Deviations from Raoults law and the activity coefficient

As discussed in Chapter 4, the vapor-liquid equilibrium between an ideal gas and an ideal liquid solution is governed by Raoult s law  

Raoult s law states that the partial pressure of a species in the vapor phase is proportional to the mole fraction of the species in the liquid phase. The constant of proportionality is the vapor pressure of the pure species. Mathematically, this expressed as 

For most systems, Raoult s law is not obeyed. If we actually measure the partial pressure of a given component above a mixture as a function of its mole fraction, it will most often deviate from a straight line. For example, see the dashed and dotted lines in Fig. 6.1. In order to characterize the deviations from Raoult s law, we define the activity coefficient for component a, which is denoted by 7a, as  

Note that in general, the activity coefiicient depends on the temperature, pressure, and composition of the system. If the system obeys Raoult s law, 7a = 1. When 1, the system is said to exhibit positive deviation from Raoult s law, and when 7a 1, the system is said to exhibit negative deviation from Raoult s law. 

Although Raoult s law is not a good approximation for many systems, there are two points at which 

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