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How does resonance lower the potential energy of the molecule? Take $\ce{O3}$ as an example.

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    $\begingroup$ Although 'resonance' can be useful it is better to think about how the electrons are delocalised among the bonds. This leads more naturally to thinking about molecular orbitals and so distributing, usually $\pi$ electrons, among the atoms. The sigma bonds remain as they are. The MO picture leads naturally to an understanding of why the energy is lower. $\endgroup$ – porphyrin Jun 29 '16 at 9:33
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With the concept Resonance you can describe delocalized electrons in some molecules. To go with your example:

Ozone Resonance (source)

Imagine the ozone molecule to be frozen in one of those two states. Positive and negative charges are localized, which is generally connected to a higher energy, i.e. a more reactive species. This would be an extreme case for ozone - in reality those electrons will be delocalized all over the molecule. So, what is the reason that molecules with localized electrons/charges have a higher total energy and are, hence, less stable?

Maybe you remember the Particle in a box. I wont go into the quantum chemistry here, but one of the take-away-messages is, that the energy for particles in a infinite square well, which is a very rough approximation of the potential in which the outer electrons reside in, does decrease with $ L^{-2} $. $L$ is the size of the box in which the particle can exist. So, the more delocalized the electrons are, the less total energy in a system.

With this, to correct you question a little bit: Resonance is not the reason why molecules are more stable, it is a concept which describes the bonding in a molecule, in which electrons are delocalized, better than a single Lewis Structure.

I would like to have a feedback if this answer is somewhat understandable.

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Strictly speaking resonance doesn't stabilise molecules. This is because resonance is merely a descriptive way for chemists to extend simple pictures of bonding to molecules where the simplest model of bonding doesn't work. We observe that some molecules are more stable than the simple picture, or a different shape than the simple picture would suggest and we explain that difference by adding the idea of resonance.

The problem arises because, when we draw simple pictures of the bonding in molecules, we assume each bond consists of two shared electrons. So we draw benzene like this:

simple benzene bonding

This picture neatly accounts for all the electrons in the C-C bonds and is often good enough for understanding and tracking the electrons and bonds in reaction mechanisms. But the picture is clearly wrong as it doesn't match the known properties of benzene: in particular all the bonds in benzene are the same length. The stability of benzene is also understated compared to the (hypothetical) molecule with isolated double bond. The real reasons for this are pretty complex and involve all sorts of quantum-mechanical molecular orbital gobbledygook. But this is way too complex to be useful when drawing simple molecular pictures or describing reactions or bonding.

To avoid this problem and to help retain the simple picture we add the idea of resonance. This allows us to use the simple picture where a line representing a bond still means two shared electrons but we have to draw more than one structure to capture the real molecular structure. We say the multiple structures "resonate" but this is really just shorthand for saying that the real structure is an in-between mix of the resonance structures we draw. For benzene we draw like this:

benzene resonance structures

In the first structure there is a single bond between atoms 1 and 2; in the second structure there is a double bond. Real benzene is a mix of the two resonance structures where all the bonds are a sort of mix of a single and double bond. In fact benzene is sometimes drawn like this:

circle benzene structure

The problem with this structure is that it is is less useful most of the time than the (incorrect) structures with single and double bonds as it makes counting electrons in bonds less clear and this is annoying when trying to follow reaction mechanisms.

So resonance is basically a pragmatic way to retain simplistic pictures of bonding in molecules while recognising that that simplistic pictures is often a poor representation of reality. And thereby avoiding having to do complicated quantum stuff with orbitals every time you want to understand a molecular structure or reaction.

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Let us first discuss the more fundamental phenomenon of covalent bonding. How do you think a covalent bond "works"? Let us say we have two hydrogen atoms. We know that the nuclei of these atoms are positively charged and the electrons negatively charged. Coulombic repulsions act between the two nuclei, and between the electrons from the two atoms. Coulombic attractions act between the electrons and nuclei within the same molecule and betweem those of the two different molecules. If the two atoms are far apart from each other, attractions between the electrons of one atom and the nucleus of the other are greater than the repulsions. If the atoms get too close to each other, repulsions are greater than the attractions. At exactly some seperation, attraction balances repulsion and the atoms settle for a seperation called the "bond-length", and the atoms are said to be "covalent-bonded".

After that ridiculously long explanation of what a covalent bond is, let us get to the essence of it. The reason why a covalent bond "works" is because electrons are holding atoms 'together'. Without the electrons, the atoms would not have anything to 'bind' them. In essence, two electrons are holding two atoms in place, thereby bringing stability, and causing a lowering of potential energy of the system.

In a benzene molecule, the same thing happens. The p-orbitals of the induvidual carbon atoms in benzene overlap with each other, thereby allowing the electrons in these p-orbitals to de-localise, meaning that an electron in the p-orbital of one carbon atom no longer belongs to only one atom, but instead acts to bind all other carbon atoms in the benzene ring, just as the two electrons in the $H_2$ molecule helps bind the two atoms of hydrogen together.

enter image description here

  • Image credits: chemwiki.ucdavis.edu

Since the electron belongs to the orbitals of many other atoms, and not only one or two (as in the case of the H-H covalent bond), it holds all these six carbon atoms in place, and thereby acts as a bond between the six carbon atoms, which in turn brings stability to the system and lowers its potential energy.

Appendix:

Why doesn't an electron in an atom fall into the nucleus ?

The picture we often have of electrons as small objects circling a nucleus in well defined "orbits" is actually quite wrong. The positions of these electrons at any given time are not well-defined, but we CAN figure out the volume of space where we are likely to find a given electron if we do an experiment to look. For example, the electron in a hydrogen atom likes to occupy a spherical volume surrounding the proton. If you think of the proton as a grain of salt, then the electron is about equally likely to be found anywhere inside a ten foot radius sphere surrounding this grain, kind of like a cloud.

The weird thing about that cloud is that its spread in space is related to the spread of possible momenta (or velocities) of the electron. So here's the key point, which we won't pretend to explain here. The more squashed in the cloud gets, the more spread out the range of momenta has to get. That's called Heisenberg's uncertainty principle. Big momenta mean big kinetic energies. So the cloud can lower its potential energy by squishing in closer to the nucleus, but when it squishes in too far its kinetic energy goes up more than its potential energy goes down. So it settles at a happy medium, and that gives the cloud and thus the atom its size. (from https://van.physics.illinois.edu/qa/listing.php?id=1226)

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  • $\begingroup$ "Coulombic attractions act between the electrons and nuclei within the same molecule and betweem those of the two different molecules." then why don't electrons just fall into the nucleus? $\endgroup$ – Dissenter Jan 3 '15 at 14:42
  • $\begingroup$ @Dissenter I'm not sure if you're trying to ask this, but wasn't that made clear in the chapter "atomic structure" ? Maybe I didn't understand your question that well. Please don't take it in poor taste. $\endgroup$ – Gaurav Jan 3 '15 at 15:09
  • $\begingroup$ I'm suggesting that you add more about the structure of atoms so others might not think that electrons fall into nuclei. $\endgroup$ – Dissenter Jan 3 '15 at 15:11
  • $\begingroup$ @Dissenter Oh, but I think the OP is already familiar with atomic structure since these topics are usually taught after that. Why do think it would be relevant to spell out something that has already been taught ? Are you trying to imply that I should explain about how the delocalisation happens ? $\endgroup$ – Gaurav Jan 3 '15 at 15:19
  • $\begingroup$ also the idea that Coulombic considerations are important at the sub atomic level is fundamentally incorrect - hence the reason atoms don't collapse $\endgroup$ – Dissenter Jan 3 '15 at 15:31

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