Which state of matter is highly compressible, is made of particles moving independently of each other, andis present in large quantities near earths surface?

The highly compressible state of a matter is its gaseous state. The gaseous molecules are highly compressible due to presence of maximum space between the molecules than the other state of the same material. As for example the gaseous form of water that is vapor has the maximum space between the H₂O molecules and lowest in the solid state that is ice.

 The motion of the particle have some postulates which is called the kinetic theory of gas. The gaseous particles of any particular gas can move independently in the vessel in which it is kept. The motion of the gas in a vessel is described by the Brownian motion.

The gaseous state of the material like carbon di-oxide (CO₂), oxygen (O₂), nitrogen (N₂) remains nearest to the earth surface which is stratosphere.  

vanderwaal's forces of attraction are the electrostatic intermolecular forces that exist in a molecule due to the temporary or permanent dipoles that are developed in a molecule. in , the major intermolecular forces are dipole-dipole interactions as the molecule is polar (bent structure). so the vanderwaal's forces of interaction in between molecules are the permanent dipole-dipole interactions that develop due to the dipole that exists in between the polar h - s bond. the positively charged hydrogen atom is attracted towards the negative end of the dipole that is sulfur of the adjacent molecule. therefore, these forces of attraction are relatively stronger than that of london dispersion forces that exist in non polar molecules.