Familiar Physical Laws

The Everyday Macroscopic World

 

Liquids & Solids

Liquids behave much like the gases except that the liquid molecules are so close together they affect each other through the mechanism of long-range forces between their molecules. For Ideal Gases there is no interaction between atoms or molecules except during simple repulsive collisions between hard spheres. Liquid behavior is a difficult subject but some simple things can be said from what we already know: they are dense and they have molecular motions. A mole of anything still contains NAv particles, but they no longer fill one gram molecular volume (i.e., the volume is much less than 22.4 liters/mol or 22.4 m3 /kmol at NTP).

Let’s look at water. Its density is ~1.0 g/cm3. Also 1.0 g of water is 1/18 of a mole (H = 1.0 and O = 16.0 and H2O overall = 18.0). Hence 1.0 cubic centimeter contains 6.023 × 1023/18 = 3.35 × 1022 molecules – again a staggering number. If a water molecule is about 0.27 nm in “diameter”, the occupied volume alone by all of these molecules is ~0.35 cm3. Thus the free volume among these molecules is only ~0.65 cm3 for 3.35 × 1022 molecules and their mean free path is only ~0.33 nm. In other words, in a liquid the average distance between molecules is only about equal to their molecular diameter. Crowded!

How about a solid? Similar rules apply. In diamond, an allotrope of carbon, the atoms of carbon are each in exact relation to each other such each one is connected to its four nearest neighbors in a tetrahedral cage surrounding the focus atom. The density of diamond is 3.5 g/cm3 and each cubic centimeter contains 3.5/12 moles (C = 12 g/mol) or 3.5 × 6.023 × 1023/12 atoms = 1.76 × 1023 atoms. The “covalent” radius (i.e., the size it appears when in compounds) of a carbon atom is 0.154 nm. In a 1.0 cubic centimeter crystalline cube of diamond[1] the atoms occupy virtually all of it and the remaining free volume is limited. In fact, the adjacent atoms of carbon “touch”. The only free volume is in the interstices. These facts are intimately related to the renowned hardness of diamond.

When we talk of atoms “touching” what do we mean? The gas kinetic model said they were “hard point spheres". That’s simply untrue. In reality, the atoms have a very small nucleus containing virtually all of the atoms mass and which are surrounded by clouds of electrons. Actually, since the mid 1920’s we think of the electrons as being contained in orbitals that simply relate to the probability of finding an electron in that particular element of volume. The shape of these orbitals is the stuff of quantum mechanics, but briefly they can be spherical about the diameter of an atom or pear-shaped and perpendicular to it. It’s these orbitals that define the outer “edges” of the atom. Essentially when we push down on something hard, the resistance we feel is the mutual repulsion of these electron orbitals against those in our fingertips (more clouds of electrons). The AFM works on similar principles.

Footnotes and References

[1]. You should be so lucky – that’s 17.5 carats!