# Do bond lengths vary across molecules of the same kind?

I only have superficial knowledge of chemistry, and today I found out about bond length for the first time. For example, on Wikipedia it says that all C-C bonds of benzene have a length of 140 picometres (both C-C and C=C, I think). But is this exactly true for all benzene molecules?

Or does bond length of C-C vary slightly for 10 molecules of benzene? Is 140pm an average distance for a million molecules, or each and every benzene molecule has bonds of length 140pm? Is this a fundamental and unvarying length of the benzene molecule, so that a different length cannot possibly occur?

I know that during studies of the bond length in the laboratory, each individual measurement has a slight error. I'm not asking about that.

• "All C-C bonds have the same length" is about as precise as "All men have the same height". Jun 22, 2017 at 8:42
• ''both C-C and C=C, I think'' there are no fully "single" or "double" bonds in benzene, otherwise they wouldn't have equal lengths. Jun 22, 2017 at 15:34

The atoms within a molecule are not stationary, but are constantly vibrating, twisting, etc. Thus, the value given for a bond length between two atoms must be an average. Specifically, the average distance from the nucleus of one atom to the nucleus of the other is what constitutes the definition of bond length.

• This is very interesting. How much does a bond length fluctuate? And how fast? Does it fluctuate more-or-less the same for all molecules of a kind (like all benzene molecules)? The same, meaning they have very similar minimums and maximums and standard deviation etc. Also, temperature and gas pressure will affect the fluctuation, right? Jun 22, 2017 at 8:52
• @CamilB You might like to read about infrared spectroscopy - as that relies on those vibrations, explanations of it include information about the vibrations of interatomic bonds. Jun 22, 2017 at 12:19
• @CamilB , good idea by Andrew. Another good resource, though doesn't answer all you questions, can be found here. Jun 22, 2017 at 14:47
• @airhuff That animation of the $CH_2$ group rocking and wagging made my day. Jun 23, 2017 at 5:20
• @CamilB , likewise ;) Jun 23, 2017 at 14:57

In a simple molecule such as oxygen, the bond length measured will alway be the same as the interaction between any two oxygen atoms is the same since one oxygen atom is indistinguishable from another. Thus by extrapolation in any molecule the same bond has the same length.

Now by length we usually assume equilibrium bond length and this is because in every molecule the bonds vibrate and, obviously, the bond length is instantaneously changing.

Note that most experiments are done on a very slow time scale such that the vibrational motion (period of a few femtoseconds, $10^{-15}$ s) is completely averaged out. The range of bond extension for the lowest vibrations is small just a few percent of the total length. You can work this out from spectroscopic results.

The equilibrium value, i.e that at the minimum energy is usually defined as the bond length although one could take the average which in most cases differs very little from this.

• This answers all my remaining questions, thank you! Jun 23, 2017 at 5:17