Distillation

This apparatus is what a chemist uses to distill things. There is a long cylindrical tube connected to a flask that sits on a heat source. The tube connects to another, similarly shaped tube that sticks out from its side, and is pointed downward. This tube, called the "condenser" has water running through a cavity between the inside and outside of the glass -- sort of like having a glass tube within a slightly larger glass tube. This tube ends in a spout, where some sort of receptacle is placed for collection. In the picture above, the receptacle is a graduated cylinder with a red plastic bottom.

What occurs macroscopically in a distillation is pretty common to everyday experience: You add heat to some liquid, and the liquid evaporates up the tube and eventually travels through the condenser, where the water quickly cools the vapor, and drips out of the spout and into the receptacle. In particular, this is how liquor companies obtain higher concentrations of alcohol. When you make alcohol, the alcohol is fully dissolved in water -- like beer, or wine. The trick to higher alcohol content lies in... Chemistry!

So, suppose a beaker full of recently made alcohol -- it will be clear, and from appearances look to be the same liquid. This is because alcohol is miscible in water, which is the opposite of what happens when you mix oil and water. No matter how much water and alcohol you mix together, they will always freely intermingle. So, you're left with a beaker of water and alcohol molecules:

Behold the power of paint! The blue atoms with two red atoms coming off of them is a water molecule. The other one is a molecule of the drinking variety of alcohol. It has a blue atom as well because both water and alcohol have Oxygen in them.


How would you separate these?

A quick look at ethanol's MSDS sheet tells us that the alcohol has a boiling point of 78 degrees Centigrade. Water's boiling point is 100 degrees centigrade. Attempting to boil the mixed liquid seems like a good idea. And, in fact, this is how alcohol and water are separated -- first the alcohol evaporates and is collected, then the water will stop evaporating. If you want to keep them separate, you stop the distillation once you have collected the majority of your alcohol. How does one tell when that happens?

You'll notice in the photograph a thermometer. If we plot a graph of the amount of liquid collected on the x-axis versus the temperature of the vapor (which corresponds to the liquid's temperature) on the y-axis, you'll see something like this:

I chose this image on purpose because it displays the two types of distillation on the same graph -- simple and fractional. They both have roughly the same shape, only fractional distillation has a much larger spike in its temperature. We'll come back to this sh0rtly.

Note also that alcohol, which evaporates first, has a lower boiling point than the water. Also note that the temperature in the graph climbs as the distillation occurs. This is because the vapor evaporating has an increasing number of water molecules, which require a higher temperature to vaporize. So, you know that you have collected as much alcohol as you can when you reach a mid-point on the graph, which you can determine experimentally by running the whole distillation once through.

Also note in this graph that the fractional distillation has a much sharper jump in temperature. This is because, initially, you are evaporating mostly alcohol and leaving most of the water, but then suddenly you only have water. In the simple distillation, the rate of change of the ratio of alcohol to water is much more gradual (prepositional phrase glory, right there). That is because...

*fan-fare!*

The fractional distillation simulates doing a simple distillation hundreds of times over! Well, I'm uncertain about the actual factor, but it does simulate it going over and over again. The photograph above shows a set up for fractional distillation. If it were a simple distillation, the flask carrying the mixture wouldn't be connected to a long vertical tube, but would be next to the condenser. In the vertical tube are placed several glass beads. As the vapor rises, it condenses on the beads (since the beads are cooler than the vapor), and the heat from more vapor gradually warms up the bead until the condensate evaporates again. This occurs time and time again, with some of the liquid pouring back down into the initial flask. Each time this occurs, the mixture becomes a little more concentrated in the chemical with the lower boiling point -- in this case, the drinking alcohol. With a simple distillation, this occurs only once, but the beads essentially simulate many simple distillations in a row.

Now, an oddity here -- you'll notice from the Paint drawn beaker diagram above that the alcohol molecules are actually larger than the water molecules. The molecular weight of alcohol is, roughly, 46 grams per mole. Water's molecular weight is 18 grams per mole. Yet, despite having more mass (thereby giving the impression that it will need more heat, which can be roughly thought of as energy, to turn into a gas), the alcohol has a lower boiling point. Stay tuned for this explanation next time! Whenever next time is. This is a busy semester.

Derivations

Two years over and done with, and I have a good feeling for reading equations. This isn't always the case -- I'm still unpacking things as complex as, say, the Schrodinger equation, but give me something along the lines of chemical kinetics, a classical mechanics problem, or the ideal gas law: Yeah, I feel pretty good about reading the relationship. Just as I feel comfortable with reading equations, this year has a new angle being thrown at me: Deriving equations from other equations.

Holy shit, derivations are difficult. So far, I have no real "feel" for where to begin in deriving. I just write down two or three related equations, isolate some variables, do some substitutions, and play with the rules of logarithms hoping that all my random math play will, in the end, give me the equation that I'm looking for. To say the least, this doesn't help. I've been walked through deriving the ideal gas law using classical mechanics, and the derivation itself makes complete sense. But now, left on my own, I feel entirely stuck.

The current problem: Derive P^gamma V = constant from PT^f/2 = constant, where gamma = f+2/2, and f is the degrees of freedom. So, I have both forms of the ideal gas law, the first law of thermodynamics, a definition for work, and the equipartition theorem of energy... I think I could google something up, but this wouldn't help me in knowing how to actually derive equations, rather than follow arguments.

If you have any kind of method for deriving equations, then this is my desperate cry for help. In the end, I'll get it. But it'd be nice to see what other people do if and when they derive equations.

EDIT: In solving, I found a new "method" for derivations. Working backwards. By playing with the "end" result in the same way that I played with the beginning result, I was able to see a familiar form that I knew I could convert the beginning result to. Other than that... no method, really. More intuition.

Teaching Experience, 2

Alright, so teaching is much much more complicated than tutoring, granted, but it's where I get my practice in the craft at this point in time. And as it's easier, it's a good place to practice, because I get to directly see results. It probably also helps that the people I tutor come willingly and are paying for their classes. So, it's like baby-teaching. Nevertheless, it's a good field to practice and develop my teaching skills, so I'm still labeling it "Teaching Experience"

Today, we covered Unit Conversions and basic chemical nomenclature. Nomenclature is hard to teach because there aren't any real patterns to pick out, and there is quite a bit of data to memorize. As such, you just have to memorize by use, so the best way to teach it is to do it. In a tutoring session, that seems difficult, but upon reflection now, I think naming drills may have been the ideal solution. Must pocket this idea for the future.

Unit Conversions are fairly simple, but they still stump a lot of people. So, like most people, I use the picket-fence method, AKA Dimensional Analysis -- However, I've found in teaching that the use of big unfamiliar words gets in the way of the concept, so it's usually better to introduce the concept first, and then the big unfamiliar word attached to that concept. There isn't a real reason I can think of why, other than the big unfamiliar word sounds scary, so those who are low on confidence (like those who like to go to tutoring sessions) will often shoot themselves down before the concept is introduced. Further, something else that I've found great for tutoring is to start doing the work on the board, but only write what is stated by the students. That way they have to do the thinking, and you're not stuck there giving another lecture that the students have already heard. It's a bit silly to do that in a tutoring session, especially when the lecture didn't get through to them. Sometimes I throw hints in there, or to make things easier I'll explain a single step and do it so they don't become frustrated, but overall I find letting students do the work teaches them better than doing it for them.

Also,I love having more than one student at tutoring. I haven't experienced this until recently, as I'm only recently in a position where we have open tutoring. But today, when one student understood the problem and the other didn't, the first student jumped right in to answer the other students question: So the first student was reviewing the material while the second student was having it explained in a way that maybe is a little simpler than I'm explaining it -- I'm used to dimensional analysis, as well as Chemistry in general, so the terms I'm used to working in may in fact be above the head of those taking Freshman Chemistry. In fact, not just may, but ARE. That is one of the great difficulties in teaching -- you become proficient in a subject, but it becomes difficult to explain the subject because in becoming proficient you generally forget some of the simple steps in between that you used to have to take consciously in order to solve problems. Or you just assimilate simple terms into more complex terms in order to store a greater amount of information. Then you have to unpack all that knowledge, and lead people along step by step from the beginning while not intimidating them, entertaining them, and being there friend while still maintaining a position of authority and respecting their values and way of thinking but modifying it in such a way that they become better thinkers and learn the actual subject matter.

Fascinating. Difficult. Rewarding. Undervalued.

Heisenberg

I'm currently reading "Uncertainty" by David Cassidy in conjunction with my P-chem class. While I can't currently write a review of the book, as I haven't finished yet, I do have to say that reading about his early life is a serious motivator for myself. He learned how to apply Calculus to Physics during his high school years through self-study. I'm in my mid-twenties, and while I've progressed in that direction to a point that I'm feel pretty confident with it now, man! I did that with the help of professors lecturing me on that very topic. Looking at the educational ability of the greats around the turn-of-the-century is humbling and inspiring.

Also, interesting fact: Max Plank, Albert Einstein, and Werner Heisenberg all graduated from the same "Gymnasium" -- early 20th century German equivalent to our High Schools. Implicated reason for this: the rich ensured that the best teachers were teaching at their Gymnasium by way of spending money on them. This isn't pointed out to denigrate the ability of these great men, but it does make you wonder about those who think teachers are already payed enough. (Totally anecdotal evidence reinforcing my personal bias in action)