## Sunday, April 11, 2010

### Equilibrium, Basic Chemical Approach

In a previous post I mentioned that there are two things one must consider in analyzing a chemical reaction: thermodynamics and kinetics. The model of equilibrium covers the first of these.

Equilibrium, in its most basic sense, is the ratio between what is created in a chemical reaction and what was used in a chemical reaction. Suppose the following general chemical reaction:

This reads as "Chemical X and Chemical Y react to yield Chemical XY in equilibrium" Many chemical reactions will include a simpler notation for their "react to yield" symbol such as "→" because most reactions that one is introduced to in a general chemistry course fully react to products. The vast majority of chemical reactions do not have this feature, however, and the double arrow symbol above is used to indicate that both products and reactants are being formed when the system has reached chemical equilibrium.

However, the relative amounts of product and reactant can be predicted through the use of an equilibrium constant. Each chemical system has its own equilibrium constant, but the equilibrium constant remains the same for systems prepared with the same chemicals and under the same surrounding conditions. This constant can be found from the following:

This states that the concentration of chemical XY divided by the product of the concentrations of chemical X and Y equals a constant -- specifically, the equilibrium constant. This means that given a certain reaction and its equilibrium constant, one should be able to predict the concentrations each species will have when equilibrium is reached -- and you can do so. This is a very tidy result because chemists have to model ~10^23 particles all interacting at once. This allows one to predict effects in the physical world while ignoring things such as electric fields, momentum, and position. For example, if one has the equilibrium constant one can be a qualitative prediction about the relative concentrations of products to reactants. If the equilibrium constant is greater than one, then products are highly favored. This is the case with many introductory chemical systems one studies, which is when the symbol → is used since products are so highly favored. However, if the equilibrium constant is smaller than one, then reactants are more favored than products in this particular chemical reaction.

This equilibrium relationship governs the reverse reaction as well: if one where to look at the reaction , then the equilibrium constant for this reaction would be the reciprocal of the previous reaction. This is easily proven if you simply place the concentration of the products of this reaction multiplied together over the concentration of the reactant.

Of course, it also has its own set of limitations. The equilibrium constant is only constant for a given temperature. It can also be somewhat difficult to actually obtain the equilibrium constant, though there are several methods of doing so. Further, as I've previously mentioned, the equilibrium constant says nothing about the kinetics of the reaction: Only the relative energy of the products and reactants, or how favorable the reaction is thermodynamically. This can be important in synthesizing chemicals as two different products could be likely to form, but because of one product is slow to form, the other product is the major chemical created.