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In chemistry a few months ago we were taught the resonant structure of benzene, that states the double bonds upon the six carbon atoms flicker back and forth between the two possible states it can be in:

here

This seemed incredibly distressing to me at the time, for it seemed that if the energy required to break a double bond was exactly equal to the energy gained by forming a double bond, that the benzene was a perfect engine that lost none of it's energy to the environment, and perfectly converted it's energy from one form to another. At the time, it seemed as if this was a clear violation of the Second Law of Thermodynamics, and I sure was glad when it turned out that all the bonds were actually a continuous pi bond.

Upon introspection this morning however, I wondered whether the resonant theory truly was a violation of the second law of thermodynamics. Because benzene is simply six carbons, if the resonant theory were true and the bonds truly did flicker back and forth, I don't know where energy could possibly be lost, thus making it an imperfect system. The common energy losses that I know of, such as heat and sound energy, are all macroscopic, and I don't think they pertain to energy losses at atomic levels. On another level, I don't even know if the Second Law of Thermodynamics really even pertains to benzene, because it isn't exactly a thermal engine, and also because I've read that the Second Law of Thermodynamics is a probabilistic law for large scales and can be broken at small scales.

My question then is whether a resonant benzene can exist without violating the Second Law of Thermodynamics, and if it really cannot physically exist, than an explanation on the real reason why.

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  • $\begingroup$ From wiki The second law is only applicable to macroscopic systems. The second law is actually a statement about the probable (my emphasis) behavior of an isolated system. As larger and larger systems are considered, the probability of the second law being practically true becomes more and more certain. For any isolated system with a mass of more than a few picograms, the second law is true to within a few parts in a million. How much mass does a benzene molecule have? $\endgroup$ – user81619 Jun 4 '15 at 9:13
  • $\begingroup$ The second law of thermodynamics is the definition of temperature. Where is a temperature bath involved in the quantum structure of benzene? I have a felling that you need to read the second law of thermodynamics again. $\endgroup$ – CuriousOne Jun 4 '15 at 17:23
  • $\begingroup$ The verbs "break" and "form" don't really capture what is going on with the pi bonds; it is a smooth evolution, not a discrete behavior. $\endgroup$ – dmckee --- ex-moderator kitten Jun 4 '15 at 20:06
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When one is talking of the behavior of molecules, atoms, nuclei and even crystals, one is not in the classical realm, particularly not in classical thermodynamics.

One could say that is one of the reasons that Quantum mechanics was discovered. Quantum mechanically the electrons about the nucleus are in perpetual motion, without losing energy, except not in classical trajectories, but in orbitals..

An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom.1 This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus.

A resonant molecule is similarly in a stable quantum mechanical state , i.e. a stable solution of the quantum mechanical differential equation with the appropriate boundary conditions. It just has more elaborate molecular orbitals than the simple hydrogen atom, for the electrons and the nuclei of the atoms that compose it. The resonance you describe needs a time dependent solution, but since it is observed there is no problem to define one.

Classical thermodynamic laws do not apply.

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This is a more accurate representation of benzene:

A More Accurate Representation of Benzene

The delocalized pi electrons don't really spin around the ring. They are located within molecular orbitals that are delocalized throughout the molecule, meaning they are not confined to any single atom within the molecule. They belong to the entire molecule, and are distributed across its entire carbon skeleton.

enter image description here enter image description here

It is good to remember that we are looking at models. None of these is an actual picture of benzene.

Benzene is very stable and seems orderly. However, so are many atoms and molecules. You should ask if atoms and stable molecules, in general, break the second law of thermodynamics. I believe someone has tried to answer you that.

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  • $\begingroup$ In other words, the bonds don't flicker back and forth between the two possible states it can be in. $\endgroup$ – John Rennie Jun 4 '15 at 11:29
  • $\begingroup$ Yes, exactly! That would be nonsense, but a mistake I've seen professors make! $\endgroup$ – Bionic Person Jun 5 '15 at 16:07

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