Is the transformation of pi bonds to sigma bonds always energetically favorable?

Question

Is the move from pi bonds to sigma bonds always favorable?

My professor claims so, except in the case of conjugated pi bonds. I can see how pi bonds going to sigma bonds might be favorable; I know that double bonds are actually not twice as strong as single bonds because of poorer overlap ... but are there any exceptions to this guideline that the reduction of pi bonds to sigma bonds is favorable except in the case of conjugated systems?

EDIT: what about in the case of organic chemistry? It certainly seems that hydrogenation (a way of transforming pi bonds to sigma bonds) is generally a favorable move.

Answer 1

When thinking about questions along these lines, I always try to remember the bent-bond description of ethylene. In all aspects related to physical reality (structure, electron distribution, etc.) the bent bond model pictured below on the right is equivalent to the pi model shown on the left (at least within the scope of all measurements made to date).

The "nice" thing about the bent bond model is that it casts ethylene as a highly-strained, two-membered ring. When wouldn't releasing this strain and forming sigma bonds be an energy lowering process. Aside from conjugated examples, I think that transformation of a strained, ethylenic system to a saturated, sigma-bonded system would always be energy lowering.

EDIT: Further Thoughts

Instead of analyzing hydrogenations or other reactions where the starting material and product have a different number of atoms, let's consider the following isomerization reaction.

Thermodynamically, cyclohexane is the most stable $\ce{C6H12}$ isomer in this series by a significant margin. All we've done is convert a C-C pi bond into a C-C sigma bond and convert 3 $\ce{C(sp^2)-H}$ bonds into 3 $\ce{C(sp^3)-H}$ bonds. Which (at least as I read it) was the OP's premise. So I would say that, in carbon-hydrogen systems, pi bonds generally prefer to transform into sigma bonds, as pi bonds are inherently destablilized due to poor overlap (pi model) or strain (bent bond model).

That said, I retract what I wrote above that carbon-carbon pi to sigma transformations would "always" be energy lowering. Consider the photolysis of benzene to produce dewar benzene, prismane and benzvalene. These conversions are examples where one or more pi bonds have been converted to one or more sigma bonds and the reaction is not energetically (thermodynamically) favorable.

The products are much less stable (due to the strain in the small rings that have been created) than the starting benzene. Because of these relative stabilities, the forward reaction does not occur thermally (in fact, thermally, each of those 3 products will revert to benzene), but by pumping in excess energy photochemically, the transformation can be brought about.

To summarize, I would maintain that generally, in model, carbon-hydrogen systems, ethylenic linkages are destabilized (due to poor overlap in the pi model, or strain in the bent bond model) and will thermodynamically prefer to exist as thermodynamically more-stable saturated linkages.

Answer 2

This is certainly not generally true. Have a look here for example: There you find that the bond energy for an $\ce{O-O}$ single bond is 142 kJ/mol while that of an $\ce{O=O}$ double bond is more than thrice as large with 494 kJ/mol. So, a reduction of $\ce{O=O}$ that would produce two $\ce{O-O}$ bonds would not be favorable. The same is true for $\ce{N-N}$ (167 kJ/mol) and $\ce{N=N}$ (418 kJ/mol) bonds. For nitrogen you even have the rare case that the $\ce{N#N}$ triple bond with 942 kJ/mol packs more bond strength than two isolated $\ce{N=N}$ double bonds.

In the context of organic chemistry you often have the situation that a reaction destroys a $\pi$ bond while in the process creating a new $\sigma$ bond. A double bond will always be stronger than a single bond, so going from double to single costs energy in any case. But usually when you reduce a double or triple bond you create new bonds at the expense of them. Only when those new bonds + the reduced bond are stronger than the old double/triple bond then the reaction is favorable. There are reactions where the opposite is the case. Phosphorous is infamous for its affinity to oxygen and very prone to form $\ce{P=O}$ double bonds. In the Wittig reaction (see for example here) you have an oxaphosphetane intermediate with a strained 4-membered ring with 4 $\sigma$ bonds that springs open to form one $\ce{C=C}$ and one $\ce{P=O}$ double bond.

Another case comes to mind. Hemiacetals (or 1,1-geminal diols), having two $\ce{C-O}$ $\sigma$ bonds, are usually unstable and prefer to destroy one of the $\ce{C-O}$ bonds by expelling the $\ce{R-O}$ group (or one of the $\ce{O-H}$ groups) thus forming a $\ce{C=O}$ bond. So, in this case one $\ce{C=O}$ bond beats two $\ce{C-O}$ bonds.

If you want to read more on the matter of the relation between single and multiple bonds concerning the strengths of the $\sigma$ and the $\pi$ interactions have a look at this paper by Kutzelnigg.

Answer 3

The answer to your question is no.

In terms of organic chemistry, consider the two hydrocarbons, $\ce{H_3C-CH_3}$ and $\ce{HC\equiv CH}$. The $\ce{C-C}$ bond dissociation energy is 368 kj/mol while the $\ce{C\equiv C}$ triple bond has a bond dissociation energy of 682 kj/mol, nearly twice that of the single bond.

The transformation of this triple to single bond may be thermodynamically favorable via hydrogenation but may not always be the case. How does temperature affect hydrogenation and can $\Delta H$ be positive under other conditions? Furthermore, if we want to talk about the 'strength' of the CC bond, then clearly the triple bond is stronger.

Phillip brought up a good point in the comments that merits attention. Hydrogenation contains an appreciable barrier for this process to occur. When we take into account the formation of the additional single bonds by hydrogen then the energy is lower. However, if we consider strictly a pi to sigma transformation (between two carbons in this example) and not the formation of other bonds, based on the energetics of the bond we are transforming, the energy will increase.

Reference for bond energies: http://web.chem.ucsb.edu/~zakariangroup/11---bonddissociationenergy.pdf