[curiouscat]

Just like Water (a Liq.) is anomalously more dense than Ice (a solid) (and so is Bismuth Liq. vs. Solid); are there any examples of this at the Gas-Liquid transition?

i.e. Any substances where the Gas is more dense than the corresponding Liquid? If not, is this fundamentally forbidden by some physical law constraint? Or just happens that we don't know of any.

[fledarmus]

What is the fundamental physical difference a liquid a gas? How do you determine physically whether something that you see in a test tube is a liquid or a gas?

[curiouscat]

What is the fundamental physical difference a liquid a gas?

Lack of long range order?

How do you determine physically whether something that you see in a test tube is a liquid or a gas?

See if there's a distinct interface? Even better, see if it were compressible?

[fledarmus]

No, it's something even more obvious than that. Go back to the definitions of the states of matter:

Solids - characterized by structural rigidity and resistant to changes of shape and volume
Liquids - definite volume but no fixed shape, molecules are free to flow and take the shape of the container
Gases - no fixed volume or shape, molecules distributed homogeneously throughout a container

So given a container which contains both liquid and gas, and the liquid has a fixed volume while the gas is free to distribute throughout the chamber, I cannot imagine any situation in which the gas molecules would be closer together than the liquid molecules.

[curiouscat]

So given a container which contains both liquid and gas, and the liquid has a fixed volume while the gas is free to distribute throughout the chamber,

Isn't that just another way of restating that in a gas:

"there's no distinct interface" / "it is compressible (alternatively, expandable)"

I cannot imagine any situation in which the gas molecules would be closer together than the liquid molecules.

That's hardly a "physical law constraint". If you'd never seen ice float on water would you have "imagined" it?

Of course, I agree with you it seems so unlikely; but that's sort of the point: Is there / Could there be a corner case?

[fledarmus]

If you are considering solids, the molecules are held into rigid frameworks. There are a number of ways to create rigid frameworks of molecules in which the average distance between molecules was larger than the actual distance between any two molecules. This is done by structural limiting the total number of molecules that any one molecule can interact with. For example, suppose the molecules want to interact at a distance of 3 Å. In a liquid, a molecule might have as many as twelve neighbors all at the same distance of 3 Å. If you put that molecule into a lattice at the vertex of a cube, however, you reduce that number to 6 nearest neighbors, and the average distance between molecules increases as the number of molecules at that distance decreases - the solid is less dense than the liquid. If you add voids to the crystal structure, as in foams or zeolites, you can get further reductions in densities of the solids.

You do not have these rigid arrangements in gases and liquids. In fluids, the density is fixed by the preferred distance between the molecules, and the total number of molecules at that distance is determined only by the volume the material is occupying. In gases, there is no preferred distance between the molecules - the molecules will disperse to fill as much space as possible. Increase the volume, density decreases. Liquids do have a preferred distance between molecules - as you increase the volume of the container, the volume of the liquid stays constant. Increasing pressure on a liquid does not change the distance between molecules very much, while increasing pressure on a gas will change the distance between molecules until the energetics of condensing to form a liquid become favorable.Then the liquid will condense, leaving the gas with more space to move around.

[curiouscat]

If you add voids to the crystal structure, as in foams or zeolites, you can get further reductions in densities of the solids.

True. Yet you can't make them less dense than the corresponding liquid, right? i.e. A crystal X no matter how many voids you add in its lattice, never floats on its own melt ever? Or can it? I wonder.

Water and bismuth (and maybe a few others) are special in that respect?

[fledarmus]

Yet you can't make them less dense than the corresponding liquid, right?

Yes you can - that is how ice floats on water. Due to the rigidity of the ice crystal lattice, the molecules in an ice crystal are ON AVERAGE further apart than molecules in water. This doesn't mean that the nearest neighbors are further away, only that there are fewer nearest neighbors. That makes the ice less dense than the corresponding melt liquid, and it floats.

The same thing with foams - if the melt liquid cannot fill the voids due to the solid structure surrounding the voids, then the solid will float on the corresponding melt. Each void that you introduce into the crystal structure lowers the density of the crystal - enough voids and the solid becomes lighter than the liquid.