Chapter 7 : Vapour-Liquid Equilibria

Section 5 : Raoult’s Law for VLE
 

Next consider the point V in the above diagram. At this state the mixture is at the same overall composition as at L, but the state is one of single phase, superheated vapour. Increasing the pressure at the same composition eventually brings the mixture to the point B1, where any further increase of pressure leads to the formation of the liquid phase, whose composition is given by the point A1. Thus this point is said to be the dew point corresponding to the vapour phase composition given by  while the pressure at this point is termed the dew pressure.

We revert to the discussion on the system state at the bubble point A3. If one reduces the pressure progressively the more formation of more bubbles of vapour occurs, which coalesce and lead to the development on a bulk vapour phase.  The system state eventually reaches the point B1 where practically the entire mixture exists in the vapour form; further reduction of pressure renders the mixture superheated and finally one reaches the point V (and beyond). Let us focus on what happens as the system transits through the two-phase region defined the end points A3 and B1. Note that the overall composition of the system remains invariant as the pressure reduces. However, since now the original amounts of each species need to be distributed across the co-existing vapour and liquid phases the actual composition in each phase must change in accordance with the following mass conservation: where, are compositions of the liquid and vapour phases at equilibrium, and  are the relative amounts of moles (per mole of the original mixture) in the liquid and vapour phases, respectively (thus . The liquid phase composition progressively changes along the line A3 to A1 (bubble curve), while the composition of the vapour phase in equilibrium with the liquid phase transits from B3 to B1 (dew curve). At each pressure between the bubble pressure (Pb) and the de pressure (Pd) the equilibrium vapour and liquid phase compositions, as well as the relative amounts of mass in each phase are constrained by the relations: