Partial molar Gibbs free-energy change

The partial derivative on the right hand side of Eq. (3.8) is the partial molar Gibbs free energy change, AGi. 

To find how AG changes with composition, we need to know how the molar Gibbs free energy of each substance varies with its partial pressure, if it is a gas, or with its concentration, if it is a solute. We have already seen (in Section 8.3) that the molar Gibbs free energy of an ideal gas J is related to its partial pressure, P(, by... 

Consider location 1. The total enthalpy of the mixture is xoj/ JfojHn2, where Hi is the partial molar enthalpy of species i in the mixture. At location A, the enthalpy of pure oxygen is xq Hq since there are Xoj gmols of pure O2, whose molar enthalpy is Hoj. Since we have ideal gas behavior, = Hoz- Similarly, at location C, where the enthalpy of pure N2 is xn /Hn. Note that this O2 semipermeable membrane allows O2 to come through at the feed partial pressure similarly for the N2 semipermeable membrane. Calculate the Gibbs free energy change as follows ... 

Thermodynamically, if there is an equilibrium between a solution and a solid state, the Gibbs free energies AG of a polymer species in solution and in the solid state are equal. The equilibrium concentration of the polymer species in solution is then called the saturated concentration, Cs. In the case of a polydisperse polymer, there will be polymer species with different MWs, both in solution and in the solid state, all of which will feature unique energies and saturated concentrations. To describe their contributions, chemical potentials of species /i, are used, which are partial molar quantities and represent the change in the overall Gibbs energy of the system upon addition of one mole of the species in question. 

The energy of a system can be changed by means of thermal energy or work energy, but a further possibility is to add or subtract moles of various substances to or from the system. The free energy of a pure substance depends upon its chemical nature, its quantity (AG is an extensive property), its state (solid, liquid or gas), and temperature and pressure. Gibbs called the partial molar free heat content (free energy) of the component of a system its chemical potential... 

In a homogeneous mixture each component i has a chemical potential pt, defined as the partial molar free energy of that component (i.e., the change in Gibbs energy per mole of component ti added, for addition of an infinitesimally small amount). It is given by... 

Solubility of water in chlorine. Expressing the free energy of a system in terms of partial molar quantities (chemical potentials) and comparing the result of differentiation of the whole function with an expression for the rate of change of free energy with composition leads to what is known as the Gibbs-Duhem relation [55,56]. The Gibbs-Duhem equation can be written as... 

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