# Why does sulfur, but not oxygen, catenate?

Oxygen is a rather boring element. It has only two allotropes, dioxygen and ozone. Dioxygen has a double bond, and ozone has a delocalised cloud, giving rise to two "1.5 bonds".

On the other hand, sulfur has many stable allotropes, and a bunch of unstable ones as well. The variety of allotropes, is mainly due to the ability of sulfur to catenate.

But, sulfur does not have a stable diatomic allotrope at room temperature. I, personally would expect disulfur to be more stable than dioxygen, due to the possibility of $\mathrm{p}\pi\text{-}\mathrm{d}\pi$ back-bonding.

So, why do sulfur and oxygen have such opposite properties with respect to their ability to catenate?

First, a note: while oxygen has fewer allotropes than sulfur, it sure has more than two! These include $\ce{O}$, $\ce{O_2}$, $\ce{O_3}$, $\ce{O_4}$, $\ce{O_8}$, metallic $\ce{O}$ and four other solid phases. Many of these actually have a corresponding sulfur variant. However, you are right in a sense that sulfur has more tendency to catenate… let's try to see why!

Here are the values of the single and double bond enthalpies: $$\begin{array}{ccc} \hline \text{Bond} & \text{Dissociation energy / }\mathrm{kJ~mol^{-1}} \\ \hline \ce {O-O} & 142 \\ \ce {S–S} & 268 \\ \ce {O=O} & 499 \\ \ce {S=S} & 352 \\ \hline \end{array}$$ This means that $\ce{O=O}$ is stronger than $\ce{S=S}$, while $\ce{O–O}$ is weaker than $\ce{S–S}$. So, in sulfur, single bonds are favoured and catenation is easier than in oxygen compounds.

It seems that the reason for the weaker $\ce{S=S}$ double bonds has its roots in the size of the atom: it's harder for the two atoms to come at a small enough distance, so that the $\mathrm{3p}$ orbitals overlap is small and the $\pi$ bond is weak. This is attested by looking down the periodic table: $\ce{Se=Se}$ has an even weaker bond enthalpy of $\ce{272 kJ/mol}$. There is more in-depth discussion of the relative bond strengths in this question.

While not particularly stable, it's actually also possible for oxygen to form discrete molecules with the general formula $\ce{H-O_n-H}$; water and hydrogen peroxide are the first two members of this class, but $n$ goes up to at least $5$. These "hydrogen polyoxides" are described further in this question.

• Do the rest of the elements follow the expected order? I mean the order is: S-S > O-O > Se-Se > Te-Te ? – Piyush Maheshwari Apr 18 '18 at 14:35
• Expanding upon this answer, we may need to reconsider what we consider as "catenating". Does it mean it's easy to form bonds with itself to form polymeric substances? If so, easy at what temperature? I believe oxygen catenates just as easily as sulfur albeit at a lower temperature range. – Pritt Balagopal Nov 26 '18 at 17:32

## protected by Martin - マーチン♦Mar 8 '16 at 10:01

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