Double vs Single Bond Length

name         Margaret
status       educator
grade        9-12
location     DC

Question -   Why are double bonds shorter than single 
bonds?  Is it because there are more electrons to be shared by 
the two atoms, so the nuclei are more attracted? I would expect 
the bonds to be longer because there are more electrons and the 
electrons would repel each other more.
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The general rule of thumb is "longer bond -- weaker bond; shorter bond --
stronger bond". And that correlation applies to most all 
circumstances. You are correct that there is increased repulsion 
between the electrons forming multiple bonds, but the strength of 
multiple bond formation out-weighs the energy debt due to 
repulsion. So for example, going from single, to double, to triple 
bonds in carbon the average bond energy varies as: 348, 682, 962. 
If there were no energy "debt" due to repulsion one might expect 
the trend to be 348x1=348, 348x2=696, 248x3=1044 (all energies in 
kJ/mol). In reality it's a bit more complicated than that because 
the types of the chemical bonds change -- they are not just balls 
and springs -- but that does not minimalize your perceptive observation.

Vince Calder
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Margaret,
The short answer is that the atoms have to be closer
together for more electronic orbitals to overlap to
form a second bond--yes, there is more sharing of
electrons between the atoms.

Below is a much more complete and detailed answer.

Single bonds are formed by head-to-head overlap of
orbitals.  For example, H2: Each hydrogen only has one
electron in a spherical s-orbital.  These s-orbitals
overlap to form a sigma (single) bond.
In the next example, let us think about ethene (C2H4)
Here, the carbons are double bonded to each other, and
each carbon is single bonded to two hydrogen atoms.
The carbon atoms are both sp2 hybridized--in other
words, their s and 2 of their p-orbitals have mixed
together to make three identical orbitals.  The left
over unhybridized orbital is a p-orbital.

The sp2 orbitals overlap with the Hydrogen's s
orbitals  to make single bonds. There is also
head-to-head overlap of orbitals from each carbon to
form the single bond.

Now we can answer the question: what makes the double
bond.
The extra p-orbitals from each carbon (the ones that
didn't hybridize) overlap to form a pi bond (the
second bond between the carbons).

A double bond is composed of both the sigma bond (from
head-to-head overlap) and a pi bond (from overlapping
p-orbitals).

Now for the real answer to your original question: the
double bond is shorter than the single bond because
the atoms have to be close enough together for those
unhybridized p-orbitals to overlap.

Hope this helps.
--Michelle Weinberger
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