Are All Processes Leading to Equilibrium Exothermic?

[Beer-monster]

Homework Statement

It's a simple question but I'm confusing myself when thinking about it.

The heart of the problem is: as equilibrium is (presumably) the most stable and hence lowest energy state of a system, would I be correct in saying that any process that leads to a relaxation towards equilibrium would be exothermic? Or does it depend on the exact nature of the process in question?

Thanks to anyone who can help. I'm sorry if I'm being vague but I'm trying to understand the general concept.

BM

 

[Ygggdrasil]

Your understanding is almost correct. Equilibrium is the most stable state in that it is the lowest free energy state of the system. Free energy is a concept that takes into account not only the enthalpy (potential energy) of the system but its entropy (disorder) as well. To achieve a lower free energy, one would like to decrease the enthalpy of the system and increase its entropy. So, from this idea, exothermic processes (which decrease the enthalpy of the system by transferring heat to the surroundings) tend to lower the free energy of the system. However, this is not always the case. Often, one will encounter processes that increase the enthalpy of the system (are endothermic) but also increase the entropy of the system. Will the system increase its entropy at the expense of also increasing its enthalpy? In this case, one needs to compare the relative magnitudes of benefit from entropy gain to the penalty from enthalpy gain in order to see which one is more important (temperature is a key factor determining whether the system would prefer decreasing enthalpy or increasing entropy).

A good example of this situation is the melting of ice. Melting is an endothermic process because the system absorbs heat energy from the surroundings in order to break the intermolecular hydrogen bonds that hold the water molecules together in ice. Melting, however, also increases entropy because ice is more ordered than liquid water. At room temperature, ice is not the equilibrium state of water, liquid is, so in order to move toward equilibrium the ice will melt. Therefore, this represents an example where a system is moving toward its equilibrium state via an endothermic process.

 

[Beer-monster]

I see. That makes a lot of sense, but I'm now getting confused when I apply it to a specific situation.

If we take a metal at high temperature with a large number of vacancies and quench it to room temp. We'll have a material with far more vacancies than it should have for equilibrium at that temperature. To restore equilibrium you would need to fill the vacancies, but that requires input energy so would be exothermic. But wouldn't that decrease the entropy and hence be impossible.

 

[Ygggdrasil]

The situation you describe is a bit different because the answer does not have to do with thermodynamics (enthalpy and entropy), but instead involves kinetics.

It is incorrect to say that filling the vacancies is endothermic (I assume you mean endothermic here). If you compare the energies of a metal with vacancies to the enthalpies of metals without vacancies, you would find that the metal without vacancies has a lower enthalpy (i.e. moving a metal atom into a vacancy gives a more stable state). Even though you need to heat the metal in order to get the atoms to fill the vacancies, you have a net release of energy and the process is exothermic overall. A similar situation is the combustion of gasoline in your car. Even though you need to provide an energy input (a spark) to ignite the gasoline, you end up getting more energy out from the combustion than you initially put in.

So, what is the heat doing in your example if it is not going toward increasing the enthalpy of the metal? In this case, it's providing the activation energy needed for the necessary rearrangements to occur. In order to fill vacancies in the metal, you need to first break some of the chemical bonds in the metal, a process which requires an initial input of energy. This initial input of energy is the activation energy. Of course, when the bonds re-form and fill the vacancy, you will form more bonds than you started out with, and therefore, the process will release more energy than the activation energy you put into the system.

The type of system you describe is referred to as a meta-stable state: a non-equilibrium state that will persist for prolonged amounts of time. In this case, the system is trapped in this meta-stable state and cannot relax to equilibrium because the reactions that rearrange the atoms to fill the vacancies are too slow at room temperature. Only by heating up the metal can you get these reactions to occur at a non-negligible rate and allow the system to relax to equilibrium. Because it is the kinetics of the reaction (the speed of the reaction) that lock the system into a non-equilibrium state, we would refer to this state as a kinetically trapped state.