Equilibrium between different phases in ideal solutions

1 Equilibrium between different phases in ideal solutions 

Component a making up a liquid phase (L) in contact with a gas phase (G) forms a two phase system. In the equilibrium state, the chemical potential of component a in the gas and contacting phase are equal. The equilibrium saturated vapor pressure of pure component a in the gas phase over the pure liquid phase a can be designated with p. Using the expression for a perfect gas, Eq. (4-1), for the chemical potential of a, one gets an expression of the chemical potential of component a in liquid a, p (L), in the equilibrium state  

For a two component liquid phase composed of a and b whose partial pressures in the gas phase at equilibrium with the liquid phase are pa and pb, one can write  

In a so-called ideal solution, that is a mixture of several components with very similar properties, the ratio of pa/p is equal to the mole fraction x of component a in the liquid phase. Thus Raoult s law is valid  

If two pure liquids, one composed of only na moles of component a and the other of only rib moles of component b, are mixed and the total free enthalpy of the two liquids in separate initial states, Ga, is considered, then the enthalpy of the mixture Ge for an assumed ideal solution can be calculated. Because na + nb = n, na/n = xa and nbln = xb Eq. (4-8) results in  

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