# Have "molecular clusters" for azeotropes been identified?

A different question about azeotropes got me thinking about this point again. Azeotropes have a very specific composition so it seems that the azeotrope ought to have some sort of physical structure. It seems to be a "molecular cluster" of some sort.

The azetrope for water and ethanol is about 95.5% ethanol by weight. A little fiddling and it seems that the ratio is 8 ethanol molecules to 1 water molecule. Is there some particular physical configuration of molecules to which this would correspond?

• For the cluster of 8 my perception would be something like a cube where the water is in the center and the 8 ethanol molecules are on the corners with the OH groups pointing in. Such a structure would be a cube, but something in between a more like a ball. I can't visualize how the OH groups would pack though.
– MaxW
May 28 '16 at 13:29
• No, it doesn't work like that. May 28 '16 at 22:01

## 3 Answers

No, in the absence of extra data, there is no reason to suppose that there is any vapor-phase cluster formation.

Cluster formation in the gas phase would demand very, very strong departures from ideal-gas behavior. To the contrary, the ideal gas law is an excellent descriptor of gas phase mixtures of ethanol and water.

Check out a Wolfram Demonstration for the ethanol-water system. It says:

You can vary the pressure $P$ to any value between 50 kPa and 200 kPa (i.e., low to moderate pressure so that the ideal gas-phase assumption holds).

If the ideal-gas assumption holds, then there is no significant structure formation in the vapor phase. The "ideal" gas law describes negligibly small particles that have no attraction or repulsion to each other. Structure formation means that molecules must be strongly attracted to each other in order for arrangement into a persistent structure to occur.

An "extended" form of Raoult's law that is valid for non-ideal vapor as well as non-ideal liquids, and thus is applicable to azeotropes, is

$y_i \phi_iP = x_i \gamma_i p_{i, \mathrm{sat}^{\star}}$

Here, $\phi_i$ is the fugacity coefficient and takes into account vapor-phase non-idealities (i.e. deviations from the ideal gas law), and $\gamma_i$ is an activity coefficient and takes into account liquid-phase non-idealities.

For many, many systems of interest, $\gamma_i$ is the driver of non-ideality, including azeotropic behavior. Fugacity coefficients $\phi_i$ are negligible (except at enormous pressures) a much higher percentage of the time than activity coefficients $\gamma_i$. This is because liquid phases are often far more dense than vapor phases, meaning that intermolecular forces govern behavior to a much stronger degree than in vapors.

Azeotropes are not about molecular clusters at all. In the relatively rare cases where certain intermolecular compounds with specific compositions indeed do exist (examples include $\ce{H2O + N2H4}$ and $\ce{H2O + HClO4}$), they manifest themselves on the phase diagram in a quite different manner. First and foremost, they should be expected to appear as peritectics on the melting diagram, which is not the case for the water+alcohol system.

In positive azeotropes for which the boiling point is less than the boiling points of any of the constituents the intermolecular interaction of the different molecules is less than in the pure liquid phase. Therefore it is not very likely that clusters involving the different molecules will be formed.

In negative azeotropes that have a higher boiling point than the constituents cluster structures in the liquid phase are more likely. E.g. for concentrated hydrochloric acid the existence of clusters has been suggested1.

1 Agmon, N., Structure of Concentrated HCl Solutions, J. Phys. Chem. A 1998, 102, 192-199
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