Sunday, April 25, 2010

Free Energy

A point I found difficult in studying thermodynamics as a chemist is that the concept of Free Energy is much more important to chemical study -- but it is a more deeply derived concept based upon thermodynamics and energy transfer in general. I often try and think of ways to build a conceptual framework within chemistry without referencing the physics that it is based upon, because in the end, the physics isn't totally necessary for gaining an understanding of the chemical picture. This is why I began blogging this month from the "end-point" of thermodynamics with respect to chemistry: Equilibrium. If you can understand equilibrium in general, then one should be able to understand chemical equilibrium. And, hopefully from this, one should be able to understand Free Energy.

In the previous two posts I attempted to explicate equilibrium as a general model and as a model for chemical systems. This works if you think about atoms as "billiard balls" connected to one another through "Bonds". When a chemical reaction occurs, the bonds in the reactants are broken and the bonds in the products are formed through some kind of process. To deduce an equilibrium expression the step-by-step process does not necessarily need to be known: All that need be known are the ending concentrations of the products and the reactants. The reason that these concentrations are constant is not that the chemicals stop moving due to some mystical equilibrium constant that brings out the golden tablet of concentration stating "Thou shalt not react!" Instead, the chemical species continue to react both in the forward direction (Towards products) and the backward direction (from products to reactants), it is just that at equilibrium these processes occur at the same rate. What those rates are is another story -- but what those concentrations are when the rates are equal is driven by Free Energy.

Free Energy, as a concept, is simple enough to understand from the words alone. It's the amount of energy available to do stuff. The reason why we need this concept is a more difficult issue, and is directly related to the second law of thermodynamics. However, the concept itself can be understood in stating that there is some quantity we call energy, and of this quantity we can not use all of it because of the second law. That quantity which can be used in a process, however, is called Free Energy.

I skip around the second law because I myself found it hard to understand, there are several ways of explaining it, and with reference to chemical thermodynamics I don't know which is the best way to go about explaining it. In fact, I think it unnecessary to understand the second law when first approaching chemical phenomena so long as we conceive that there is this concept that limits the amount of energy that can be obtained from any process, and that concept is the second law of thermodynamics.

The way in which Free Energy applies to equilibrium is through a relation (or equation, expression, what-have-you) of a certain type of Free Energy, that is conveniently defined for standard laboratory conditions. This type of free energy is called "Gibbs Free Energy", because it was invented by Josiah Willard Gibbs. This is the energy available to do work when the system is under constant pressure (or nearly so), such as you find in a laboratory at a given height above the earth. In a chemical reaction taking place in a beaker, the change in free energy can be measured with a simple thermometer. Further, the change in free energy is directly related to the equilibrium constant at a given temperature through:

ΔG = -RT ln (K)

One thing you can notice from this relationship is that if the change in free energy is positive, then raising e to the power of a negative number will give you a number less than one. Similarly, raising e the power of a positive number will give you a number greater than one. This indicates that negative changes in Gibbs Free Energy are indicative of chemical reactions where products are favored more than reactions. The converse of this is also true: Positive changes in Gibbs Free Energy are indicative of chemical reactions that favor reactants.

Naturally, one needs to know how one measures Gibbs Free Energy. The above equation is not what one would call the definition of Gibbs, or give someone a good way of measuring the change in Gibbs free energy, but only its relation to the equilibrium constant. However, I think I'll save that discussion for later. Currently what is more important to grasp is that Free Energy and equilibrium and linked together, and that Free Energy is a thermodynamic concept which is why questions of equilibrium and answered through the concepts of thermodynamics. However, in first understanding chemical reactions, one need not have the grounding principles of thermodynamics down: One need only understand equilibrium as a ratio of products of reactants in a chemical reaction, and that this ratio of equilibrium is governed by the concept of available free energy in a chemical system. That, I think, is the basic beginning to understanding the thermodynamics of chemistry without basing that understanding in the thermodynamics proper.

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