Concluding Synopsis of Gibbs Theory

It is apparent from this plot that the Debye-Hiickel theory is only correct in a narrow range of extreme dilution, showing (as might have been anticipated) that classical electrostatics is qualitatively inadequate to describe the realistic interactions in aqueous electrolyte solutions, except in the asymptotic limit of extremely large ion-ion separations. 

In this concluding section of Part II, it is appropriate to summarize the major conceptual and mathematical features of the Gibbs formulation of thermodynamic equilibrium theory, as a preface to its geometrical reformulation in the ensuing Part HI. The following equations (8.70)-(8.95) summarize the essential mathematical structure of the Gibbsian formalism, as erected on the historical foundation of Chapters 1-4 and exploited in the applications of Chapters 5-8. 

The central focus of Gibbs theory is the equilibrium state S, sl quiescent limiting condition of a sufficiently large ( macroscopic ) physical system that exhibits characteristically simple responses to attempted changes of the control variables that specify the state. 

The control variables of the state may be selected rather arbitrarily from two classes  

The first class comprises quantity-type ( extensive ) properties Xh such as the quantity of mass or spatial volume of the system. A distinctive characteristic of these properties is their additivity in subunits of the system, such that each is linearly proportional to overall scale (number of identical subunits), as measured, for example, by total mass. Arbitrary linear combinations of the independent Xh 

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