Thermodynamic equations chemical equilibria pressure effects

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

Micellar solutions are sometimes called ordered media [12]. The chemical order in a micellar solution seems to be greater than in a classical solution. Equation 2.9 shows ftiat the micellization of surfactant molecules obeys the second principle of thermodynamics. It seems that the surfectant hydrocarbon chains have a much higher freedom of motion inside the micelle core than in the water bulk [13]. The micelle structure minimizes the molecule energy. The large entropy increai of water molecules associated with the removal of nonpolar surfactant tails from the aqueous solution (hydrophobic effect) is the main micelle driving force. Electrostatic forces tend to separate the polar heads that bear the same charge. The whole micelle is an equilibrium between these forces. This equilibrium is very sensitive to any chemical additive or parameter that can act on any of the forces, such as salts, polar or nonpolar solutes, temperature and/or pressure. 

While several simplifying assumptions needed to be made so as to derive an analytical model, the model captures all relevant physical processes. Specifically, it employed thermodynamic equilibrium conditions for temperature, pressure, and chemical potential to derive the equation of state for water sorption by a single cylindrical PEM pore. This equation of state yields the pore radius or a volumetric pore swelling parameter as a function of environmental conditions. Constitutive relations for elastic modulus, dielectric constant, and wall charge density must be specified for the considered microscopic domain. In order to treat ensemble effects in equilibrium water sorption, dispersion in the aforementioned materials properties is accounted for. 

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