Gibbs and Langmuirs Monolayers Equations of State

The Gibbs monolayer is continuously in equilibrium with the adjacent solution. Hence, for an ideal solution (where C is proportional with X ) at constant temperature, combining the Gibbs adsorption equation (3.88) with (7.1) yields 

To derive the interfacial equation of state of the monolayer, relating n, F (or the interfacial area per molecule), and T, we need to know the functionality T(c). In Chapter 14, equations for T(c) at constant T, so-called adsorption-isotherm equations, are derived and discussed. Thus, anticipating Equation 14.25 for an ideally dilnted monolayer, the following equation of state is derived  

Similarly, more complicated equations of state are obtained nsing expressions for T(c) for nonideally behaving adsorbed layers. 

As mentioned in Section 7.1, Langmuir s monolayers are not in chemical equilibrium with the solution, and, as a consequence, the Gibbs adsorption equation is not applicable to such monolayers. However, relations between n, T, and T are completely determined by the number of molecules, and the interactions between them, in the monolayer, irrespective of the way the monolayer has been formed. Equations of state are therefore identical for Gibbs and Langmuir s monolayers. 

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