6
$\begingroup$

When discussing energy transformations on the molecular scale, we usually use electronvolts as the energy unit. This is handy because chemical bond energies are a few electronvolts in magnitude.

I had an idea to go through some thermodynamic tables and convert them into molecular-scale units (energy in $\mathrm{eV}$, entropy in bits, etc.) in order to get a feel for how chemistry works on the scale of single molecules. However, for talking about volume changes (that is, average volume change per molecule), I can't think of a convenient unit. All of the most commonly used volume units ($\mathrm{\mu L}$ etc.) are far too large, apart from Planck units, which are far too small. Even yoctolitres are a bit on the big side, and I've never heard of anyone tabulating values in $\mathrm{yL}$.

Of course it wouldn't be hard to define a convenient unit, for example by deriving it from the ideal gas law at a standard temperature and pressure. But it would be better to use a unit that people already recognise. So my question is: is there a unit of volume in common use that is of a convenient size for thinking about single molecules? That means, I guess, that it should be between around $10^{-31}$ to $10^{-27}\;\mathrm{m^3}$, and preferably towards the smaller end of that.

$\endgroup$
  • 2
    $\begingroup$ I guess you wouldn't just want to work with cubic nanometers? Or perhaps a cubic Angstrom? $\endgroup$ – tpg2114 May 20 '14 at 0:54
  • $\begingroup$ $nm^3$ are a bit big, but actually I guess cubic Angstroms are probably the obvious choice, I just hadn't thought of it. (But the most important thing is whether people actually use those units for this purpose already.) $\endgroup$ – Nathaniel May 20 '14 at 0:56
  • $\begingroup$ I suppose it's a matter of choice depending on the size of your molecule -- complex hydrocarbons may be on the cubic nanometer scale. But between the two, you have your $10^{-30}$ or your $10^{-27}$ as the case may be. I've seen crystal lattices described by either their Angstrom spacing and angles or the volume in Angstroms of the circumscribed sphere. $\endgroup$ – tpg2114 May 20 '14 at 1:00
  • $\begingroup$ It's for considering volume changes rather than absolute volumes. Typically, volume changes are rather smaller than the volume of an individual molecule, unless the reaction involves a phase change to or from the gas state, in which case it goes up to $k_BT/p$ per molecule ($\approx 4\times 10^{-26}\;\mathrm{m^3}$ at standard $T$ and $p$). From working through a few examples, though, it seemed like it would be more convenient to use a smaller unit. $\endgroup$ – Nathaniel May 20 '14 at 1:09
  • 1
    $\begingroup$ I still think cubic Angstroms may be the best bet, but I don't know what kinds of calculations you're dealing with. I don't mind using values from 1e-3 to 1e3 regularly so something like $0.001$ cubic Angstroms isn't unbearable for me. That's probably within the range of volume changes you would encounter maybe? $\endgroup$ – tpg2114 May 20 '14 at 1:55
3
$\begingroup$

There are atomic units, where

Length is: Bohr radius = 1

Mass is: mass electron = 1

Time is: Bohr period = 1

See above link for a full explanation of the system.

$\endgroup$
1
$\begingroup$

Crystallographers mostly talk about the spacings between lattice planes in Ångstroms, as tpg2114 says in a comment.

I have found myself tabulating number densities for different materials in atoms per barn-cm. This is because the transmission through an absorber with number density $n$, thickness $\ell$, and capture cross section $\sigma$ is $$ T = \exp -n\sigma\ell $$ and I typically have cross sections in barns and care about lengths in centimeters. A barn is an area unit equal to 100 fm2 = 10-28 m2 = 10-24 cm2. This is a very small unit of volume, but it's a very long and skinny volume.

I can't remember if I started doing that on my own or if I copied it from someone else, but it was damned useful for doing transmission calculations. Don't know how appropriate for thermodynamics, though. Interesting question!

$\endgroup$
0
$\begingroup$

A cubic nm contains 33 molecules of water. The smallest amount of H2O needed to make water, is six molecules, or 0.18 cu. nm.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.