Thursday, May 13, 2010

Process: Work

The first law is concerned with the internal energy change of a system. This is what ΔU represents. As I admitted earlier U is an odd concept to me. I think this primarily arises because, at least chemically speaking, we're mostly interested in the changes in U. Changes in energy I am comfortable with, and the way in which they change is what the right hand side of the equation describes: namely, q and W. These two symbols designate every process that could possibly change the internal energy of a given system.

"W" stands for work. Work can encompass a large number of things. Work, mechanically speaking, is defined as
In a mathematical context, and in one dimension. This simply states that a Force (From Newton's 2nd Law F = ma) applied over a distance equals the amount of work done. If you happen to be unfamiliar with integration, the long squiggly sign is the mathematical way of saying "from point A to point B", and "dx" means the change in position x (like a Cartesian grid, such as you learn about in algebra class). Work can come from more than mechanics, though: It can be performed by electric circuits, or chemical reactions (cell phones, vehicles), or some other type. In the end, however, it's still work.

Thermodynamics is largely used to describe gas phase systems. This doesn't have to be the case, but the gas phase is effected by thermodynamics more so than solid and liquid phases, at least with respect to the phases we normally encounter. As such, work is not defined in the mechanical sense. Instead the concepts of pressure, volume, and temperature are used, and work is defined as
Where P is Pressure and dV is the change in volume. The reason for the negative sign, in this context, is a matter of definition. When "negative" work is performed, this indicates that the system of interest (in this case, a gas) is loosing energy (or releasing energy, as an equivalent expression) to the surroundings. If the integration produces a positive sign (by having a negative PV), then this indicates that energy is entering the system. This is actually analogous to the above definition as mechanical work almost always gives energy to the system: A force applied to a ball from point a to point b will give energy to that ball. But in the context of gas description the application of a force would decrease the volume of a system, which mathematically would give a negative "PV", which goes against the convention of negative = release energy from system, and positive = give energy to system.

Looking at this, the "process" part doesn't seem to be coming into play at all. If you go from point A to point B, won't the distance between these points be the same regardless? As stated so far, it seems that way, but there's one other aspect of integration that works into the idea of "Process" here. An equivelent way to look at integration is that it gives you the area underneath a curve on a Cartesian grid. For example, this:

would integrate to give the area of the black shaded block here:
As such, integrating a function like this:

Would give a much larger area in comparison to the first one, as can be seen here:Sorry for the math digression, but I think it's important to understanding the concept of processes. When I took Chem I, the whole "you can go different ways to the top of a mountain" shpeal only served to confuse me further.

The great thing is there is such a function that describes gases and relates to our function for work. It is known as the ideal gas law: PV = nRT. In most thermodynamic cases, n is constant (and stands for the number of particles), and in all cases, R is constant (Specifically, named "The Gas Constant). Rearranging this algebraically gives
Which states that P is a function of T and V, or P(T, V). We can plot this in three dimensions, but there's no need: If you have two of the numbers from above, whether it be pressure, temperature, or volume, then you can find the third as n and R are held constant. Also, since we're interested in work, we might as well label one axis and pressure and the other as volume since those are the two variables that determine work. I'm not sure why this is the case, but I've never seen it otherwise, so I'll state that "By convention" the x axis is volume, and the y axis is pressure, thereby giving

Now, analogously to the Cartesian plane of algebra, every point on here is defined by some number, but here the number has a unit, or a meaning, attached to it: Namely, the pressure or the volume associated. Also analogously to the Cartesian plane above, if you "integrate" from one point to another on this plane, you will obtain the area associated with it. If you recall, integration from "Point A to Point B" [Or, rather, from point (Vo, Po) to point (V, P)] was also the definition of work. In other words, the area of a block you would obtain by moving from one point on the plane to another is equal to the amount of work performed. The actual path that one takes is the process one uses to get from one point on this plane to another. Therefore, the process described by this path:

Takes (or releases, depending on which point you start with) less energy than this path:

That is why work depends upon the process taken: Because it is the area underneath the curve which would be drawn from one point on the Cartesian Plane of Pressure-Volume to another point. If you were to decrease pressure and then increase volume, you'd be doing less work. If you instead increased pressure before increasing volume, you'd be doing more work.

Each of these paths have special names attached to them that designate what's happening. The first PV-integration example is called "isothermal", meaning that temperature does not change in the process, and the second is "isobaric" meaning that pressure does not change in the process. Some other processes I can think of are "isochoric", which means that volume is held constant (No work done), and "adiabatic" which means that energy is not lost or gained through the other process involved in determining the change in internal energy: Heat (q). I'd go into heat, but I think this one is long enough as it is, so I'll reserve that for next time around.

Friday, May 7, 2010

Penny Experiment, trial 1

When I was in middle/high school (I don't remember which) we dropped pennies into sulfuric acid to watch them react. I remembered this to be a lot of fun, and at the beginning of this semester I thought I'd try an "at-home" version with vinegar to see if dilute acetic acid would do the same thing. I expected it to, as hydronium should still be present in solution, but I expected the kinetic to be severely limited since there wouldn't be as much hydronium in solution.

So, run 1: I filled a ceramic coffee mug with "5% acidity" vinegar, and placed a penny (post 1984) into the acid and let it sit. Two months or so later (I probably should have documented this more rigorously, but it was just a curiosity on my part), water had evaporated but the penny appeared to be identical aside from some black grime (whatever that grime is made of) that was more easily removed. So, I had a shiny penny.

Run 2: I'm trying to stick with the "easily in reach within your home" type chemicals for pop-experimental purposes. It was suggested to me that I add salt in order to form a little HCl in solution. Seeing as the other experiment didn't work at all I thought why not, give it a try and see what happens.

I filled the coffee cup with fresh vinegar, and then poured salt to fill the coffee cup ~ 1/2 way. This would ensure a saturated solution of salt in vinegar, thereby possibly driving the reaction to form HCl. Then I dropped the same penny in. ~ 2 weeks after I started the experiment, I noticed that some dark splotches were forming on the salt. When I pulled the penny out to examine it, I thought I saw some zinc, but I wasn't positive if it was just me looking for it, so I through the penny back in. Just today (some odd 2 weeks after the last check) I pulled the penny out and sure enough: holes had been eaten through the copper, and some of the copper surrounding the holes was easily removed as the zinc underneath had been oxidized.

Very neat! The salt certainly sped up the reaction (though I'm not sure if it's acting as a catalyst), from my rough qualitative memory watching an at-home experiment when the fancy strikes me. There was also a pretty cool crystal layer that had formed as the vinegar had evaporated again. I think the evaporation likely helps in reacting with the penny, as the concentration of acid is increasing as water evaporates. I'm somewhat curious about the composition of the crystals (Sodium acetate? Sodium Chloride? Sodium Iodide, as it was iodized salt?). The primary thing that's mystifying me at the moment is: Why did the salt actually help in this reaction? HCl, being a strong acid, would dissociate completely, and so would likely not form to an appreciable amount -- I would expect this to hold even in a saturated solution of NaCl. If anything, I would think that the ionic atmosphere would play a larger role in interfering with the equilibrium. Of course, I also used the same penny after the last one, so I'm thinking I need to redo all this with a new penny at least. And, so that I don't have to use a pH meter (or titration... but for this I'd likely deal with the error in the meter) to find how much hydronium I have at the end, I'm going to try covering the coffee mug so that no water evaporates. Still, kind of some interesting preliminary results.

Wednesday, May 5, 2010

Thermodynamics: The Uno Law

Beyond the basic chemical equilibrium context, to understand Gibbs free energy you need to understand thermodynamics in a "ground up" fashion. The thing is, I'm not sure even I understand thermodynamics in a ground up fashion. This was part of my motivation to start blogging on it: To keep me thinking about the concepts such that they might eventually click.

The thermodynamic approach I was taught started with quantum mechanics, moved into statistical mechanics, and ended on thermodynamics. What's nice, from a chemist's perspective, about this approach is that the quantum model of the atom elucidates a lot of qualitative understanding of the atom you pick up in earlier courses, such as bond strengths, aromaticity, and IR spectra (or spectroscopy in general). Then statistical mechanics utilizes the energy levels found in quantum mechanics to make macroscopic predictions from the quantum model through statistics (ergo: statistical mechanics).

However, when approaching thermodynamics, then, outside of the basic chemical approach linked to equilibrium, I found the study to be very odd. I have been acquainted with explaining macroscopic observations through microscopic models, so it was hard to think "Macroscopically", even though the mathematics was simpler. So, in approaching general thermodynamics I think it's important to remember what it is thermodynamics is trying to describe, as that is where I lost a conceptual foot-hold in the race (and resorted to math to get me through, as opposed to understanding the concept behind the math)

Literally, thermodynamics is describing the movement of heat. But more is involved than heat: there is also work. So the name isn't exactly the best. What helped me was in emphasizing the macroscopic nature of thermodynamics. It models a large system of particles within some kind of surrounding environment. We are free to define the system, so the system is chosen such that something interesting can be measured or for conveniences sake.

In this case, the system is a beaker with a piston. The little green dots are supposed to be particles of gas floating around inside the beaker. The system stops where the beaker begins, and the surroundings begin just after the system stops. This allows measurements of the gaseous behavior alone to be recorded.

Thermodynamically speaking, there are three quantities that define this system: Pressure, Temperature, and Volume. Of these three, you only need know two to know the third as they are related through the ideal gas law. (Note: There are more "equations of state", as they are called, than the ideal gas law. But it's the simplest and gets the point across)

However, the ideal gas law isn't enough. That just defines the "State" of the system. It doesn't tell us very much about how much energy is transferred from or to the system in going from one state to another. And that, I think, is the best way to think about thermodynamics: the amount of energy transferred in moving from one state to another in a macroscopic system. Macroscopic states can be defined by the three variables of P, V, and T, and the movement between these states requires energy to enter or leave the system. How much energy enters or leaves depends upon the way in which one moves from one state to another.

That leads to the first law of thermodynamics. There are many ways of stating this law, but when trying to understanding how much energy passes into or out of a system due to a process the following is used:

ΔU = W + q

Where "U" is the "Internal Energy", W is work, and q is heat. Internal energy, to me, is a weird concept. It's this energy that's.... there?... inside the system 'n stuff? Yes. That's exactly it. Personally, I'm still wrapping my head around the concept -- the best I can do is to say that it represents every shred of energy that is within the system, from the vibration of bonds, the momentum of molecules, the mass of the atoms, the potentials of fields, EVERY source of energy that happens to be within the system. That.... I think is it. And, frankly, we don't even care about the total internal energy, but rather the changes in internal energy, because those are much easier to measure than absolute internal energies. (ergo: Δ)

So, changes occur in internal energy, and those changes are equal to work and heat. These are the processes by which energy is removed from or added to a system. They both transfer energy, but they do so in different ways. For now it is enough to understand that the changes in internal energy occur through the two processes (or mechanism, or "How-to", if that makes more sense?) of work and heat. What those processes encompass I'll blog about later.