[MackTuesday]

1.  In various sources I've read that systems seek a lower energy state.  By "lower energy" I must assume they mean "lower chemical potential energy" although that is never said explicitly.  *Why* is this?  I've never seen a satisfying explanation.  I hope it can be explained without discussing entropy, because increasing entropy is forwarded as the driving mechanism in spontaneous endothermic reactions.

2.  I've imagined a spontaneous, endothermic, *antientropic* reaction.  Please explain what's wrong with my reasoning.

We have a rigid, energetically isolated container with gases A and B in flux.  There is an endothermic reaction

A + B => AB

Where AB is also a gas.  It is unavoidable that some small proportion of the molecules will be energetic enough to join together in this way because the distribution of kinetic energy has essentially infinite support.  So when the system reaches equilibrium there will be some molecules of AB in the mix.  At this point the temperature will be lower (endothermic) and the number of particles in the system will be lower, so it seems at least possible that the entropy will be lower.  But don't the rules say that decreasing entropy is impossible in a spontaneous endothermic reaction?

[oliphant]

1.  In various sources I've read that systems seek a lower energy state.  By "lower energy" I must assume they mean "lower chemical potential energy" although that is never said explicitly.  *Why* is this?  I've never seen a satisfying explanation.  I hope it can be explained without discussing entropy, because increasing entropy is forwarded as the driving mechanism in spontaneous endothermic reactions.

Firstly, the document does indeed imply "lower chemical potential energy."  From a physical sense, imagine Wiley Coyote running off  a cliff.  He is at a high potential energy (mgh) and he falls.  We don't expect him to float.  The process is considered irreversible.  However, chemistry is not physics, and this analogy does not strictly hold, especially for reactions considered reversible, such as warming ammonium chloride.  

What happens when ammonium chloride is warmed?  It separates into ammonia and chloride, which have higher potential energy than the ammonium chloride whence they came.  This happens so long as the temperature of reagents are maintained at a high temperature.  Going back to Wiley Coyote, imagine that he's on a boat and the boat is floating on water above a cliff under the ocean.  He doesn't know the cliff is there, he doesn't fall into it because he is floating.  In other words, the potential energy well is far below the state of his system.

So let's regard the original question, and that refers to "why chemical systems tend to a lower potential energy state."  This is because of entropy- yes, entropy- which controls heat flow.  Heat cannot be maintained in the system, so Wiley Coyote's ocean is slowly being drained, and eventially he does fall down the cliff...  As the heat dissipates, the ammonia and hydrogen chloride recombine to the ghostly vapor of ammonium chloride...

2.  I've imagined a spontaneous, endothermic, *antientropic* reaction.  Please explain what's wrong with my reasoning.

We have a rigid, energetically isolated container with gases A and B in flux.  There is an endothermic reaction

A + B => AB

Where AB is also a gas.  It is unavoidable that some small proportion of the molecules will be energetic enough to join together in this way because the distribution of kinetic energy has essentially infinite support.  So when the system reaches equilibrium there will be some molecules of AB in the mix.  At this point the temperature will be lower (endothermic) and the number of particles in the system will be lower, so it seems at least possible that the entropy will be lower.  But don't the rules say that decreasing entropy is impossible in a spontaneous endothermic reaction?

What's wrong with your reasoning is that not such spontaneous, endothermic, antientropic reaction exists.  Let us know about one and we'll make trillions.

[oliphant]

However, chemistry is not physics, and this analogy does not strictly hold, especially for reactions considered reversible...

Before I get flamed, I should add...  strictly speaking, they are, but I should have said "chemistry is not classical mechanics!"

[rabolisk]

Regarding A + B  AB, where the reaction is endothermic and antientropic, it is absolutely true that some AB is likely to form. But the kicker is that endothermic and antientropic ( :delta: H < 0 and  :delta: S < 0) is defined at standard state, where the concentration of A, B, and AB are all 1. In that case, the reaction will not be spontaneous in the direction written. It will be spontaneous the other way. If you have a reaction whose K is << 1, then the equilibrium lies far to the left, and, by definition,  :delta: G < 0. The reaction is not spontaneous, but the whole spiel about spontaneity, endothermicity, etc. is defined at standard state. Of course SOME product will form. Think about a weak acid dissociation, which is technically nonspontaneous, but of course does happen to a slight degree.

As far as why systems seek lower chemical potential energy, this is related to entropy. I really cannot answer the question without referring to entropy, because that is the sole determinant of spontaneity and equilibrium. Equilibrium is where reactions seek to go (by definition of equilibrium) and that is where the Gibbs free energy of the system is at a minimum. But it turns out that Gibbs free energy is solely a function of entropy of the universe (max Suniverse = min Gsystem). Enthalpy is really "disguised" entropy, which can be proven, if you want this.