# How long can poly(ethylene oxide) molecules be?

In this video, Steve Spangler says the substance he is using is a poly(ethylene oxide): http://www.youtube.com/watch?v=m-88M75_PCI

He mentions that one molecule would go to the moon and back twice! I have a hard time believing this, but I guess it must be true.. Is it true that poly(ethylene oxide) molecules can be that long?

## 1 Answer

Short answer? Possibly, but these ones aren't.

So, the other thing mentioned in the video is that the specific material he's using has a molecular weight of approximately four million g/mol. If we assume it's ordinary poly(ethylene oxide), we can get the rough number of $$\ce{(CH2)2O}$$ subunits by just dividing by the molecular weight of the subunit:

• $$(12 \times 2) + (2 \times 2) + 16 = 44$$
• $$\frac{4000000}{44} \approx 90900$$

So, if we assume that each $$\ce{C-O-C}$$ back-bone unit is stretched out like a di-methyl ether molecule, a quick check on a fairly standard Ghemical force field gives me a subunit length of approximately 3.7 Å.

• $$3.7 \times 10^{-10}\ \mathrm{m}\times 90900 = 0.00003363\ \mathrm{m}$$

So, these molecules should be about 0.03 millimetres long. Not exactly astronomical distances, but impressively long for a single molecule.

In theory, I don't think there's anything stopping you making a molecule as long as they claim, but these ones certainly aren't. I think also that the longest (synthetic) polymers in common use are of similar molecular weights and thus similar lengths: ultra-high molecular weight polyethene seems to top out around 4.5 million g/mol for commercial applications, from a quick search.

Biological molecules frequently get longer than this, though, especially DNA: the average human chromosome apparently contains a single DNA molecule approximately 5 centimetres long.

The man explaining in the video may have erroneously given the figure for the total length of all the molecules in that beaker.

• Note that a while a millimetre (or kilometre) long molecule is surely allowed, you cannot straighten it out to that lenght. It would long before rupture under its own desire to coil up into a ball, unless it was cooled very close to absolute zero. Entropy rules.
– Karl
Jan 6, 2020 at 7:43