1.4 Raoult's law (ideal systems)
Raoult's law states that:
"The partial pressure of a component is equal to its mole fraction in the liquid multiplied by its vapor pressure."
NB: The Raoult's law is the way to express the isofugacity condition when not only the vapor but also the liquid is considered ideal.
In a binary system with two components, A and B, Raoult's law can be written as:
PA = xA PAv
PB = xB PBv
PA = partial pressure of component A;
PB = partial pressure of component B;
PAv= vapor pressure of component A;
PBv= vapor pressure of component B;
By Dalton's law of partial pressures, it is:
PA = yA P;
PB = yB P;
P = PA + PB = total pressure
Combining these equations, we obtain the following:
yA = xA [PAv / P]
yB = xB [PBv / P]
NB: the Dalton's law is helpful in this case to explicit the mole fraction of the vapor phase from the expression of the partial pressures. It is NOT another way to express isofugacity condition
Raoult's law can be represented in a pressure-composition diagram. The linear behaviour of ideal systems is represented by the red lines in the here below diagram.