if you carry it around in a bucket it's very likely to slosh over the side of the bucket nobody usually carries around buckets of gasoline now because that's very bad for the air but when I was a kid we would have gasoline and that's how you cleaned your bike chain as you dunked it in gasoline and you went back and forth and then you oiled the chain got all the gunk off it and you did that you were eleven and there was nobody around and there was no supervision and it was quite a bit of gas so you could get burned but you knew that and so you didn't light any matches and you didn't play any games the kids who did that weren't around those of us still around were cautious so viscosity if we look at it viscosity I guess will give us a clue not the ultimate clue but some kind of clue about the kind of strength of intermolecular forces and liquids and hydrogen bonding in particular can lead to very viscous solutions carbohydrates, sugars have lots of hydroxyl groups that can make hydrogen bonds and therefore if we pour a ton of sugar into water and make syrup we get a much more viscous solution and then we can boil it up and pour it into molds and harden it and then we have candy and various things like that okay let's predict the viscosity of something my goodness now look at these structures so intimidating they are not they must get lazy because they have to draw structures all the time and if you have to draw a C H H H my wrist is killing me and it's taking forever it's taking so long to draw the molecule that it's like reading a novel letter by letter you go so slowly if you read slowly you can't follow the plot because you're taking too long to read it and you're forgetting what happens but we have a shorthand and in the shorthand whenever we change direction like that that means there's a carbon and if there's one line there's a single bond between them and we don't bother drawing the two hydrogens on this carbon or the two hydrogens on this carbon the three hydrogens on the end because we know the carbon will make a four single bond we just leave it all off so that we can get on with it and when you take organic chemistry you'll be drawing all kinds of things like this very quickly and if you become an organic chemist you'll be able to draw these things so fast it's like signing your name because you'll have to draw so many of them to see what's going on but for now I'll just tell you that the first one is one propanol if the OH is in the middle it's called isopropanol or isopropyl alcohol that's often used to sterilize things but this is one propanol and then we have this with two hydroxyls and then this with three hydroxyls but they all have three carbons but all we're changing is the number of hydroxyl groups that does increase the molar mass but you never ever say gee the molecule on the right is heavier never it has nothing to do with it okay don't use terms that refer to gravity it has to do with hydrogen bonding and electrical forces the more opportunities we have for hydrogen bonding and hydrogen bonding can only occur when a hydrogen is on what atoms? oxygen, nitrogen or fluorine and fluorine doesn't occur that often so oxygen and nitrogen are the ones you want to think about if you see a hydrogen on an oxygen or a nitrogen and then there's another oxygen around you say my goodness that could hydrogen bond for sure and that would stick the two molecules together and then if I were trying to pour them and they were tending to stick together they aren't going to pour very quickly because they have to unstick to start moving and the more I have them stuck the longer that's going to take and therefore we would guess that one propanol which has one hydroxyl group is the least viscous and the propylene glycol which you probably have seen as an antifreeze ingredient for example missable with water lowers the freezing point so that the water in your radiator doesn't freeze when you go up to the right wood and then break or shatter the radiator and then finally glycerol which is very viscous and if we look at room temperature these are approximate numbers then one propanol is 1.94 millipascals seconds that's also known as centipoise that's just the units of viscosity 48.6 and then about a thousand you don't use this one then to add to your car radiator this one is about right they'll both lower the freezing point but one of them will be a lot more inconvenient to work with because it'll take you 50 minutes to pour it in and the customer wants to get moving and then of course they add dyes so that you know if you spill it that you should clean it up you don't want to be spilling chemicals around and if they're colorless which these are you can't tell where they are and so you leave them so they add dye usually some green and then they add other colors to the other fluids in your car so the guy can call you up in troubleshoots saying what's the color that stuff then he knows all your power steering is out or your transmission fluid or whatever if you add colors so you have to be sure whatever you add doesn't change the properties of the liquid and what it's supposed to do no good having a brightly colored liquid that doesn't work as a power steering fluid this experiment has been going since 1930 bit too many humans which is also known as pitch hence the phrase pitch black that's as black as this stuff it turns out that it is a liquid and the proof is you pour it into a funnel you heat it up pour it into a funnel let it cool and then you watch it for 80 years we can't do experiments these days like that very well because the funding agency comes back in three years and says what have you done and if you say well I drunk a lot of coffee and I've been watching this thing and it's barely moving then unless you're a physicist they say we are going to scram that experiment sometimes in physics you have to sit around to watch for a rare event okay but you don't want too many people doing that because it's hard to distinguish whether they're actually working this has dropped eight experiments sorry eight drops have fallen here and you become the steward of the experiment and then when Dr. Mainstone dies they will have to appoint somebody else to get over and keep watching so this becomes one of your tasks is to not do anything don't touch it keep at the same temperature and be sure you're there when the drop actually falls because that's very rare solids don't flow of course you could say how do we know maybe we should watch them how solids don't flow because the molecules or atoms are locked into place in a 3D structure and they can't move until you melt them crystalline solids have a repeating structure everything is formed from this repeating structure which we will call a unit cell and we just move the unit cell in three directions and we reproduce the whole gigantic solid the unit cell is the smallest piece that has all the parts you need to make the entire solid sometimes the unit cell is quite big in the case of macro molecules sometimes it should be quite small in the case of something simple like rock salt sodium chloride the unit cell can be tiny and the unit cell has to have the right stoichiometry therefore if I have something like zinc oxide one zinc atom and one oxygen atom the unit cell has to come out to be one to one it could have four of one and four of the other but it has to have the same size the entire material does because you just make the entire material by translating the unit cell around in space just like a cookie cutter boom boom boom boom boom you just move it around we'll talk more about that later amorphous solids don't have such a nice structure like that it could be long molecules usually round molecules or atoms or ions can pack very efficiently like eggs in a carton or oranges at the supermarket and they therefore tend to form crystalline solids but if I have a material that is long like spaghetti like snakes and I heat it up to a liquid and the snakes all get wrapped around each other and then I cool it down they didn't have time to reorganize into the best situations they got trapped they got stuck oh this guy is through me and now I've removed all the energy and they're stuck like that and they're all stuck in different places and therefore I have a disordered solid they have different properties sometimes very interesting properties and you can actually make molecules but tend to show this behavior usually you have a core like a head and then you put on strings like Medusa's hair snakes coming out and you throw all these things in and you get something that is basically an amorphous material that you can use in a car bumper like a star polymer you specifically make a material to do that that can move you don't want a crystalline car bumper because crystals tend to shatter when you hit them you want something that's more like a rubber mallet so if you back up and you hit something it's not a total disaster your bumper protects the car from damage it gives a little bit usually solids are denser than liquids what is the major major exception water water is really a unique substance and if you you've all done it you leave something in the freezer and it's too full or even if it's not too full if you freeze it wrong if you put in a bottle that is closed at the top what happens is the top will freeze now it's a solid and it can't move now the rest of it freezes it's got nowhere to go and the force is incredible and so the thing just blows up shatters did it freeze? it could be that it froze more slowly you can freeze things if you do it carefully for example if you have a long thin tube of liquid like an NMR tube in my lab and you want to freeze it to store it don't just put it in the freezer you put it in the freezer but you put the bottom in an eppendorf tube and that has good thermal contact and so it freezes from the bottom up and then you're okay because the liquid can still move what you don't want to do is trap the liquid and then have it decide and so it can depend on the shape of the container too how if it's going to be acceptable to cold damage and engineers know that that's why things have different shapes sometimes they know that fully well this is a mockup obviously it would be hard to take a photo like this so what they did is they turned an appropriately sized iceberg upside down pretend that was on the bottom but it's realistic now you can see why the titanic crashes because here's what you see and so you say well I'll sail way over here and I'll be safe far away from it and under water if you don't have sonar you can't see it it's clear there it is and then you run your ship into it and if you're unlucky it's like opening a can of sardines it's an unsinkable ship you rip it along the whole length they had all these different compartments that's why they thought it couldn't sink but you just rip a ton of them open and it sinks it's not unsinkable nobody as the ship comes off and the champagne bottles crash against it nobody ever says anymore this ship is unsinkable it seemed to be bad luck to tempt fate oh I did want to point out one thing on this if we have icebergs that melt they don't raise the level of the ocean much because they're already underwater and therefore the ocean's already gone up when they fall off if they actually melt but if we have ice on land as on Antarctica and then that melt and that runs in then the ocean level goes up a lot not a small amount a lot as in you can go bathing here which wouldn't be good okay the strongest forces are between ions and if we have an ionic solid it will typically have a very high melting point because we have an actual positively charged ion and a negatively charged ion and they're stuck together and boy it takes a lot of energy to pry those guys apart and get them to move around independently you probably have never seen a molten salt period where you can take flames and you can try to take table salt and eat it like crazy and nothing happens it just shows a brilliant yellow light but it doesn't melt if you want to melt it you have to get it much much much much much hotter which you shouldn't do on your own magnesium oxide has twice the charge we can model it as magnesium 2 plus ions and oxide 2 minus ions and therefore with twice the charge the coulombic energy is much much bigger and we would expect that magnesium oxide then would have a much higher melting point than sodium chloride and in fact if we look up sodium chloride melts at 801 celsius whereas magnesium oxide melts at 2852 celsius and if we take it to the next level and look at thorium oxide where the thorium is probably best modeled as a plus 4 ion and 2 2 minus ions that's 3390 degrees C sometimes the trend suddenly changes you have a high melting point high melting point suddenly low melting point if you see that you just say I'll bet that last one is not an ionic solid I'll bet it it's not really best modeled as ions on a lattice doing something else something happen so you can judge whether something is or is not an ionic material that way you can also dissolve it in water and see if it conducts electricity if it's an electrolyte thorium oxide won't dissolve in water however so you can't test that one that way you have to be sure that the salt dissolves and that can be tricky the difference is between ions and dipoles for example between sodium ion and water the sodium ion when we do dissolve sodium chloride in water and make salt water the sodium ion is not moving around on its own because it's this big positive charge and so the negative part of the water tends to settle up to it, it's attracted to it so all the oxygens face toward the ion like that and back up to it and they crowd around it but of course they get hit by other waters they may get knocked off and at any time you may have between 4 and 6 water molecules loosely bound to the sodium ion the first 6 waters that go on that's it there's one here one here one here and they just basically ride around with that ion forever same 6 guys this one exchanges because it's only a plus 1 your body transports sodium and potassium around and it's very important to have the right concentration of sodium and potassium if you have too much of one or not enough of another you may either be weak or your heart may stop beating suddenly which has happened to people if you eat a ton of salt which most Americans do don't put a tremendous load on your biochemistry salt was hard to find historically plants don't have any salt you put salt on plants they die and therefore it was rare so if you put out a big block of salt all the cows in the field come over and start licking the salt and they need to have some salt and they need to find some and it's hard to find and therefore you're going to like the taste of salt because you could never get enough but now that you can get enough it's like food you have to be careful because you're actually forcing your kidneys to get rid of salt all day long your kidneys are designed to not get rid of salt they're designed to produce they get rid of water and other waste and keep the salt in your blood that's what they're designed to do now of course just like a car you can run your kidneys in reverse but there's a difference if you run your car forward all the time and drive it properly it's going to last for a certain length of time because that's how it's meant to be drive driven if you shift it into reverse every day and start going like this like a madman down the freeway you will find that the transmission doesn't last as long because it's not meant to run that way and that's why health authorities are saying don't eat so darn much salt eat the track of it look at it processed foods have a ton of salt since prokaryotes need salt too we can make antibiotics just based on capturing salt and here is one menensin A there's the structure why is the structure interesting because look I've got all these oxygens these hydroxyls so I've got all these negative things like a little cavity and then a positive ion like sodium comes along and it gets trapped and now the bad acting bacteria that wanted to use that sodium to run its chemistry can't get it too bad lights out they feed this stuff to cows by the tongue as far as I can tell which is not a good idea okay let's talk about dipole dipole forces instead of ion dipole or ion ion or hydrogen bonding dipole dipole forces are between molecules that have a dipole therefore the molecule can't be symmetrical if the molecule is symmetrical and the dipole is pointing this way and the molecule is symmetrical then if I turn the molecule around the dipole would have to turn around since it follows the molecule but if it's symmetrical it's the same molecule and therefore the only thing that can be opposite itself is zero and therefore a symmetrical molecule has zero dipole moment something like molecular nitrogen has no dipole moment in liquid chloroform then these dipoles move around and they have attractive in red I'm sorry it's kind of dim and repulsive in blue forces these two positive guys repel each other but this negative guy is closer and on average there's more attraction than repulsion because the molecules orient themselves so that that's the case therefore this would probably have a higher boiling point than something that didn't have those forces and finally the weakest forces are dispersion forces those are the ones that arise from a momentary charge fluctuation the molecule itself may not have a dipole moment or a charge but nevertheless the electrons get off the molecular framework just for an instant or two and that's enough time for the other electrons which can also move very quickly to slosh over and you get a momentary attraction and you get umpteen countless repeats of this and on average you get the stuff sticking together much more than if that couldn't happen these will always occur but if we have something like a charge or a dipole basically that's so much bigger that it swamps the dispersion forces so usually we only talk about the dispersion forces being the main thing if there's no charge and there's no dipole and there's no hydrogen bonding then we go looking for dispersion forces and as I said before you can go back to the material on gases where we introduced the van der Waals parameter a for attraction and I explained that for neon in terms of these momentary charge fluctuations let's see if we can rationalize differences in boiling points by looking at the molecular forces here's a practice problem the two molecules N2 which is harmless and CO which is poisonous but unfortunately odorless are isoelectronic they have the same number of electrons which should have the higher boiling point and why qualitatively who wants to guess CO and my argument would be CO has a dipole moment and if I only knew a little bit I'd guess that because oxygen is more electronegative than carbon that the oxygen side of the CO is negative and the carbon side of the CO is positive and guess what would be wrong because in fact our current vice chancellor for research Professor Heminger when he was a graduate student proved that the carbon side is negative and the oxygen side is positive and if you draw a correct Lewis structure with formal charges and a triple bond you have to put the positive charge on carbon on oxygen and the negative charge on carbon and when you look at how carbon monoxide poisons you it's the carbon side that sticks to the metal in hemoglobin not the oxygen side and that would make sense that the carbon side is negative and the metal is a positive ion difference between carbon monoxide and hemoglobin and oxygen oxygen comes on comes back off carbon monoxide comes on and then that's it and you dye bright red like a big red tomato because your hemoglobin is even redder than normal and that's when you find a body like that it's bright red like a tomato then first of all you don't stay in that enclosed space very long and second of all carbon monoxide poisoning what are the symptoms of carbon monoxide poisoning? the first symptom is confusion that's why it's important to be a clear thinker because if you aren't you may not know you're confused if you're confused in a enclosed space for any reasons get outside there could be a faulty water heater could be anything if you just stay there and say gee I'm confused I can't think straight but I think I'll just sit here or you wait too long and you're so confused you decide not to go out then you can die or if you happen to be asleep that would be very unfortunate okay we look at this and we say yeah n2 symmetrical doesn't have a dipole moment it does we would have guessed the wrong polarity but anyway it does have a dipole moment and we expect the dipole dipole forces to be stronger in carbon monoxide than the London dispersion forces in n2 and anyway since they have the same number of electrons we expect the dispersion forces to be about the same and if we if we look it up nitrogen at 77 Kelvin and carbon monoxide boils at 82 gee it's not very reassuring because it's not a very big difference it's almost a coin toss well that's because in fact the dipole moment of carbon monoxide is very small it's about .12 device a molecule like KBR and the gas phase would have a dipole moment of about 10 Debye and most molecules have dipole moments between 0 and 10 therefore this is on the very low n hydrogen fluoride is about 2 the Debye is a unit used to characterize the dipole moment if you wonder what it is and you're curious look it up look how much charge separation it corresponds to how much positive charge how much negative charge how far are they apart that's a good thing to know if you want to characterize dipole moments now we just talked about boiling points we talked about viscosity but what about melting points and here the point I want to get across to you is that melting points are very very much more complicated than boiling points given a problem ever on a standard exam and it's about melting points yes you look at intermolecular forces but you look at a lot more than just that because solids have structure and you have to know what the structure is how the things are packing before you can be sure that it's all down to the intermolecular forces shape matters a lot round things or things like footballs even can pack efficiently in a solid funny shaped molecules like H2O can't pack as efficiently and therefore for a given amount of intermolecular forces a solid made out of round things like beach balls will have a much higher melting point than you might expect so it's not just intermolecular forces but it also has to do with packing efficiency in a solid lattice that also influences things a lot in this particular case if you have a molecule that's round and that doesn't have much in the way of intermolecular forces it'll have a very, very small liquid range it'll take forever to melt and then once it melts the forces are pretty small so then it just boils shortly after and that means the liquid range is very low let's have a look I drew these out the long chain one is called N pentane 1, 2, 3, 4, 5 and then I just move one of these guys from here over to here and I move the hydrogen from here over to there and I have a branch this is along like a snake this is a branched hydrocarbon when they're doing cracking of gasoline they want to make branched hydrocarbons they don't want these guys the car engine won't run very smoothly on those so there's a whole chemistry of how to do that efficiently unfortunately it involves a lot of energy the first thing you do with a barrel of oil is you heat the thing up like crazy and that energy to heat the barrel of oil up to crack it to make kerosene gasoline propane and then you're left with so-called asphalping at the bottom takes a lot of energy and as long as you've got lots of oil you just take one barrel of oil and you burn it and the other barrel of oil you crack it and then you burn that too you burn all of them but if you start running low you're going to be in a world of hurt if you just run low on energy even if you have crude oil you'll be in trouble and then what did I do here well I did the same trick again I moved one of these over here on this side and then I put that hydrogen over here and then I've got a CH3 here CH3 here CH3 here CH2 dimethyl propane I'm naming them correctly but I don't expect you to know the name just for information don't be over cloned I don't want to use an incorrect name but I don't want you to memorize names of hydrocarbons okay let's try a practice problem with these let's discuss the liquid ranges of these three molecules after looking up the data now we'll have the data we aren't guessing but then you have to explain the data why is it that it's this way and not that way if you look up the melting points and boiling points and these all have trivial names N-pentane, isopentane and neopentane now look at the melting point the melting point of N-pentane is minus 129.8 the melting point of isopentane is minus 159.9 this one melts at a lower temperature it's got that tinker toy sticking out we could rationalize that it doesn't pack very well, it has an odd shape maybe these guys like snakes can kind of line up okay we're guessing let's just guess for a while and then look at the melting point of neopentane it's on a cold day in Canada neopentane freezes it's that much higher now that can't possibly be due to intermolecular forces because neopentane doesn't have a dipole moment and they all have the same number of carbons and hydrogens so they have the same number of electrons and it's huge it's almost 100 degrees different and the point here is that this anomaly is due to the fact that neopentane is round and can pack into a solid extremely efficiently and so when you try to heat neopentane up these round things jiggle around but they can't go anywhere because there's no free spaces there's no voids if I have an odd shaped thing it can't pack efficiently there's a void so I heat it, it can move and squeeze through then these guys can start moving and then guess what, it's melted this one can't they all have to they can't go at once it takes a lot more energy to do that but then look at the boiling point this one's the highest and that tends to be true these long chain ones and this one is intermediate and this one is now the lowest because it has no, once it's moving around in a liquid we aren't talking about packing we're just talking about forces and therefore it boils very easily so the important thing is be careful not to assume melting points have everything to do with intermolecular forces this particular problem has made the rounds for 30 years because I was given that problem to do and it's still around and people still can't explain it but I haven't studied it okay this is just what I was saying I've given you the data again neither end pentane or isopentane can pack that efficiently but isopentane has smaller forces so it has a lower melting point but neopentane can suddenly pack extremely efficiently and that's why it has a much, much higher melting point very small liquid range okay, let's talk about crystal and solids let's start with two-dimensional we'll start with a load of circles and we'll put them together like anybody's done with pennies and there's the closest way you can get them to fit until they touch and this is the way of course there's a hexagonal symmetry there are six closest neighbors to any one central guy and I can tile the entire plane with these hexagons I can tile the plane with triangles square hexagons I can't with octagons and if you look at a soccer ball the soccer ball has facets with six sides but the soccer ball is round curved therefore I can tell you that not all the facets have six sides otherwise it would be flat and occasionally if you look at it you'll find one with five and when you put one with five it starts curving down and then if you know what you're doing you can make something round with five and you can make all sorts of shapes with crystals with different facets six, five and so forth it gets complicated but they're very very beautiful objects if you understand how they're put together they're much more interesting than you ever thought now there's only one way to do this here and you might think if I take marbles and I put them in stack them up like eggs there's only one way to do it as well that's what I thought but surprisingly that's not true, there are two ways to do it with spheres not one, there's two and they're both as tightly packed as possible now here's how it works on top of the red a layer of blue ones you can see I put them right in the divot here's the blue one on top of the three reds you know that's how they would stack up but then interestingly there are some holes in between so there's a blue one here there's a blue one here but here there's a hole so if I shine a flashlight through the light comes through that hole and there's a bunch of holes along there where there's, sorry along here where there are neither a red one nor a blue one and it's every other layer these are covered these you can see through now I have a choice to put on a third layer and the choice is I can certainly put in this divot there's three blue ones I can put another red one right on top of the other red one in that case the light still shines through or I could cover the holes in that case the light doesn't shine through they both have the same packing same density but they're different let's see now I put on top of the other red one so we can't see him and now you can see here's a blue one behind here but here's a hole I'm sorry I should have picked a darker blue here's a hole but if I do it and this is called A B A to tell us that the third layer is the same as the first just moved up just a short hand notation but we can also put the third layer I put it in yellow now it's lights out no holes and that's because instead of lining up the yellow with the red I moved it over one to cover the holes the best way to do this is to get a bunch of round things and play around with it and this structure is called A B C to show that the third layer is different from the other two the next thing to ask yourself is this have we covered all the possibilities and it turns out for closest packing the spheres we have there are no other possibilities they're both close packed they both can make the densest structures we can make with identical spheres and the A B A structure has hexagonal symmetry it's just like the 2D case like what a honey bee might put together and that's called hexagonal closest packed or the abbreviation is H C P and the other one has cubic symmetry and it's called cubic closest packed or C C P and here's a question a mathematician would ask you suppose I had a crystal made out of four dimensional sphere how many ways how many different ways are there to pack them you may have to think about that a little you probably can't imagine what a four dimensional sphere looks like most people can't imagine the fourth dimension at all but one thing a surgeon would love a fourth dimension you know why? because they could see inside you everywhere and they could probably hear everything you were thinking just like when we look down here's the two dimensional circle talking they can't see inside each other hey how you doing fine how are you that they go each other's way they can't see inside but the guy in the third dimension looks down on him he can see all their guts inside everything they've eaten everything and if we had a fourth dimension we could see all of us spread out and see everything so a four dimensional space is much cooler than what you might have thought it might be and a four d sphere is much more complicated than you might have thought too okay we'll pick this up next time with crystal and solids