Very similar components A sufficient condition for SI solutions

1 Very similar components A sufficient condition for SI solutions 

For notational convenience, we shall discuss a two-component mixture of A and B. The generalization for multicomponent system is quite straightforward. We consider a system of two components in the T, P, NA, NB ensemble. We have chosen the T, P, NA, NB ensemble because the isothermal-isobaric systems are the most common ones in actual experiments. By very similar components, we mean, in the present context, that the potential energy of interaction among a group of n molecules in a configuration X is independent of the species we 

The connection between the chemical potential and statistical mechanics follows directly from the definition of the chemical potential in (5.21), i.e., 

consider a system of N particles of type A only. The chemical potential for such a system (at the same P and T as before) is 

the chemical potential, when expressed in terms of the intensive variables T, P and xA, has this explicit dependence on the mole fraction xA. A system for which relation of the form (5.27) is obeyed by each component, in the entire range of composition, is called a symmetrical ideal solution. It is symmetrical in the sense that from the assumptions (5.24) and (5.25), it follows that relation (5.27) holds true for any component in the system. In a two-component system, it is sufficient to define SI behavior for one component only. The same behavior of the second component, follows from the Gibbs-Duhem relation 

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