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Byers and Williams ("Viscosities of Binary and Ternary Mixtures of Polyaromatic Hydrocarbons," Journal of Chemical and Engineering Data, $32,349-354$ 1987...

Question

Byers and Williams ("Viscosities of Binary and Ternary Mixtures of Polyaromatic Hydrocarbons," Journal of Chemical and Engineering Data, $32,349-354$ 1987) studied the impact of temperature (the regressor) on the viscosity (the response $)$ of toluene-tetralin blends. The following table gives the data for blends with a 0.4 molar fraction of toluene.a. Plot a scatter diagram. Does it seem likely that a straight-line model will be adequate?b. Fit the straight-line model. Compute the sum

Byers and Williams ("Viscosities of Binary and Ternary Mixtures of Polyaromatic Hydrocarbons," Journal of Chemical and Engineering Data, $32,349-354$ 1987) studied the impact of temperature (the regressor) on the viscosity (the response $)$ of toluene-tetralin blends. The following table gives the data for blends with a 0.4 molar fraction of toluene. a. Plot a scatter diagram. Does it seem likely that a straight-line model will be adequate? b. Fit the straight-line model. Compute the summary statistics and the residual plots. What are your conclusions regarding model adequacy? c. Basic principles of physical chemistry suggest that the viscosity is an exponential function of the temperature. Repeat part b using the appropriate transformation based on this information.



Answers

Temperature Data Table 1.21 gives the average monthly temperatures for St. Louis for a 12 -month period starting with January. Model the monthly temperature with an equation of the form

$y=a \sin [b(t-h)]+k$

$y$ in degrees Fahrenheit, $t$ in months, as follows:

(a) Find the value of $b$ assuming that the period is 12 months.
(b) How is the amplitude $a$ related to the difference $80^{\circ}-30^{\circ}$?
(c) Use the information in (b) to find $k$ .
(d) Find $h$ , and write an equation for $y$ .
(e) Superimpose a graph of y on a scatter plot of the data.

On question 48. We are looking at critical temperatures and pressures of a series of compounds, and our compounds in this case are CCL three CCL two, F two c c l, f three and C four in question A were asked to list intermingle of forces that occur for each compound. So, uh, this compound, because there are two different elements with two different lecture negativity is bonded to carbon. This is going to be a polar molecule. So this will have die, pull, die, pull interactions and was all. And as with all molecular compounds that this also have London dispersion forces. The same is true for this molecule. Even though there's two of each because of the structure of a tetra hydro, the polarities do not cancel. This will be a polar molecule. So this will have diable disciples and London dispersion forces. And again, with this guy it will also have die pulled I poll as well as London dispersion forces. Finally, our CIA four is a polar molecule is a non polar molecule. Sorry, So the only intermittently force it's gonna have our London dispersion forces. So that's question, eh? Question be asks us to arrange our substances in order of increasing inter molecular attraction from least to most so the what we're gonna use here is the fact that the higher the critical temperature, the stronger the entire regular forces. So we can basically list it from the lowest critical temperature to the highest critical temperature. So and it also follows that the one with the LD only L D EFS is the lowest, um, critical temperature. So are we're going to go from CIA four is our lowest, then C c L F three, then see seal two F two and then c c. L three in questions. See, it asked us to predict the critical temperatures and pressure for C seal four based on the trends and it's table above unstable number. Supposed to look it up and compare it. So for C SEAL, for that would be it would find that kind of here on our table. Um, and if I'm looking at, start off our start with the critical temperature. You kind of look at the trend. We can see that as the inter molecular forces increase, the critical temperature is increasing and the the it's also because the molecular weight is also increasing and therefore the critical temperature is increasing. And so we're looking at. There's an approximate difference of around 70 to 80 um 85. Maybe each time it goes up, it goes up by a little bit more. So if I were to take the critical temperature for the one before it for CCL three F, which was 4 71 and add, say approximately 85 we would get a critical temperature of 556 Kelvin. This compares in the sea air. See if you look it up. The critical temperature is actually 556.6 Calvin. So this is pretty close. If we look at the critical pressure again, the substance before it. CCL three f has a critical pressure of 43.5 atmospheres and we appear to be going up kind of increasing. But it looks like it should go by approximately three atmospheres following the trend. And so that would take it to 46.5 atmospheres. Um, and the Sear C actually says it's 44.6, so it doesn't go up quite a cz. Muchas might be predicted by the trend, but we're still in the ballpark

Given our the structures off. One pro panel on dhe to drop in on for option A. The boiling point off a molecule depends on the structure off molecule because depending on the structure off molecule interaction between the molecules dependent, the boiling point off one pope in all, it's 97 degrees else's via love to drop in on is 80 total results. Is auction be the compassion analysis off a compound depends on the type on number off atoms in a compound both one and to drop in on have seen number off atoms. So the results off compassion analysis provided by these compound will be the same auction. See, the molecular weight off compound is the sum, often atomic week off. All its Adam boot molecules off one and two pro panel have same number off atoms, so the results will be seen. Option D. The density is property for molecule that depends on the structure off molecule, because different structures off same mask can occupy a different William, the molecules that occupies a lesser volume will have a higher density, while the molecule that occupies ah higher volume will have a low density one drop in oil is the density off. One property is higher as compared to the density off to property. So auction A and D, other properties that can distinguish these two compounds.

All right, guys, we're doing chap chapter nine Problem one. Twenty. So the organic molecules shown here are through hours of Ben's E, which is a six member ring and in which six memories refused Quote unquote fused at the edges of the hexagons, termed the empirical form of benzene of and of these three compounds. So on the left you have benzine and on and on the centre left, you have a nap telling on center right, you have anther scene. And on the centre and on the far right you have Tetris E. And if you count the number and when we do this skeletal structure for organic molecules remember every point here that count as that counts as one carbon and I drew the high options one. So we have for Benzino Peric from a C six h six ex for art. Yes, sorry, Our molecular friendly for Benjie C six h six for because for Natalie, it's C ten age eight for Anderson and C fourteen h ten and for interesting it's C eighteen, eight twelve. So remember differently Molecular formula and NPR conformed. Empirical formula means that that it will be a simplified formula like It just shows thie. It just shows the proportion of the elements you have in your in your sample. So this is C sixty six, so there's so we can write that as C each. This is C ten a. J. So we could hit that as C five h for there's a C fourteen. Jane H ten is going to see seven No. H h five and this won't see eighteen h twelve. This can be C three age, too. So there's going to be the empirical formulas of our samples now for B. Suppose you were given a sample of one of the compounds. Could combustion analysis be used? Determined? Unambiguously. Which Which of the three it is? Well, yes. Well, let's say we're giving one the sample that we burn it in an oxygen and it gives us a certain amount of energy and the amount of energy that we have that's going to be the man of energy given off his going depends on on which sample we have. The more ch bonds you have, basically, the larger your organic structure is the more you're going bust, the more energy you want to produce. So tetrazzini is going to Bruce or algae. That anther scene is going to produce more energy than naphthalene, which is going produce more energy than Benzie. So we can accurately determine which of these is the are unknown sample based on how much energy based on how much energy based on how much energy is given off. Now see Napoli, the active agent active ingredient mothballs is white sought in a bounce equation for the combustion of Napoli in Teo too. Who? And to see a to gas as and water so us So we know what our now as s so we know what our naphthalene structure is And hold on I'll just make a new page So our nap our nap Dellin that is going to be the C five. Um I can choose Thie and I'll go to Milica Formal See ten h eight So plus oh to gas yield Seo too has Sorry, this is aged two of gas as so Let's bounce this out So we have tense in the carpets on this I mean to have ten on this side we have If it had shins and this side we have put a four in front of here four times two is going to be eight now having options we have on the right side. We have two times ten So twenty plus four. Twenty four. That means we have twelve over here. That's going to be our balanced equation. You shouldn't put the combustion of Napoli soon after party day once use a Lou short For now, Epling and the average bond of puppies found in table eight point three estimate the heat of combustion of napped Aleen in villages promote. So remember heat of combustion. We're going has his law. Delta h of that's his reaction is equal to Delta. Is your products minus Delta h of reactant? So let's see how many bonds we have A personally First we're going. Yes. So this so let's look at the kind of bonds we have. So we're going to have Cee Cee, we're going to have a C see with a double bond. See? Age. Oh, oh, Double bond toe. Oh, Oh, See the Laban toe and a Joe. So we're gonna look at her table. So for C c Super ch, it's for thirteen killed Jules promoting H for CC. It's three. Forty eight killer jewels for more for C double bonded at six fourteen kilograms. Promote. Oh oh, it's for ninety five Killer. Jules. Promote us. And for seven ninety nine that sorry First see double bind toe oxygen seven. Ninety nine kilometers promote. And for oh age, it's going to be for sixty three killer deals. Promote. Sorry for sixty three. Kill a Jules Promote. Now let's look at how many of each bond we have. So for our so far, our issue A We have two of these get to a wage bonds for CEO that carbon dioxide. We have two of these. Well, for each two for O two, we have one of these. And now for ch. Since we have eight age hydrogen is that means we have eight of those bonds. That's for C. C. Let's see, we have one, two, three, four, five. Not for seat. See? Single bonds. We have one, two, three, four, five, six. I think so. Yes. So wanted three. Four, five of your Dubonnet. Then we got one too. Two, three, four, five, six. All right, now we're going to use. Has his law dealt h er prices equal? Don't mention reaction is equal. Delta H of products mind still teach of reactions. So about the age and that's going to be two times No for sixty three. Hey, as four times two times four sixty three Because we do have to add the coefficient plus ten times, two times seven ninety nine minus as we have twelve and we have one of each month. So we have four. Thank you for ninety five. I've and let me see if I can pull this down. So I know I'm not good enough for him for this. Twelve times for ninety five. Plus, yes. And we're looking at the number of months and we only have one more. So we're going to be looking at and thanks times three for eight plus as a plus five times six one four plus eight times for one three. Now we're gonna place and put this in our calculator. So before times two, that's for sixty three plus ten times. Two times seven ninety nine. So twelve times minus trial test for ninety five plus six times three forty eight plus five times six fourteen plus eight times for thirteen May twelve. Us. From there five plus six times plus three times three eight three. So that means the Delta H. So because the delta h for this reaction uh, Ellen, I've made mistake for sixty three plus ten times, two times in the neck, nine minus twelve times forty five plus six times three, three, eight, five times six thirteen eight times for thirteen That's going to be equal to to a delta H value. Fuck five thousand eight hundred five thousand two hundred eighty two Killer Jules Promote No, no party. Benzene Appling Anther senior Karlis But Tetra Xena's orange Where's this imply about the relative home A limo energy gap ramp in gap in these molecules. So let's remember what our home a loom Oh, energy gap is so are you know us. So we have energy levels for specific electrons. Your homo is your highest occupied molecular orbital and your loom Oh, and let me just draw an electron Here you're Lu Mo is your lowest unoccupied molecular Corporal, you're Lou Mo is higher in energy than your homo is. So when so Remember when we talked about light we're talking as us an electron is as absorbs a certain frequency of light. And that frequency? Yeah, yes, And that will excite electronic for to go from the homo to the loo. Mo us. So our electron will go from our homo us, and it will go to our limo that us and the different energy between your home on limo that's gonna correspond to a specific wavelength of light that you're absorbing. Conversely, when you're excited, electron goes down, too, to go to the homo that's going to correspond to a specific wavelength of love like that being released, like when we see that something is orange that's not is not absorbing orange light. It's reflecting blue light. Wait that it's reflecting blue light and that's what us and sorry. It's absorbing blue light and it's reflecting orange light. And that's the light that we see in our eye. So So how did like I said before, the difference in energy between the home a loom? Oh, Gap. Yep, that that's depend that determines what color you're going to see now when we talk about what white light is. E is the e is the combination of the number of his combination of all light in the visible spectrum, so If we see something that looks white, that means that it's not absorbing any light. And it's reflecting. And for collecting all the wavelength of this belief light bright back down this snus. So if no light is able to be absorbed, that means the difference between our home own limo is so great that you can't make that entered. You can't excite your electron using visible light so that so That means that, for example, are benzene is going to have a greater home, AlumAl gap. Then our tetrazzini does so and we can see that as you go from Ben seen nothing Answer scene to ten tracing. Eventually we are going from white salad to a color solid. And so that means that as we are adding more and more rings to r us to our organic molecules, then that means that you're you're ah, what was the word before? Fine, you're you're shortening the distance between your homo and your loom. Oh oh, and so that means that at for Tetro Zine, it's home. A limo gap is sure enough that are. Electrons can be excited from our homo to our limo and then and you can make the transition from the limo to the Homo and that will cause. And that energy transition causes the orange light that we're seeing. So that means that as so like I said, that means that as you were adding more rings to your organic molecules, then you're gradually, gradually the you're gradually closing the gap between your homo and your loom, a levels levels so that so that transition, which from home gloom Oh, that becomes a lot more energetically favourable. And that's it for this for this question.

Surface tension, and here we're taking a look at viscosity in the context of surface tension. So we have a few different parts to this podcast to cover. And so, with our ethylene glycol, this has the greatest mass, and therefore we have a higher viscosity on greater hydrogen bonding, whereas acetone on ethanol are very similar and mass, really. But ethanol does have hydrogen bonding between its molecules, which leads to a greater viscosity. Acetone is slightly more polar in nature compared to di ethyl ether. And so this leads to some amount of dipole dipole interactions that we may observe. And therefore we have a higher viscosity for acetone than di ethyl ether. So in the second part here, so ethylene glycol has extensive hydrogen bonding, and so that's what has a high surface tension on the surface. Tension of ethanol on acetone are roughly the same


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