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X ¯ ∂tNα T,p,tNα =α ∂tNα ∂t Nα ¯ α Nα X = α X(T, p, N1 , N2 , . . 6) α The value of any extensive property of a system is equal to the sum of the partial molar properties of each component multiplied by the amount of each component in the system. Therefore, we can “divide” the property of a mixture , such as the volume or enthalpy, between its individual components according to their partial molar properties. One important example of this, which we will utilize later, is the Gibbs free energy G.

Mathematically, this means that know the form of the functions μ◦α (T, p). Physically, this means that we know everything about the thermodynamics of the pure species. Once we know the Gibbs free energy of a system as a function of temperature, pressure, and composition, we know everything about its thermodynamics. 2) α where Vα◦ is the molar volume of pure species α, and we have used the relation Vα◦ = (∂μ◦α /∂p). The total volume is equal to the sum of the volumes of the pure components. Therefore, there is no change of volume on mixing for an ideal solution.

1. In order to characterize the deviations from Raoult’s law, we define the activity coefficient for component α, which is denoted by γα , as: γα = pα . 2) Note that in general, the activity coefficient depends on the temperature, pressure, and composition of the system. If the system obeys Raoult’s law, γα = 1. When γα > 1, the system is said to exhibit positive deviation from Raoult’s law, and when γα < 1, the system is said to exhibit negative deviation from Raoult’s law. 1: Variation of the partial pressure of component α in the vapor phase with its mole fraction in the coexisting liquid phase.