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Why does oxygen form a double bond in $\ce{O2}$ but sulfur, also from group 16, forms single bonds in $\ce{S8}$?

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This is essentially the same question as to why carbon concatenates through up to four bonds with binding energies low enough to be broken again yet stable enough to last given typical terrestrial environmental conditions. Great for entities like us.

On the other hand, the binding energies of Silicon, Germanium, from the same group IV, for instance, are higher. The binding energies are directly related to the bond length/bond distance, which is great for determining the energies through crystallography, along with proper model fitting.

Sulfur is one of few elements amenable to catenation, - forming long molecules with each other.

So whichever configuration releases the greatest enthalpy is typically the most stable one, but depends upon the initial energies thus giving rise to allotropes - elemental structures of different molecular configurations. The bound system typically has lower potential energy. If a double bond lowers the overall energy of the bound system more it will typically form over a single bonded one.

Update: I found this (see also this table of dissociation energies):

Update 2: I'd like to add that from a quantum mechanical perspective, which is a viewpoint much closer to nature, the bonds arise from 3D space where electron densities are highest - which means most energetically favorable.

Since for whatever weird reason, nature is really quantized, and I cannot stress that "really" part enough, one gets standing waves for the electron equations around a given nucleus - rather than a continuum - as is the case of a sphere, like say a falling waterdrop to add a few exterior forces into the mix as well. The classical and the quantum object have only in common the "energetically favorable" state.

Somehwat simplified then, those standing waves become "orbitals" when doing the calculations for 3D space. The orbitals change in shape with increasing interference with other electrons and higher potential energies due to larger nuclei , meaning higher positive proton counts.

The energies involved result in very different packing i.e. different lattices. A necessity for life is breaking bonds or "bond accessibility". There simply isn't "enough energy" in today's protein-scaffold based catalyists on earth, to use anything else than the constituents of the periodic table with few protons in case of homogenous bonds (i.e. atoms of the same species like say Oxygen O2).

It does not have to be this way. We from earth are biased by our own biochemistry we observe. Every human generation breaks down the biases of the previous ones and encounters new ones.

Bond energies

  • 1 S8: 1808 kJ/mol
  • 1 O8: 1168 kJ/mol
  • 4 S2: 1408 kJ/mol
  • 4 O2: 1976 kJ/mol
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The relative difference in energy between the double bond and single bond is much greater in oxygen than in sulfur, and so is the more stable $\ce{O2}$ diatomic molecule with a double bond, than molecules with multiple single bonds like $\ce{S8}$.

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