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Chemistry LibreTexts

Relaxation to Equilibrium

In chemistry, we are not only interested in the properties of reactants and products, but also how these reactions come about. It is important to understand the rates and mechanism by which molecules come together to form a product. Reactions in solutions occur so fast, it is complete the very second you get the reactants mixed. Studying them under these conditions is impossible and requires special techniques to overcome this difficulty.

Relaxation Method

The focus of our study is going to be Relaxation Method or “Relaxation to Equilibrium”. The name already gives away its meaning. It has to do with the equilibrium of the reaction. When the equilibrium has been established, we disrupt it with a temperature jump or by other means (i.e. pH) and watch it come back to a new equilibrium. Hence, this allows us to measure the rates of fast reactions as they approach to equilibrium.

For example, let's look at the formation of liquid water:

From the above reaction we can formulate the equilibrium rate law

However, disrupting this equilibrium with a temperature jump (Le Chatelier's Principle) would change the concentrations of the reaction and a new equilibrium would be established. Adding heat to the system will drive the reaction to the left. As a result, the concentration of the reactants would increase and for products it would decrease.

 

Now, because a new equilibrium has been reached, we have to write an equation that will explain this change. The new reaction rate law would look like this:

 

Rearranging the equation we get,

 

 

 

Relaxation time is very useful in this process, because it tells us how long it takes for the new equilibrium to establish. As you may have guessed also, that we can use this information to obtain the forward and reverse rate constants.

Finally, our new equilibrium constant is:

 

Summary

Up until now, we have been discussing about one of three ways in which we can measure the rate constants for fast reactions. Relaxation method, is a very useful tool used in chemistry to study the rates for these incredibly fast reactions. Changing or disrupting the reaction equilibrium, we measured the time (relaxation time) it took to reach a new equilibrium. Finally, from this information we derived the forward and reverse rate constants, later the new equilibrium constant.

References

  1. Atkins, Peter, and Julio De Paula. Physical Chemistry for the Life Sciences. New York: W.H. Freeman and Company, 2006.

Contributors

  • Anna Kazaryan (UCD)