# How to estimate the physical size of a molecule?

I'm reading some chemistry-related papers that employ concepts of droplet evaporation. Since I am no chemist, I am wondering:

How can I estimate the actual size of a molecule, say succinic acid?

An order of magnitude would suffice. I'm aware of the fact that most molecules can not be approximated by simple assuming that they are spherical.

Evidently, I don't want to do this bottom-up from quantum mechanics. A broad explanation or just a reference would suffice.

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I'm going to have a wild guess, $1.26\cdot10^{-22}\,\mathrm{cm}^3$, and wait for an actual answer... :) – Keep these mind Jun 11 '13 at 13:27
Perhaps (I'm a total nitwit), you may also have a look at structure of the molecule, plug in a few bond lengths, some angles and some room for electrons, and... perhaps get something similar. – Keep these mind Jun 11 '13 at 14:34
@Gugg thanks, this is a classic example of turning a simple problem into smth overly complicated. :-) – seb Jun 11 '13 at 14:38
Shouldn't this go to ChemestrySE? – jinawee Jun 11 '13 at 15:54
@jinawee It would have been on-topic there too, but the physical scale of molecules comes up in a lot of physics contexts (crystalography, various questions of quantum limits in semiconductor design and other condensed matter topics, attosecond physics, and so on). – dmckee Jun 11 '13 at 16:59

The order of magnitude given by Gugg is correct. The molar volume for the succinic acid is

$V_m=\frac{M}{\rho}=\frac{118.09}{1.59}\frac{cm^3}{mol}=74.27cm^{3}/mol$

where $M$ is the molar mass and $\rho$ the density. From this, you find the volume of the molecule to be

$V_{molec}=\frac{V_m}{N_A}=1.23\cdot10^{-22}cm^3$

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thanks. this is why I love this site! :-) – seb Jun 11 '13 at 14:39

I answered a question much like this in my Chemistry finals, and that was a several page essay. You'll excuse me if this answer is a rather shorter!

The definitive way to measure molecular size is X-Ray crystallography. This gives you the structure of the crystal including the positions of all the atoms, so you automatically get the molecule size. This method works for any material that you can crystallise even including huge molecules like DNA and proteins.

In the gas phase the size of molecules can be easily measured for simple molecules using rotational spectroscopy. This gives you the moments of inertia about various axes and from these you can calculate the bond lengths. The method doesn't work for molecules that are too big and complex or (like succinic acid) that aren't easily vaporised, however the bond lengths are pretty constant across most molecules. So once you have bond lengths for simple molecules you can put these into molecules like succinic acid and calculate the size of the molecule that way.

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I had a feeling that this is gonna be much more complex than I initially thought! thanks for outlining how it's done. this will be helpful when I dig deeper into the field. – seb Jun 12 '13 at 8:46

## protected by Qmechanic♦May 17 '15 at 6:29

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