11. Substances with Higher Density

If one changes from dilute (ideal) gases to real gases with higher density, the interaction between the particles and the phenomenon of condensation cannot be neglected any longer. The consideration of such effects results in the van der Waals equation, a modification of the general gas law. A closer look at the process of condensation leads us to the critical phenomena, meaning the unusual physical properties displayed by substances near their critical points. If we are interested to know how the phase transition liquid ⇄ gaseous can be influenced by factors such as temperature and pressure, we can use the T and p dependence of the chemical potential for calculating the boiling pressure curve (vapor pressure curve) of a given pure substance. This curve illustrates how the vapor pressure of the substance varies with temperature and is an example of a so-called phase boundary. The other phase transitions can also be represented in a p(T) diagram in the form of phase boundaries, producing a complete phase diagram. Such a diagram is a kind of “map” which shows the conditions of temperature and pressure at which a certain phase is most stable and illustrates the ranges of existence of stable phases.