Lecture 21. Second Midterm Examination Review


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Lecture 21. Second Midterm Examination Review
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Martin, Rachel
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UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 21. Molecular Structure & Statistical Mechanics -- Second Midterm Examination Review. Instructor: Rachel Martin, Ph.D. Description: Principles of quantum mechanics with application to the elements of atomic structure and energy levels, diatomic molecular spectroscopy and structure determination, and chemical bonding in simple molecules. Index of Topics: 0:01:33 IR Spectrum of Carbon Monoxide 0:10:36 Electronic Spectroscopy 0:15:17 Frank-Condon Factors 0:19:34 Term Symbols and Electronic Transitions 0:25:05 NMR Spectroscopy
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morning everybody today they wouldn't talk about the exam would anybody have any questions before we do what's the mean I don't know on you again it takes you guys an hour to take the exam multiplied by 207 or whatever the 4 of us breeding and take as life as integrated as sophisticated but it's not going to be all graded and ready to go by by the next class period sorry we we just there's only 4 of us we can't do that so it's almost done being graded on will get that finished today than it gets sent to while wherever it goes for scanning and then as soon as I get the fact I will give them to you but I have 0 control over how long it takes to the sky and stuff so I know you're making this year's forum but it just takes a little while that in class OK so I I was struck what the exempt list ?question mark In looks people done OK it looks looks alright but people rent time I expected that that's fine that's normal but overall seems pretty reasonable OK so let's get
started going over it's so 1st question by a spectrum of carbon monoxide why is there a gap in the sun 2 yeah there's no there is no way Delta Jaipal 0 transition so anything anything mentioning that that transition is is forbidden or that there is that the specific selection rules of prohibits that anything like that got full credit OK so then the next question is what is the energy in way members of this transition and yeah this is really straightforward you just read off a spectrum right because since there is no Delta date 0 transition that spot in the middle where there's no line is something that's worthy new equal zeroed in Newark was 1 transition areas and so if you just read off a spectrum you get something like this it's hard to read from that little plot so if you got anything close that counted OK so the next question is all using the spectrum Chu as make the force constant for the CEO bond and I'm not gonna work all this out in the interests of time but I basically you need to use that transition frequencies so that's that's what we knew of course this is the reduced Mass and k is news for meter and the actual value if you look looking up for carbon-monoxide it is about 1860 you know again it's hard to read to me transition frequency of that little plot and that is that sort of determines the answer you get so if it was consistently that something close your article .period so that was really straightforward it's just kind of remembering which equation using pointing Stephane as always with such things there opportunities to make mistakes getting the unit's wrong and you know forgetting to convert things but otherwise I was pretty straightforward OK next question is carbon-monoxide a perfect rigid River and so it's not so and on a lot of people wrote because life's not perfect which is fine and probably reasonable all but it said it doesn't it doesn't count as a good justifications so yeah I guess I guess John Marks said that during the session but have well here here also about to learn that life's not fair because that doesn't get the I got so in order to in order to get full credit you had to right that the arm the centrifugal distortion and you can tell because the spacings on the spectrum are not exactly equal famous question one-sided and stretched from the other yes or no yeah I was just looking at the time of the blast was used to use this way this all the place of the right of the hole following was I I didn't agree that 1 you can help your team is a nicer than I am so I think that's light you know when you go to iTunes anew by a song and they charging 99 dollars instead of 99 cents that calls and offers is completely wrong I know what I think so but you cannot this year is a nice and I am not sure that some that's like you gave the baby a thousand times too much medicine and he died it's bad while it is those order of magnitude errors caused huge problems in real life here Mars rover crashes into the surface of the planet partial credit you get fired the others that like yeah yeah yeah by making fun but like the you know the things where you have a small area in the last couple decimal places or whatever because round of problems that's not really a huge deal but the orders of magnitude matter OK I alright so how would the Roman spectrum of C look different so if you're looking at a Roman spectrum instead of the entire spectrum of how would you be able to tell us OK so you have to give at least 2 differences and you're the ones that I could think of you would have a really lying in the center of the spectrum which is not called a Q Branch it's a really line so the Q Branch is if you have a you know something like a radical over there's electron orbital momentum and so on the central transition is forbidden then you see that Fuhrman spectrum it's really on other things could the spacing is 4 times the rotational constants for the line intensity is and so any any 2 of those were 5 questions that but
you definitely got something for that I don't I don't remember exactly how we develop a fiesta the name of the man in the street violence and realize that this is not the best way is to restore order in the the thing that you the rest I know that that is if OK if you if you had labeled all 3 branches there then that that would be fine but just riding it has a Q Branch doesn't doesn't do it because that's you know that's life we can talk about it later if you want but it seems like not worth spending a lot of time I'm very active during the label all 3 branches and that's something different than yes when he made a difference in number repeats you it would be pretty hard to tell the sir but it's the same it's the same molecule and it's a linear molecule Sophie if you had a year if you had complex Polly atomic molecule that would definitely return you would see different vibrational modes by this thing only has 1 it's a diatonic molecules so that it's only got 1 vibrational modes that's that wouldn't really be applicable here but you're right if you had a complex .period on a molecule that would be totally true OK I don't know let's go on to the next 1 operates so for this 1 it's some sort of a it's a standard Berge broader plot with a little bit of a twist which is that there's a break in the middle of it so it's that what that tells you in practical terms as it has a weird potential so this was from a paper in Science a few years a few years ago on a brilliant Daimler and looking at Umberleigh environment of forming and so at 1st the I'm near the dissociation energies of brilliant diner was estimated incorrectly because it has this weird shape in the experimental potential and DVD it's really strongly from a normal force potential so why does it have this weird shape what you think about the electronic structure of beryllium dimer you can kind of tell it's not going form a very strong bond which is true and you since it has this this week bond it's kind of strange potential this was something that I thought that was a relatively recent recent result wasn't science was a few years ago OK so what does this mean for during the problem it means you can't really look at the you know the value for new Macs so used to the X intercept telling you something about the convergence limit and you know here that's that's kind of hard to get because you know we have these 2 breaks in the plot but on so anyway to him was to use the party that's consistent with remorse potential which was the 1st part which is shown by this this line here and so on you could do that and so as always for these things the slope tells you something about the potential so then we know that the y intercept which is normal In this plot Dean is just operates and that was about 625 and so that's it pretty straightforward so the only part time the only part that had information content here was just knowing which equations to users being able to to get this off plot Tokay so then moving on to on gas well does that make sense I mean so so it's kind it depends on you know you're thinking about it's it's an absolute value thing when you're thinking about putting in years to put energy into the molecule submitted to dissociate rates so that saw so right over the use of take the absolute value but that's just that's that's 1 of those things words you know that the convention is sort of it hinted it could be either way depending on whether your chemistry and engineering what you're doing so as far as whether it's association accused positive or negative yes the question is I it think it is for that's the yes but the 1 thing on like a point it's not it's not a big deal OK so now the next 1 is looking at Frank
common factors OK so the question is writing expression for Franklin factor for transition between these 2 states and I I wanted you to put in the States but which is which is why I wrote down functions but so you've got to almost all points for doing it indirectly tuition so we have these 2 states and Frank uninfected is so that got almost all the points people were really worrying during the exam but which ones the initial which once the final state it doesn't matter right so we're talking about a transition between them and that amplitude is going to depend on which 1 is initial which one's final so you know it doesn't really matter yes that Oh yeah that's true that's that's so here's 1 of these cases were direct notation is ambiguous and so that's why it's it's best to rein in the States so young waiter saying is these quantum numbers are relevant to anything yet true but so what I wanted you to actually do is you know right out like there integral and so I said I new prime equals 0 so that's I and an age right and you have to evaluate it no responded great expression so doing it in direct irritation got you most of the points but I wanted you to make the connection right down the functions OK so next question is we want to sketch this transition on an interview with life around a so we've got some electronic states and you know it doesn't really matter what they look like as long as they vaguely look like a moth potential and then we have some vibrational states in there and he should know that you know there's some 0 . energy so that would be new prime you don't prompt sorry and so that's basically it and then of course we needed to label the transition and right away drew it is difficult to do that and so there's not really much overlap the way I do it but there you go the next question is going to be a few year going down is that fine to yes because we didn't specify which ones initial which once the final stage so as long as you're consistent enough I just wanted to see if you can make the connection between you know writing down these expressions sort of employment terms plugging in actual functions you know not not evaluating it but putting it again and I do you know being able to go from that to looking at the end of potential diagram OK the next 1 term symbols so for those
who have spent endless hours in office hours rating all the other possible excited streets of 0 2 and it was time well spent OK so the 0 2 molecules in its ground state and here another was something there was some potential for confusion because the book served doesn't distinguish between the various electron configurations that you can get with the ground state electron configuration but Of course there is an actual ground state it's you know you you have to use means ruled again that sits on rehab most unpaired electrons so let's look at this and in terms of the molecular orbital diagram so and destroying the P were but also so I've got Sigma yes RE that's my so that's my molecular orbital diagram from General chemistry of 2 and I'm ignoring me as sawmills because there it's filled and they don't give me anything and so I ran out the electron configuration for this molecule which gives me this and again senses the ground state we use funds rule and putting the configuration with the with both of these electrons and their and suffered orbitals OK everybody with me so far "quotation mark OK so then the next question is what Lander ends it is going to be 0 so we get a Sigma terms and then if we sentences so we have to decide whether it's Geary you and so we've got these 2 electrons in the UN they're both in highest stodgy orbital so that's due times G so this term is even and they're in different orbitals so it's minus and what suits us spend multiplicity it's no just getting its report state as we have to enter electrons I was getting my head of myself and that in the next 1 OK so that's the arms the ground state and you know there were a couple of you know Corsican but those electrons in different places and write a couple more term symbol there's a Delta from symbol etc. on something just ask for the the lowest energy 1 that was essentially waste of time if he did it on on this question OK so the next 1 is I believe we have 1 electron promoted from the home owed to the loom and so on the young again General Chemistry highest occupied molecular orbital and lowest unoccupied molecular orbital some people asked about that I think people just get nervous forget stuff sometimes OK so you have these guys are all the same and then there a couple choices here I'm not labeling the orbitals but obviously they didn't change yeah and these things give you there are 2 states and if you only got 1 above sea had to get both of them to get full credit feeling not 1 of them we took off of .period so what do you think there various other side conversations but does it seems like everybody moralist gets is that it's not true a pagan rites so far but you know the the endless hours that we spent redrawing the picture paid off OK so the next question it has to do with Panama alright so this was this question was about writing the matrix elements for for life plus the raising operator 1st one-half and so it's full definition was here and you wanna write this out as so you know that I plus operated on Alpha is 0 this is 0 and then so break the full thing there we go right so this gives us theory on that so that's more like it sold 1 times alfalfa and so the answer is and if you just wrote the Matrix because you had written down the sheet sheet that didn't get full points he needed to show some understanding of how to do it to get full credit so he rode out the full matrix or just out symbolically Europe you put down that held a matrix elements work that all counted as long as they showed that they knew how to do it on this collection of constants in front in the definition of the raising lorry operators understand letting you know for purposes of taking the final year comes out to 1 in this case but if it wasn't us than one-half it wouldn't have you remember if we on you know from doing some examples of office hours OK so now let's look at
a more spectra so this is 1 of the things where exhortations to read the directions before doing it were really really important so people didn't sad time-wasting things like there were people who I didn't just spectrum for the protons that were labeled they like some people actually crossed out my labels and relabeled the whole thing and all the protons and it was sad that must have taken forever and you know that people don't have time for the things on people tried to draw a Proton for the 1 that's labeled with the stock which of course has for bonds to that program so you know I'm not being mean and this playing out like I read the directions serving other things in there that are meant to save you time and you know like not having to draw the spectrum for all of protons OK so let's look at what we have to do
1st to get that's OK so we have a chemical shift table and so
1 of the 1st things to do here is identifying your various functional groups so we have 80 here so we have our 2 protons here and some people made the mistake of saying that this thing was a Kerviel so that would be and the others so they put it in the chemical shift range and that's not what it's right it's got units between these 2 oxygen so it's anything so it would be toward the you know higher chemical shift the end of the ether because it's got to them it so it should be somewhere around St you know 4 or 5 ppm somewhere in there for now AFP something OK what else have we got so d here an aromatic it has a proton as its neighbor see is a methyl group being as a proton there and it's got so is going to be a complicated the multiplex right because it's got 2 neighbors on 1 side and 3 and the other in the not equivalent but so OK we figured out what chemical shift everything should be so we can start growing the spectrum so you get points for labeling the axis and all let's start on the San Acacio so are aromatic here is going to be on you know between 7 and 9 ppm salutes you know put down here and it has 1 neighbor so it'll be a Dublin and then Aretha is going to be the next 1 along the chemical shift scale and it just has to oxygen is next to it which we can probably assume our new 0 16 and so it's just going to be a single and then our methyl group here is going to be a further steps toward 0 and it's going to be a double because it only has 1 neighbor and then were left with what is being so it's got 2 sets of neighbors better in equivalent and I'll be there's there's 2 Perkins on 1 side and 3 on the other and I didn't tell you which J coupling is larger so it is either a truckload of quartets or a quartet of triplets if you wrote something like that and drew near this that's fine on some people really carefully through the the picture out you know again and I wanna know if you understand it not not your ability to draw these things beautifully because as you can see I'm not so great and I yes for the chemical shift range you got points if they were in the right order relative to each other and the chemical shift scale was something reasonable but you know thinking that that this thing is a Kerviel and putting it at 12 ppm was not reasonable yes it doesn't because it's exchangeable it means it's popping up on and off all the time In an interview exchanges with the solvent but although you know people who who are mixed in the nitrogen per ton in the think just a couple .period Web site In the interest of the rest of it that's not a huge deal OK so that is that is that 1 and then
we said a new spectrum His collected with that the carbon decoupling turned off we want to see the signal for the proton labeled a case of the carbon coupling is turned off so that means in our sonar previous spectrum we didn't see any coupling the 13 now the decoupling is turned off and we're going to see 13 assists and 1 half and proton a River that was the 1 that was any further and it didn't have any neighbors so it was a single it before and so if it's not be coupled it's a Dublin that that was either right or restaurant and so then we had all moved an inversion recovery experiment is performed on the 13th of molecules this is the experiment that we do to measure the um the longitudinal relaxation time so we put everything we have looked all the spends signalman wait for it to relax and measure how long it takes to relax fact equilibrium and remember what causes relaxation to equal to equilibrium it's fluctuating magnetic fields local to that nucleus so something that has direct dipole dipole couplings with protons directly bonded to a proton that's can relax faster than something that doesn't have that I remember another important source of authority when relaxations methyl rotation on and also just molecular motion and so in all of these respects New Year's our here's are
molecule again the 1 that's labeled with star is not permitted it's aromatic so it's probably going to be rigid confirmation and is is a mouthful so the 1 that returns to equilibrium more quickly is seen as apple and basically any 1 of these explanations works so if you have any reason why it so why it's going to have a quick relaxation time that was good yes so so what do you mean by steric hindrance I don't see how that has to do anything that has anything to do with it but you know where we need over ones that have to do with the b this is the argument that the new kind but it's not it's not that it's starting in had like a T Beutel group that would still relax pretty fast because those levels can still retain so sorry now that you have to have something about conformational rigidities yes you don't have the the best of the lot well but can so it's which 1 is connected to more Adams this what well but it's not right both connected to 3 2 4 other Adams it depends on it matters what those items are so you know if you if you on we can talk about it later I With the arresting if you just if you got which 1 took a longer time right and not be explanation to back a partial credit yesterday OK all along that's it that's the exam
so Armageddon the grading is almost done will get done as fast as we can today and incentive to get scant pans next time Morgan start talking about statistical mechanics


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