00:06

the cost of the various and In the other day we don't lose the support of the day any more than you need for a will be the and you have to look at the house but there to a state that if the United News of India and Poland 12 years after the date said there was a tendency to go ,comma states that the people that were constructed with the variant of the name of of what the people sitting around a lot the security of the United States the influence the little part B please state the bonds Soviet Union in between please the take lines and more television and telephone calls there are about you In the head of the I'm just going to go back to work because that he's the guy who were there on that and the president the the World War Two that is all I can make this want In the letter and the implementation of the law moderates within the statistical the evidence and all the way it is the setting for extended periods of low and half of them are you out on the rest of the day the handling of the descendants of article was the very reason the museum also got hold of healthy but I raised the first one losers last view of molecules there a chance of the press here at all I understand more about what Johnson extended range the future and when we were doing often enough on surprisingly good enough and when you do all the things close enough and that there is a 10 you would be the continuity of the people of this state is really committed to it it and got arranged to me on and reaction morphine there are others that story of the until now accurately and in this sense of itself more than 100 grams of In the end and the United States and Britain agreed that it was there that brings the country of the holding but now you can go out there and we found responsible thing on the other end the line but 1 I'm on and not Nunavut and In the brains in something like this the guys in the land of the living cell in part because of the this signals that right at the sort of war the preference would be to admit that there is certainty and on the remark about the destruction of the the example of the brief but from the start the winner of the presidency the EU the during the war about if they

05:34

are to be offered no communities of this year but no danger of that 1 of these the problem it would be firing on them and that they wrong the In this various things here and know it's the only thing about all I know what I have to it's not their fault is and what the hell out of the the state up yesterday at the top of the list of the names and development the facts that only on and on and on they all have basically the the same time as the use of more accurate I don't think that there is a a new things she did and the more we need to work very well go all the way you play a role India the idea of the all were on the number of people here over and holding you are what you intend for the at the end of the year 0 . 1 6 and 18 0 1 cost level the that with use of the gas on the fire had started in the fall the idea is to use on here with the usually leader of this blog along with her because they actually community and not just for a few years back on and it is the way is I was Bloomberg probably not this company and heard you have in at the nonimmigrant where all but 1 of the problem is that that's all there is to know that you know the kind of man you hold on to all kinds of people no 1 would not to have to do with the population the world I think people want very kind but I never meant I'm not going to be in Boston at the time of this writing for a year that work but I want to go out there you the this was the 1st of all in the well you have to turn the and moral and we're practically all the costs of their or the U.S. although more than I expected to be the standardize the agent for the reasons stated GM you also forces were excluded along something new about small things that we were all also on the same day did you wrestling along and on the floor and not only in 3rd detrimental earnings this year it's going to write on the way to the in end the of last month but it will be like books formal was also by the last Over these years the receded in recent press it increases the pressure because the real pressure he is too small and the reason why the deal pressure he is too small because the gas is tending to shrank in other words it's always attracting so it's not hitting besides as hard as it could but for any has something to do with attractive forces In the vendor walls equation what we did is we added a term that he we added that term is and squared over the square that's 1 way to do it here were multiplying it by something that's bigger than once that's a slightly different way do it it may

11:00

have some advantages in at some we intercepted see this equation is theoretically interesting look at a number of people and there are people publishing papers in 2001 and 2003 and so forth about this

11:18

equation but there still actually looking added that the topic of research in some but he is repulsive or excluded volume and attractive forces well the molar volume has units of liters per mole and because we're subtracting B he has to have the same unit you can subtract something that has different units the master of the universe of leaders from all for it's a little bit more subtle but we realize that no term in any exponential function and have any unit so they have to have the same units since it's on the top as party times India and I'll let you work out with the units on a R over the weekend might come in

12:19

useful now for the last

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part remember that we want to have an equation if a guessing and it turns out that a calculator methods that doesn't have both sides changes and when I

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did previously moles problem inventor was great divided 5 1 over an because that just seemed like the most obvious thing for me to do fuck me not be the best thing to do and now not decided that probably the best thing to do it's get everything on the left side and make the the right hand side 0 because if your calculators says a negative number you know you're too small and you calculators as a positive number you know you too big an ornament than that faster than the comparing where . 6 . 3 for the increase you

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just try to get at the 0 and it turns out your calculator if you're trying to get 0 but will do that for you that is what we do we take our equation which was written in this form this is just out was presented working in a reference and we multiply both sides by the molar volume minus be so we bring them over here and with then we multiplied both sides by either the they over RTV and then we still end up with the art over here we could start dancing with this together the for example or we could go 1 step further and subtract .period from both sides make both sides 0 and when you're rearranging the equation but the way the

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correct way to think about it is that whatever you do on 1 side of the equals sign because the same exact thing on the other side I don't know how'd they taught me to to do it in high school but sometimes it seems like too little money for a clear way to think about it is just guarantee that you're doing the same thing both sides if taxes equal to widen the times that is equal to 2 times what a lot of people along line of work the monitoring is equal to 1 just make sure that you're doing

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the same thing the both sides now with this equation it turns out that see what this 1 and this is not so fancy the 83 plots I don't think that's a Super Duper fancy calculator but I confess I don't know OK so oops please me but once we have it in the form on the 3rd line below once we have it in this form your calculator we'll solve it if you know how however once I get the solution for whatever I'm looking for here I would put it back in 1 time to check the answer because I don't like a little black box telling me what grade then again in court I like to

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verify myself but the solution is to make sure when I put it in the balances out about right let's

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have a look the 1st government well 1st of all I should hit you complete the 1st turned your

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calculator on don't than the rest of the instructions don't work and then you go

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up to the start their words as white people when you get them and you're going to use that for this 1 here have final maybe there's more showing 5 Y 1 1 2 1 3 1 4 and for the 1st 1 5 entered the equation yeah with numbers will do it in a 2nd I'll show you the number you have to type in your equation you don't have to

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simplify it it can be a messy as you like but yet the parentheses in the right places it would be wrong missing

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parenthesis or send fax error when you calculate the way will be and then for White to you just type in wide to equals 0 for the 2nd equation and then for the rest of the new major

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showing nothing at all this black on this 1 here is highlighting the equal sign for the ones that it's actually going to crash 4 what 1 and White who are highlighted and it's going to show that those 2 it is and

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then you have to select a region to plot we can do that in all these problems because we we have

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estimates for the From the ideal gas and we can from smaller than the bigger than the if you let the calculator to Samaniego crazy choice on its own light from 0 to some number and then when the 0 equation may fall or become nonsense so you

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may want to control what it does and then if it isn't it if you want to assume you can select the region plot assumed menu where you can let the calculated chooses by 0 In the manager and you're equations pastor the the variable you're solving for has to be acts not the or anything else and it has to be in the form some function of X equals to 0 not some of number but that's not a big deal especially if you practice than he did graphic to functions come up you're what I wanted function and a function White to equals 0 which is sometimes odyssey because it might be right on the axis and then the calculator will figure out for you where the 2 graphs intersect and that's your solution the press 2nd and then you go on the trade the press 2nd trades and then once you get on that menu you press 5 on this calculator words as intersect on your calculator you press whatever and then you hit Enter a couple of times I've found and it may

19:55

I ask you a few questions like I can't recall but what was important 1 of them was a mutual initial guesses something like that I thought forever because I could put it the idea of desecration of should and that pretty much guarantees that we calculated the doesn't go with the way way off somewhere else give me a crazy number

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OK and and then it should it quite a while because what it's doing is destiny guessing and

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knowledge that wait a while on the Net users who number and the 3rd time I tried the number was correct I made 2 mistakes practice

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if you going use this on Tuesday you're welcome to try the less time with our gas functions here's our numerical equations if you want you can go go ahead and enter sentence at the end user units mind here have 5 times quantity X minus . 1 finds the quantity . 0 5 over 24 . 4 6 5 4 4 times that just went ahead and multiplied are times tea and of course I would never the so in such a hurry that I would use 25 Celsius because there would be a disaster and that I put in this sphere of minus . 4 6 etc. That's my function and for wide too I put 0 0 and then on this

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calculator which has some funny variables set for acts I have to go to window and talent the plaudits from X equals 1 because it was from some other problems in the ancient pastor was negative values of x and volume is positive

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I just X equals 1 to 10 and I didn't I didn't give it again that's the 1st time I tried it and they go

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they came out and said Texas 4 .

22:43

9 9 1 and that's exactly right that's right that was very interesting is that so quickly you can try

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this slides and all the other ones will be without their consent and I'm back my office the prior practices if you want to use this I would be in favor

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of this I would have told you about this right at the beginning that I've been using this calculator but I cannot use calculators much the ladies and computer or I'll use this and that's in fact correct the molar volumes about 5 leaders and that seems to be a very good method and it'll work with any equation that you can enter and you're not which is any

23:45

inquiries and I'll ever give you on Tuesday it doesn't matter what it is right as long as you have a good guess to start with from the ideal gas equation you're pretty much in like Flynn but

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if you don't have such a fancy calculator as that 1 like I said I don't think it's that fancy but if your calculator will not solve it automatically you can still get it with guessing let's just try the same equation is 5 times Waller volume miners .period 1 finds the exponential function of this spinach minus the same thing equals to 0 and let's figure out our ideal gas estimate the molar volume for the ideal gas Justice Party over the because honest 1 and I put in the hard times In 5 atmospheres and my ideal Gasquet estimate was 4 . 8 9 309 leaders

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costs among many of those digits we are not important usually I only need to and let's just try guessing and now we're going to get

25:14

and try to get to the 0 well I guess the ideal gas and I get mine is about a half for the function I want 0 but too small and I could see right away by looking at

25:41

the 5 atmospheres finds the but if I change the 5 . 1 that's going to give me the right answer but let's suppose we didn't know that let's get us a little bit bigger

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let's 5 . 1 now I see that it's about equally on the other side a little bit bigger part value is 0 2 big while I'm going to guess halfway in between because this is -minus hasn't is lost it happened in a guest spot and then go it's very close but it's a little bit too vague therefore I'm going to drop it down just that a smidge 4 . 9 9 now it's a little too strong Back in usually

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stop here on an exam because I know that you did answer 5 . 0 and finally want because the true answer is between 4 .

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9 9 which is too small and 5 . 0 0 which is to so I know that the 2 digits rounds of 5 . 0 0 noon done but not really too much no longer depending how what kind of facility you have a typing equations and you will calculators you'll have to decide which method this is madam and then I just a little bit more and boy it's very very close that's certainly OK my my comment here is that if you need a lot of digits then the calculator method is superior because it will give you a lot of digits in it's worth doing but if you don't need a lot of digits it

27:39

depends how fast you can fight the equation and the white 1 equals whatever and how quickly you'll be able to get try that and

27:53

see how it works no 1 I quit last lecture I was talking about carrying the baby and there are lots of substance on because there are lots of different kinds of equilibrium constants 1 for any kind of chemical reactions and certain kinds of reactions Ternopil while you're working in a biochemistry lab you're going to be working with acids and bases a lot making up buffers and you're going to want to know or as you'll see in a more advanced course you're gonna 1 and all he to learn about him and take always refers to an acid associated that's what it means and it's always this kind of equilibrium constants concentration of age plus concentration of A-minus divided by the concentration 1 of the the reactant gasses at equilibrium baby I always refers to bed for example which of this last time if we play days and we had to water then we get the conjugate acid and hydroxide and baby is always the concentration of this and the concentration of hydroxide divided by the concentration of this and you notice that it does

29:38

not there's not there's not a not contained the concentration of water the reason why it

29:52

doesn't contain a concentration of water is a little bit of a subtle .period but just keep in mind that if you've got a purely with or water as the solvent you don't included in the equilibrium concept and you likewise do not include solids when things are dissolved but we don't include concentrations of water 1 it's a solvent nor do we include pure solids or pure liquids in the equilibrium constant the final OK that's interesting to know about these days yes he which is called the solubility Prop a fall like sodium chloride dissolving water give sodium plus sign chloride minus sign on chaos he is just there concentration of the last time the concentration of text minus and I do not divided by the concentration of the solid whatever that was

31:02

part of a clue is when you look at something and say Well what is concentrated in the solid start in a way that make any sense ,comma going nowhere that what is the name of the game that the clue to leave it out all voted in its MX too

31:25

it's the concentration of air times the concentration of squared because there to it and it's Amex 3 it's a concentration of them France a concentration of Hughes because there's a three-year that's our rule further reaction quotient there's nothing knew about that he says he is listed for all kinds of things and Feist is important to know because if we can make something insoluble we can make it come out of the water

32:03

therefore for doing something like we're trying to remediate some pollution and water if we can get the bad guy guys precipitate by putting in some other stuff then we may be able to and filter out the solid and let the clean water go along and there's a lot of interest in doing stuff like that because water is being recycled more and more and more and more because we want users many times before actually gets to the ocean because fresh water is very pressure

32:43

if we had better funding system we would not have drinking quality water going to the toilet because we

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1st we cleaned up the water like crazy so you could drink it if you wanted and what happens to it as well as pretty much drinkable fairly quickly we could actually have to find something in every house have gray water in the toilet and drinking water only coming out of the taps and that would be much more efficient but we would have Have you thought about that back then when we wired up every house with plums and nobody did it didn't seem important at the time so it's not done

33:31

anyway let's figure some solubility here and see how it works solubility it just tells us how many moles per liter of of Hong Kong Will dissolved in a solvent for example some kind of salt dissolving in water and chaos he is going to tell us what the solubility years because once we know OK as the we solve an equation could figure out but here's an example all the solubility products for calcium hydroxide I found is 5 . 0 2 times 10 to the minus said what is the solubility calcium hydroxide and water what that means is

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how much how many moles per liter of calcium hydroxide neutron water before it hasn't got the ball no moral resolve OK let's

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let's see how to do it so we have an an X 2 the equation well anything that's an equilibrium constant if

35:00

UCK on the exam you don't start doing anything at all until you write the chemical equations you write the chemical equation down and then everything is crystal clear yet sure but if you

35:24

don't write down the chemical equation it seems obvious to attend but it's not obvious that Europe Canada and training you may

35:32

start doing things calculating venues and go around in a circle like a cat chasing its own tail because you never wrote down the proper chemical reaction balances and see what's what whatever UCK adult and or anything you say What's the chemical reactions that occur what this referring and for solubility it's always this stuff dissolving

36:06

left out water the water kind riding along in this state but obviously we need some water on this side dissolved but we don't know who water in equilibrium constant protests anyhow so doesn't matter and we don't include appears solid Yeager was just the guys the chaos the this number 5 times 10 miners said is equal to the concentration of calcium times the concentration of hydroxide square and now we have to say OK we don't know what either of these but we know the story geometry every time 1 of these guys dissolves we get 1 of these and we get 2 of the so we know exactly what we're getting with let x moles per liter is all we don't know what exit we get X moles per liter of calcium to pass in there and we get to act moles per liter of hydroxide therefore in terms of our variable facts that we're going to have to solve for Our solubility product equation here are algebraic equation becomes the following 5 . 0 2 tons known minus 6 people's backs and boy do I love the brand of the year because I have seen

37:48

fiddle so many times by not squaring the too and if you don't square to hear a factor of 2 wrong and I think you know by now it happens on my if you're a factor of 2 wrong and you get axed

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times forex squared which is for excuse and this equation is easy to solve because there's there's nothing to really isolate we just divide by 4 take you brew that's what I've done here acts it is 1 4 times 5 . 0 the times spent of minus 6 race to the 1 the power or the cube roots and I got out is equal to 1 . 0 8 times 10 to Moeller

38:42

that's how much calcium hydroxide dissolved water about 100 of the mold Her liter it's not very soluble the

38:58

concentration of hydroxide this was the concentration of calcium therefore if anything on problems then instead of the solubility of what is the

39:16

concentration of hydroxide you go

39:20

through all that and then you can use a concentration of

39:25

hydroxide is too wet the

39:28

concentration of calcium is that and so you have to to multiply this by 2 and you get 2 . 1 6 times 10 to the minus 2 lower for the concentration of hydroxide and I've just made a little summary here Of all the common cases for regular one-to-one salt OK as he is that squared you want theater solubility you just take the square root of fans paid out pretty quick for assault like calcium hydroxide of the formula and next to OK as he is for times x because we had to square the kids for assault like aluminum chloride Annex 3 chaos the is 27 which comes from 3 Q I'm sex to the 4th and then the 1 I always hated it when I

40:46

was a student which is the 1 we always got well so

40:53

salt like this aluminum harmony diabolical we have to act squared here on 3 factors 1 the you year we 27 times for we end up with X to the FA and you can just count the number of clients and that's the power of that there's 3 guys here that for fight that's the power of facts but this number is important and this 1 in particular is very error-prone because you have to square the 2 and you have to keep the 3 and if you don't you get it wrong but whatever it is just right out the reaction see how many malls have each ion is made and then raise it in parentheses that the appropriate multiple for the appropriate power and then sold it and they're very easy to solve because there is nothing to 2 do accept take effect rooted 4th through something like that OK let's set up a bit of a review on something else tents along we're going back to natural of has a body said Boy this is already every word means something chancellor metal has a body sent to cubic lattice y that means a lot and should be used as well it has a density of 16 . 6 5 grams per cubic centimeter what is the atomic radius of Crown in the matter the cost

43:05

of periodic table because you have to know the molar massive famine otherwise all bets are off the let's assume we have

43:15

a periodic table and I had 1 so I'll give you here's what we're thinking here while Senator Hubert as harmony Adams of tantalum in the little well I

43:29

have to to remember that or knowing there is 1 the center there's 8 times 1 8 on the corners that's bodies and giving me that there's too Adams of panels in a little you In the final company GM literally the 2 atoms of panel but I figure out the size of the little you the because you have to

44:01

come out the same method the fields also said the overall stuff literally made out these little and then I have to to remember see how I figure

44:12

out the atomic radius always take a path where they touch environments and this from 1 corner of the EU 3 of the big guy the center the other corner there's 1 radius to 3 4 radio and then used president me square at 3 times the which you can get anything right triangles and that's so when

44:49

I see them I said Gee I could do that 1 and they go on to another problem amazing what I've already done cost you do

45:01

have to write down an example that you know sometimes you can just put a mail placeholder and go on some of the problems that I can get them my sleep OK here we've written about this

45:17

1 and in the center the 1st aid on the corner and that means I have to realize what body BCC means bodies said here but others too and the ball a massive channel I need to know there's 180 . 9 4 7 9 grams 1st 6 . 0 0 2 2 1 4 1 5 times 10 of the 23 Adam therefore I can figure out the mass in grams of a single atom of Tennessee it turns out to be free times 10 to the minus 22 grant very very light using that as the number of the the total mass in the Union itself which is twice this is about 6 times that of the minus 22 grams you itself and now I have to figure out how big unit-cell should be so that this much mass Her volume in cubic centimeters comes out to 16 . 6 5 grams per cubic centimeter obviously since this is very small the size of the unit so it's going to be very small and then makes sense because its atomic itself both from the density we can determine the hatchlings the unit itself because we can't figure out the volume and knowing take cube root of volume atomic radius is related by by going across the bodies of 2 for Iranistan squares 3 and I will

47:07

let you work this out this the or not depending on your predilections and then

47:20

check your answer if you do work it out but that the atomic radius of talent ceased to see if makes sense OK let's do another 1 we're going back again he then felt the vaporization Delta age that I should have said the molar and the the unit's giveaways the Moeller at the altar of vaporization of told the 3rd 27 . 2 4 killer jewels from all and the normal boiling point which is where the vapor pressure is 1 atmosphere is 34 . 6 degrees and here's the question Is that I have all the they're likely to have extensive structure in the liquid state is making long change elaborate had booking not to sell or is ran well 1st of all we have to make a connection between what we're being asked and what we anything that has to do with randomness or structure we immediately think of entropy but what this

48:53

problem is asking about is is the entropy of vaporization consistent with random order in the liquid and the gas we assumed to be ran and we

49:12

did that but it's been a while so let's go back to the conditions for equilibrium between the 2 phases there is always the delta G should be 0 and I have a relationship between delta G and dealt age minus the dealt best their equal the adult age minus teed off after the 0 or therefore the normal boiling point Delta should be dealt with age of on when you put in the numbers of course I don't put in 34 . 6 degrees Celsius because by now I automatically convert everything the Calvinist fast as possible Delta Gas vaporization it is 27 . 2 4 times that of the 3 fuels from all provided by 273 . 1 5 posted a 4 . 6 and that comes out 88 . 5 jewels from and a number like this should ring a bell because we had this we had this rough rule that if you want from a completely distorted liquid completely distorted gas but that would create the same amount of chaos independent of what the stuff while and that's called trappings rule it says that the other up entropy Excuse me vaporization from a random liquid to a random gas would be about 88 for so and since this is close to them I would say I believe has no structure in the liquid state and when I look at the the

51:06

molecular structure of happily there I see that can hydrogen-bond like water or methanol or some other molecules and so confirmed if this number

51:19

dealt as massive vaporization were something like 100 then I would say high it has

51:26

structure In the liquid because when I converted to a gas I'm creating more chaos and if it were a randomly would therefore tend had to be structured as a liquid and I 1st had to break up the structure and then you have to go to the gap this

51:47

gives us a useful trek in fact themselves show you what this is trickier you can decimate the boiling point but almost anything without knowing too because Delta has and measured you can look it up if we've already got the enveloped and and felt the vaporization and we think that the liquid will follow drowns rule now we can estimate the normal boiling point by just taking whatever they NFL felt the vaporization is and dividing it by something like 88 books vary on the number some books insists it's a 7 . 5 other boats say it's 88 . 5 but if it's about radiator so the Baltic don't worry about the exact number because this is not going to be that accurate anyhow and although you can do this with vaporization and although sublimation follows exactly the same

52:55

equations classes for pirate equation as a liquid and therefore violated

53:02

the vapor pressure above solid O 2 it'll be lost he is minus age of sublimation over a hard 1 over the what's the ,comma same equation but there is no trappings role for sublimation because solids are certainly not random and condensed phases solids usually have structured because when things form a solid base they often former repeating lad depending how the toys together and often times they exclude other things that don't fit and that's why water 1 it's frozen this pretty much purer unless youthful flash freezer because if you freeze it slowly given the saltwater fish but when the water on the ice crystals the bonds of salt and he was you don't get out of here is that the use during an in the form of the question the line like that and that's a good way to purify and in factories to crystallize them and in organic chemistry lab next year you'll probably do some crystallization of purified the way to do it OK let's try there is

54:28

a problem estimated the boiling point of hydrogen sulfide Page to us and To the policy gas at room temperature knowing that there can now be of vaporization values are listed as 18 . 6 killer jewels from all for H 2 S and 6 . 4 killer jewels from all for pardon well OK we need to pieces of information get the 1st if the 2 phases at present which they are the normal boiling point that's why it's called boiling point at that exact temperature delta G A 0 that's why they can both be there so what could either be the liquid or he could be the gas and the 2nd is well will just assume that they follow trounced role in Iraq used a 7 . 5 therefore at the unique temperature where delta G A 0 0 the boiling point Delta H is equal 18 . 6 times that of the 3 get the same units I assume what Delta essentially saying that the liquid is totally random and gas is random and I get 213 Calvin which is minus 60 degrees C. Russell I'm not going to worry about the . 1 5 because I have no the illusion that this is so accurate that I didn't bother "quotation mark actually like that into this kind of problem infra are gone doing the same thing but with a different value here of Delta age 6 . 4 times that of the 3 I 73 Calvin which is about minus 200 Celsius and I I looked up the values and they are bad the true value this is justice a fluke that it's that they came out that close minus 60 . 2 and this 1 is off less than 10 per cent 5 per cent yeah so it can be useful because you can get sometimes the boiling point of things without knowing OK here's another 1 to remember remember this 1 How can you might say

57:36

2nd that was close to the ongoing him right there with all running has the reason why it was non-interference into it because I don't have a color printer they're all crazy it's not very very well because you can't help and I don't like to just make things different sizes but I have all week in so I can replace

58:03

this with some patterns that you can see the

58:10

OK bank Of course it may

58:14

not be this exact 1 Barium tied the let's go through it again anyhow we have a Titaniums 4 plus sign on right in the center of this cubic we have the oxygen is on each face so the cut in half and we had the barium song corners so the cut in aid if there were 1 right here would be cut into off or you don't actually have to remember you just have to say look nothing could be outside the queue if it's outside the you when I put the kids together they are gonna fit just saw off this and that and as you just say there's a little 1 inside the EU that's all I can see I can't add anything poking out of my unit itself because I'm going to produce the solid by pasting them together you don't actually have to memorize which once was what's here that is what we said before 8 times 1 8 for the barium is 1 the Titaniums in the center so that's 1 it is totally inside and 6 oxygen run 6 faces the current have 6 times 3 and the charges also help us because too 4 and -minus 6 means it's solved is neutral and it better be and therefore the formula is very tightening you wouldn't necessarily know from the structure that various tightening but from the name we would put whichever one's 1st as the first one in the molecular formula but I wouldn't care if you wrote the the old that's fine at this stage here's observations the 68 problem that's a lot but there's more

1:00:27

than 68 hours our problems not that big a deal go over them nature but if the same stupid problem appears that was just up here in Technicolor but it's still out but nothing but net turn them

1:00:55

around and solemnly the other way so offer all the independent variables but just do it 1 way and then turn it sideways and salt as well and when you saw that pay attention to unit pay attention this significant figures and pay attention to actors and as far as I know our exam his on Tuesday at 10 30 In this round will be fine with me if you come to

1:01:41

bed early but if you come a bit late but we actually do have to get out by 12 30 the future on top of ,comma only get organized crime saying seated here last assigned