[petelamana (OP)]

I have a nagging question of sublimation...

As a mathematician, and therefore entrenched in the asymptotic nature of the limit, a function becoming infinitely close, or in this case a unit of time becoming infinitely small, I have a problem with the concept of sublimation.  While I can completely understand how, to an observer, the "skipping" of a state of matter, i.e. "dry-ice" to vapor seems possible, I see it differently. 

There must be an immeasurable instant at which, under "normal" conditions, solid CO2 would exist as a liquid.

Someone help me out here, other than telling me that sublimation is a law.

[chiralSPO]

I can try to provide an explanation based on a molecular-scale view of what is going on.

But first, I want to address an aspect of your question that is more mathematical. The solid, liquid, gas spectrum is not 1-dimensional. The state of matter depends both on temperature and pressure. Even a 1 dimensional (say just change in temp) can cross directly from solid to gas without coming close to a liquid region, provided a specific range of temperatures. The phase diagram for CO₂ looks like this:

phase diagram.jpg (124.69 kB . 1331x1052 - viewed 3288 times)

Which indicates that any pressure below about 5 atmospheres, CO₂ is not stable as a liquid.

The liquid state is also not pre-requisite for gaseous states either. The interactions between molecules that determine how strongly they stick together are essentially electrostatic in nature. CO₂ is a small nonpolar molecule that is also not very polarizeable. But the molecules do have a quarupole moment. These interactions are only attractive at extremely close range, so any molecule of CO₂ that has enough energy to move a little bit out of place in a solid probably has enough energy to escape entirely into the gas phase. ie there is no intermediate range where the molecules are essentially touching, but free enough to move past each other as they would in a liquid. However, if the gas above the solid becomes saturated with CO₂ molecules and the rate at which the CO₂ molecules escape the solid and becomes a gas is the same as the rate at which CO₂ molecules condense out of the gas, then there is an equilibirium (this can be solid-gas or liquid-gas), and as the pressure of CO₂ gas increases eventually there is enough to hold the molecules close together while they have enough kinetic energy to move around liquid).

[evan_au]

@petelamana asked a question about the macro-scale (a kg of dry ice).
The answer from @chiralSPO focussed on the molecular scale of 1-10 molecules.

There is also a view on the nanoscale of a million to a trillion molecules:
- Liquid behavior represents a large number of molecules that are able to jostle past each other, but still held together by surface tension
- It requires a fairly large number of molecules to get behaviors that we would recognise as a tiny drop of liquid
- Below the nanoscale, quantum effects often distort the behavior we would expect to see in a macroscopic sample
- Statistically, a block of dry ice at atmospheric pressure and a temperature around -50C just doesn't have enough molecules that are close enough, with the right energy range to be bound together in a tiny droplet.
- If the vapor pressure is greater than the external pressure, you get boiling (the liquid turns into a gas)
- So macroscopic liquid effects can't exist under these conditions, because they are extremely unlikely and fleeting at the nanoscale.