## Monday, April 12, 2010

### Equilibrium as a General Model

I think I'm going to have a series of posts on the basics of thermodynamics and its application to chemistry because, well, it's so darn interesting.

In the previous post I outlined some basic concepts of chemical equilibrium. But the case that I gave was very specific and would only apply to a system that operates in a similar manner -- namely, that one molecule of X would combine with one molecule of Y to form one molecule of XY. This is not always the case. But before going into specific chemical equilibrium, I think it better to look at where the model for equilibrium comes from.

A model for physical systems can be constructed from the concept of a system and surroundings. Both are selected by the modeler, usually specifically selected for convenience of calculation, and in that sense are arbitrary. The system is simply what you are interested in. The surroundings includes everything else, but usually only the immediate surroundings are all that are taken into account -- a chemical example would be what is in a beaker for a system, and the lab that the beaker is in for the surroundings.

In designating a system/surroundings, you have some quantities that can describe both: Energy, Pressure, Temperature, Volume, and moles of gas. Any of these quantities can be exchanged between the system and the surroundings, and which quantities can be exchanged often describe the type of system that you are looking at.

A common example from physics is the mechanical equilibrium of a spring represented by the following force diagram.
(Do forgive my Paint abilities). According to Newton's Second Law

ΣF = Fs + Fg
Fs = -kx
Fg = mg
And, because this system is in equilibrium ΣF = 0
Therefore, Fs + Fg = 0, and Fs = -Fg, which means by substitution kx = mg

Which happens to usually be a highly convenient situation. In particular, note that the previous solution had no reference to time. This is something unique to equilibrium solutions: There is no reference to time, only to what each respective variable is at when no variable of interest is changing.

However, when dealing with the system/surroundings model, usually forces aren't the variables of interest. A close analogue. A common example of pressure equilibrium would be a balloon which has been tied off. The gas within the balloon would have a higher pressure than the exterior pressure, but pressure would not be exchanged between the system (the gas in the balloon) and the surroundings (the room the balloon is in).

This situation can occur between any variables of interest -- Pressure, Volume, Temperature, Energy, and chemical concentration. The final one is the one that chemists are first introduced to. This is, ultimately, just the application of thermodynamics/statistical mechanics to chemical systems. Ergo, the study of the model of equilibrium is actually the study of thermodynamics, which is one of the main branches of chemistry. The above explication of equilibrium should also clarify why it is that kinetics, despite being related to energy just as thermodynamics is related to energy, is a separate case of study: The concept of equilibrium requires things to not change with time, and the concept of equilibrium is the model within thermodynamics most often used to model chemical systems as, regardless of the time it takes, the system will tend towards concentrations which satisfy the equilibrium constant.

I think this is done mostly to simplify predictions: thermodynamics, I must admit, is still a bit of an impenetrable thick fog as it is. Not having to worry about time-dependence makes things a little easier.