Chemical potential partial molal free energy

Chemical potential Partial molal free energy, a )Xi = Si... 

In these equations is the partial molal free energy (chemical potential) and Vj the partial molal volume. The Mj are the molecular weights, c is the concentration in moles per liter, p is the mass density, and z, is the mole fraction of species i. The D are the multicomponent diffusion coefficients, and the are the multicomponent thermal diffusion coefficients. The first contribution to the mass flux—that due to the concentration gradients—is seen to depend in a complicated way on the chemical potentials of all the components present. It is shown in the next section how this expression reduces to the usual expressions for the mass flux in two-component systems. The pressure diffusion contribution to the mass flux is quite small and has thus far been studied only slightly it is considered in Sec. IV,A,6. The forced diffusion term is important in ionic systems (C3, Chapter 18 K4) if gravity is the only external force, then this term vanishes identically. The thermal diffusion term is impor-... 

Partial molal free energy of compound j in phase l (chemical potential)... 

Partial Molar Free Energy Chemical Potential.—The partial molal free energy is an important thermodynamic property in connection with the study of electrolytes it can be represented either as G, where G is employed for the Gibbs, or Lewis, free energy, or by the symbol /i, when it is referred o as the chemical potential thus the appropriate form... 

Concentration Cells with a Single Electrolyte Amalgam Concentration Cells.—In the concentration cells already described the e.m.p. is a result of the difference of activity or chemical potential, i.e., partial molal free energy, of the electrolyte in the two solutions it is possible, however, to obtain concentration cells with only one solution, but the activities of the element with respect to which the ions in the solution are reversible are different in the two electrodes. A simple method of realizing such a cell is to employ two amalgams of a base metal at different concentrations as electrodes and a solution of a salt of the metal as electrolyte thus... 

The chemical potential is the partial molal free energy, and by modifying Equation (2-3), we obtain... 

The symbol Pi was first used by Gibbs and called by him the chemical potential of component i. It can be seen from Eq. (6-52) and the definition of partial molal quantities [Eq. (2-5)] that Pi is the partial molal free energy /( and is an intensive property. 

We note that the chemical potential of component i, /t, is not the partial molal free energy in the presence of an electric field. 

Thermodynamic quantities which have the same value throughout a homogeneous compartment (temperature, T pressure, p) are called intensive. Those which are proportional to the amount of component i in that compartment are called extensive (enthalpy, H entropy. S free-energy, G). An extensive quantity may be converted to an intensive one by dividing by the amount of component i present. For example, the partial molal free-energy or chemical potential. 

Thermodynamic Aspects of Solubility At equilibrium in a saturated solution, the chemical potential, or partial molal free energy, of the solute must be the same in the solution as in the solid phase. If we consider two different saturated solutions, there-fore, both in equilibrium with the same solid phase, the chemical potential of the solute must be the same in both. The chemical potential ( ) and activity (c) are related by the equation p — po — RT In o, where Po is the chemical potential of the substance in the standard state. Hence, if the same standard state is chosen for all the solutions considered, the activity of the solute must be the same in all. 

An extremely useful quantity in the thermodynamic treatment of multicomponent phase equilibria is the chemical potential. The chemical potential for component /, is the partial molal Gibbs free energy with respect to component i at constant pressure and temperature ... 

As the partial molal (Gibbs) free energy G is usually called the chemical potential, designated by /X , it follows immediately that... 

The concept of free energy is introduced in Chapter 2 (Section 2.2A,B) in presenting the chemical potential of species /, fij. The chemical potential is actually the partial molal Gibbs free energy with respect to that species that is, fij equals (8G/drij)TPEh (Eq. IV.9 in Appendix IV), where the subscripts on the partial derivative indicate the variables that are held constant. We must consider the Gibbs free energy of an entire system to determine the chemical potential of species j. In turn, G depends on each of the species present, an appropriate expression being... 

Equation 3 defines the excess chemical potential for one solute if more than one solute exists in the solution, a weighted sum of the excess chemical potentials of the solutes may be called the mean partial molal Gibbs free energy of solutes, y ... 

On account of equation (4) chemical potentials are called partial molal (Gibbs) free energies" by Lewis and Randall.2 This expresses possibly the most important, but not the only, property of chemical potentials, as is clear from equations (2) and (5). 

---