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This collection consists of digital images of the correspondence of John Muir from 1856-1914. The vast majority of the letters were sent and received by Muir, although the collection also includes some correspondence of selected family members and colleagues. Muir’s correspondence offers a unique first-hand perspective on his thoughts and experiences, as well as those of his correspondents, which include |
many notable figures in scientific, literary, and political circles of the 19th and early 20th centuries. The correspondence forms part of the John Muir Papers microfilm set that filmed letters located at over 35 institutions. A Scottish-born journalist and naturalist, John Muir (1838-1914) studied botany and geology at the University of Wisconsin (1861-1863). He worked for awhile as a mill |
hand at the Trout Broom Factory in Meaford, Canada (1864-1866), then at an Indianapolis carriage factory (1866-1867), until an accident temporarily blinded him and directed his thoughts toward full-time nature study. Striking out on foot for South America, Muir walked to the Gulf of Mexico (September 1867-January 1868), but a long illness in Florida led him to change his plans |
and turn his interests westward. Muir arrived by ship at San Francisco (March 1868), walked to the Sierra Nevada Mountains and began a five year wilderness sojourn (1868-1873) during which he made his year-round home in the Yosemite Valley. Working as a sheepherder and lumberman when he needed money for supplies, Muir investigated the length and breadth of the Sierra |
range, focusing most of his attention on glaciation and its impact on mountain topography. He began to publish newspaper articles about what he saw in the California mountains and these articles brought him to the attention of such intellectuals as Asa Gray and Ralph Waldo Emerson, both of whom sought him out during their visits to California. Encouraged by Jeanne |
Carr, wife of his one-time botany professor, Ezra S. Carr, Muir took up nature writing as a profession (1872). He set up winter headquarters in Oakland and began a pattern of spring and summer mountaineering followed by winter writing based upon his travel journals that he held to until 1880. His treks took him to Mount Shasta (1874, 1875 & |
1877), the Great Basin (1876, 1877, 1878), southern California and the Coast Range (1877), and southern Alaska (1879). Muir found that he could finance his modest bachelor lifestyle with revenue from contributions published in various San Francisco newspapers and magazines. During this period he launched the first lobbying effort to protect Sierra forests from wasteful lumbering Some of the materials |
in the John Muir Correspondence Collection may be protected by the U.S. Copyright Law (Title 17, U.S.C.) and/or by the copyright or neighboring rights laws of other nations. Additionally, the reproduction of some materials may be restricted by privacy or publicity rights. Responsibility for making an independent legal assessment of an item and securing any necessary permissions ultimately rests with |
Giant Manta Ray Giant Manta Ray Manta birostris Divers often describe the experience of swimming beneath a manta ray as like being overtaken by a huge flying saucer. This ray |
is the biggest in the world, but like the biggest shark, the whale shark, it is a harmless consumer of plankton. When feeding, it swims along with its cavernous mouth |
wide open, beating its huge triangular wings slowly up and down. On either side of the mouth, which is at the front of the head, there are two long paddles, |
called cephalic lobes. These lobes help funnel plankton into the mouth. A stingerless whiplike tail trails behind. Giant manta rays tend to be found over high points like seamounts where |
currents bring plankton up to them. Small fish called remoras often travel attached to these giants, feeding on food scraps along the way. Giant mantas are ovoviviparous, so the eggs |
Topics covered: Ideal solutions Instructor/speaker: Moungi Bawendi, Keith Nelson The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view |
additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: So. In the meantime, you've started looking at two phase equilibrium. So now we're starting to look at mixtures. And so now we have more than one |
constituent. And we have more than one phase present. Right? So you've started to look at things that look like this, where you've got, let's say, two components. Both in the gas phase. And now to try to figure out |
what the phase equilibria look like. Of course it's now a little bit more complicated than what you went through before, where you can get pressure temperature phase diagrams with just a single component. Now we want to worry about |
what's the composition. Of each of the components. In each of the phases. And what's the temperature and the pressure. Total and partial pressures and all of that. So you can really figure out everything about both phases. And there |
are all sorts of important reasons to do that, obviously lots of chemistry happens in liquid mixtures. Some in gas mixtures. Some where they're in equilibrium. All sorts of chemical processes. Distillation, for example, takes advantage of the properties of |
liquid and gas mixtures. Where one of them might be richer, will be richer, and the more volatile of the components. That can be used as a basis for purification. You mix ethanol and water together so you've got a |
liquid with a certain composition of each. The gas is going to be richer and the more volatile of the two, the ethanol. So in a distillation, where you put things up in the gas, more of the ethanol comes |
up. You could then collect that gas, right? And re-condense it, and make a new liquid. Which is much richer in ethanol than the original liquid was. Then you could make, then you could put some of them up into |
the gas phase. Where it will be still richer in ethanol. And then you could collect that and repeat the process. So the point is that properties of liquid gas, two-component or multi-component mixtures like this can be exploited. Basically, |
the different volatilities of the different components can be exploited for things like purification. Also if you want to calculate chemical equilibria in the liquid and gas phase, of course, now you've seen chemical equilibrium, so the amount of reaction |
depends on the composition. So of course if you want reactions to go, then this also can be exploited by looking at which phase might be richer in one reactant or another. And thereby pushing the equilibrium toward one direction |
or the other. OK. So. we've got some total temperature and pressure. And we have compositions. So in the gas phase, we've got mole fractions yA and yB. In the liquid phase we've got mole fractions xA and xB. So |
that's our system. One of the things that you established last time is that, so there are the total number of variables including the temperature and the pressure. And let's say the mole fraction of A in each of the |
liquid and gas phases, right? But then there are constraints. Because the chemical potentials have to be equal, right? Chemical potential of A has to be equal in the liquid and gas. Same with B. Those two constraints reduce the |
number of independent variables. So there'll be two in this case rather than four independent variables. If you control those, then everything else will follow. What that means is if you've got a, if you control, if you fix the |
temperature and the total pressure, everything else should be determinable. No more free variables. And then, what you saw is that in simple or ideal liquid mixtures, a result called Raoult's law would hold. Which just says that the partial |
pressure of A is equal to the mole fraction of A in the liquid times the pressure of pure A over the liquid. And so what this gives you is a diagram that looks like this. If we plot this |
versus xB, this is mole fraction of B in the liquid going from zero to one. Then we could construct a diagram of this sort. So this is the total pressure of A and B. The partial pressures are given |
by these lines. So this is our pA star and pB star. The pressures over the pure liquid A and B at the limits of mole fraction of B being zero and one. So in this situation, for example, A |
is the more volatile of the components. So it's partial pressure over its pure liquid. At this temperature. Is higher than the partial pressure of B over its pure liquid. A would be the ethanol, for example and B the |
water in that mixture. OK. Then you started looking at both the gas and the liquid phase in the same diagram. So this is the mole fraction of the liquid. If you look and see, well, OK now we should |
be able to determine the mole fraction in the gas as well. Again, if we note total temperature and pressure, everything else must follow. And so, you saw this worked out. Relation between p and yA, for example. The result |
was p is pA star times pB star over pA star plus pB star minus pA star times yA. And the point here is that unlike this case, where you have a linear relationship, the relationship between the pressure and |
the liquid mole fraction isn't linear. We can still plot it, of course. So if we do that, then we end up with a diagram that looks like the following. Now I'm going to keep both mole fractions, xB and |
yB, I've got some total pressure. I still have my linear relationship. And then I have a non-linear relationship between the pressure and the mole fraction in the gas phase. So let's just fill this in. Here is pA star |
still. Here's pB star. Of course, at the limits they're still, both mole fractions they're zero and one. OK. I believe this is this is where you ended up at the end of the last lecture. But it's probably not |
so clear exactly how you read something like this. And use it. It's extremely useful. You just have to kind of learn how to follow what happens in a diagram like this. And that's what I want to spend some |
of today doing. Is just, walking through what's happening physically, with a container with a mixture of the two. And how does that correspond to what gets read off the diagram under different conditions. So. Let's just start somewhere on |
a phase diagram like this. Let's start up here at some point one, so we're in the pure - well, not pure, you're in the all liquid phase. It's still a mixture. It's not a pure substance. pA star, pB |
star. There's the gas phase. So, if we start at one, and now there's some total pressure. And now we're going to reduce it. What happens? We start with a pure - with an all-liquid mixture. No gas. And now |
we're going to bring down the pressure. Allowing some of the liquid to go up into the gas phase. So, we can do that. And once we reach point two, then we find a coexistence curve. Now the liquid and |
gas are going to coexist. So this is the liquid phase. And that means that this must be xB. And it's xB at one, but it's also xB at two, and I want to emphasize that. So let's put our |
pressure for two. And if we go over here, this is telling us about the mole fraction in the gas phase. That's what these curves are, remember. So this is the one that's showing us the mole fraction in the |
liquid phase. This nonlinear one in the gas phase. So that means just reading off it, this is xB, that's the liquid mole fraction. Here's yB. The gas mole fraction. They're not the same, right, because of course the components |
have different volatility. A's more volatile. So that means that the mole fraction of B in the liquid phase is higher than the mole fraction of B in the gas phase. Because A is the more volatile component. So more, |
relatively more, of A, the mole fraction of A is going to be higher up in the gas phase. Which means the mole fraction of B is lower in the gas phase. So, yB less than xB if A is |
more volatile. OK, so now what's happening physically? Well, we started at a point where we only had the liquid present. So at our initial pressure, we just have all liquid. There's some xB at one. That's all there is, |
there isn't any gas yet. Now, what happened here? Well, now we lowered the pressure. So you could imagine, well, we made the box bigger. Now, if the liquid was under pressure, being squeezed by the box, right then you |
could make the box a little bit bigger. And there's still no gas. That's moving down like this. But then you get to a point where there's just barely any pressure on top of the liquid. And then you keep |
expanding the box. Now some gas is going to form. So now we're going to go to our case two. We've got a bigger box. And now, right around where this was, this is going to be liquid. And there's |
gas up here. So up here is yB at pressure two. Here's xB at pressure two. Liquid and gas. So that's where we are at point two here. Now, what happens if we keep going? Let's lower the pressure some |
more. Well, we can lower it and do this. But really if we want to see what's happening in each of the phases, we have to stay on the coexistence curves. Those are what tell us what the pressures are. |
What the partial pressure are going to be in each of the phases. In each of the two, in the liquid and the gas phases. So let's say we lower the pressure a little more. What's going to happen is, |
then we'll end up somewhere over here. In the liquid, and that'll correspond to something over here in the gas. So here's three. So now we're going to have, that's going to be xB at pressure three. And over here |
is going to be yB at pressure three. And all we've done, of course, is we've just expanded this further. So now we've got a still taller box. And the liquid is going to be a little lower because some |
of it has evaporated, formed the gas phase. So here's xB at three. Here's yB at three, here's our gas phase. Now we could decrease even further. And this is the sort of thing that you maybe can't do in |
real life. But I can do on a blackboard. I'm going to give myself more room on this curve, to finish this illustration. There. Beautiful. So now we can lower a little bit further, and what I want to illustrate |
is, if we keep going down, eventually we get to a pressure where now if we look over in the gas phase, we're at the same pressure, mole fraction that we had originally in the liquid phase. So let's make |
four even lower pressure. What does that mean? What it means is, we're running out of liquid. So what's supposed to happen is A is the more volatile component. So as we start opening up some room for gas to |
form, you get more of A in the gas phase. But of course, and the liquid is richer in B. But of course, eventually you run out of liquid. You make the box pretty big, and you run out, or |
you have the very last drop of liquid. So what's the mole fraction of B in the gas phase? It has to be the same as what it started in in the liquid phase. Because after all the total number |
of moles of A and B hasn't changed any. So if you take them all from the liquid and put them all up into the gas phase, it must be the same. So yB of four. Once you just have |
the last drop. So then yB of four is basically equal to xB of one. Because everything's now up in the gas phase. So in principle, there's still a tiny, tiny bit of xB at pressure four. Well, we could |
keep lowering the pressure. We could make the box a little bigger. Then the very last of the liquid is going to be gone. And what'll happen then is, we're all here. There's no more liquid. We're not going down |
on the coexistence curve any more. We don't have a liquid gas coexistence any more. We just have a gas phase. Of course, we can continue to lower the pressure. And then what we're doing is just going down here. |
So there's five. And five is the same as this only bigger. And so forth. OK, any questions about how this works? It's really important to just gain facility in reading these things and seeing, OK, what is it that |
this is telling you. And you can see it's not complicated to do it, but it takes a little bit of practice. OK. Now, of course, we could do exactly the same thing starting from the gas phase. And raising |
the pressure. And although you may anticipate that it's kind of pedantic, I really do want to illustrate something by it. So let me just imagine that we're going to do that. Let's start all in the gas phase. Up |
here's the liquid. pA star, pB star. And now let's start somewhere here. So we're down somewhere in the gas phase with some composition. So it's the same story, except now we're starting here. It's all gas. And we're going |
to start squeezing. We're increasing the pressure. And eventually here's one, will reach two, so of course here's our yB. We started with all gas, no liquid. So this is yB of one. It's the same as yB of two, |
I'm just raising the pressure enough to just reach the coexistence curve. And of course, out here tells us xB of two, right? So what is it saying? We've squeezed and started to form some liquid. And the liquid is |
richer in component B. Maybe it's ethanol water again. And we squeeze, and now we've got more water in the liquid phase than in the gas phase. Because water's the less volatile component. It's what's going to condense first. So |
the liquid is rich in the less volatile of the components. Now, obviously, we can continue in doing exactly the reverse of what I showed you. But all I want to really illustrate is, this is a strategy for purification |
of the less volatile component. Once you've done this, well now you've got some liquid. Now you could collect that liquid in a separate vessel. So let's collect the liquid mixture with xB of two. So it's got some mole |
fraction of B. So we've purified that. But now we're going to start, we've got pure liquid. Now let's make the vessel big. So it all goes into the gas phase. Then lower p. All gas. So we start with |
yB of three, which equals xB of two. In other words, it's the same mole fraction. So let's reconstruct that. So here's p of two. And now we're going to go to some new pressure. And the point is, now |
we're going to start, since the mole fraction in the gas phase that we're starting from is the same number as this was. So it's around here somewhere. That's yB of three equals xB of two. And we're down here. |
In other words, all we've done is make the container big enough so the pressure's low and it's all in the gas phase. That's all we have, is the gas. But the composition is whatever the composition is that we |
extracted here from the liquid. So this xB, which is the liquid mole fraction, is now yB, the gas mole fraction. Of course, the pressure is different. Lower than it was before. Great. Now let's increase. So here's three. And |
now let's increase the pressure to four. And of course what happens, now we've got coexistence. So here's liquid. Here's gas. So, now we're over here again. There's xB at pressure four. Pure still in component B. We can repeat |
the same procedure. Collect it. All liquid, put it in a new vessel. Expand it, lower the pressure, all goes back into the gas phase. Do it all again. And the point is, what you're doing is walking along here. |
Here to here. Then you start down here, and go from here to here. From here to here. And you can purify. Now, of course, the optimal procedure, you have to think a little bit. Because if you really do |
precisely what I said, you're going to have a mighty little bit of material each time you do that. So yes it'll be the little bit you've gotten at the end is going to be really pure, but there's not |
a whole lot of it. Because, remember, what we said is let's raise the pressure until we just start being on the coexistence curve. So we've still got mostly gas. Little bit of liquid. Now, I could raise the pressure |
a bit higher. So that in the interest of having more of the liquid, when I do that, though, the liquid that I have at this higher pressure won't be as enriched as it was down here. Now, I could |
still do this procedure. I could just do more of them. So it takes a little bit of judiciousness to figure out how to optimize that. In the end, though, you can continue to walk your way down through these |
coexistence curves and purify repeatedly the component B, the less volatile of them, and end up with some amount of it. And there'll be some balance between the amount that you feel like you need to end up with and |
how pure you need it to be. Any questions about how this works? So purification of less volatile components. Now, how much of each of these quantities in each of these phases? So, pertinent to this discussion, of course we |
need to know that. If you want to try to optimize a procedure like that, of course it's going to be crucial to be able to understand and calculate for any pressure that you decide to raise to, just how |
many moles do you have in each of the phases? So at the end of the day, you can figure out, OK, now when I reach a certain degree of purification, here's how much of the stuff I end up |
with. Well, that turns out to be reasonably straightforward to do. And so what I'll go through is a simple mathematical derivation. And it turns out that it allows you to just read right off the diagram how much of |
each material you're going to end up with. So, here's what happens. This is something called the lever rule. How much of each component is there in each phase? So let's consider a case like this. Let me draw yet |
once again, just to get the numbering consistent. With how we'll treat this. So we're going to start here. And I want to draw it right in the middle, so I've got plenty of room. And we're going to go |
up to some pressure. And somewhere out there, now I can go to my coexistence curves. Liquid. And gas. And I can read off my values. So this is the liquid xB. So I'm going to go up to some |
point two, here's xB of two. Here's yB of two. Great. Now let's get these written in. So let's just define terms a little bit. nA, nB. Or just our total number of moles. ng and n liquid, of course, |
total number of moles. In the gas and liquid phases. So let's just do the calculation for each of these two cases. We'll start with one. That's the easier case. Because then we have only the gas. So at one, |
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