Chemical potential Molar Gibbs energy

Here, is the chemical potential of component in ideal solution, and Gi is the chemical potential (molar Gibbs free energy) of the pure liquid at the same temperature and pressure. 

In view of Eq. (4-47), the chemical potential and the partial molar Gibbs energy are therefore identical ... 

When the adsorbed components are electrically charged, then the partial molar Gibbs energy of the charged component depends on the charge of the given phase, and thus the chemical potentials in the above relationships must be replaced by the electrochemical potentials. The Gibbs adsorption isotherm then has the form... 

In open systems consisting of several components the thermodynamic properties of each component depend on the overall composition in addition to T and p. Chemical thermodynamics in such systems relies on the partial molar properties of the components. The partial molar Gibbs energy at constantp, Tand rij (eq. 1.77) has been given a special name due to its great importance the chemical potential. The corresponding partial molar enthalpy, entropy and volume under the same conditions are defined as... 

For any single-component system such as a pure gas the molar Gibbs energy is identical to the chemical potential, and the chemical potential for an ideal gas is thus expressed as... 

Since AmixGA = fiA - pA, the integral molar Gibbs energy of mixing can alternatively be expressed in terms of the chemical potentials as... 

A particular component of a given phase can be characterized in terms of its content and ability to partake in various processes (chemical reactions, transport processes) using the partial molar Gibbs energy. For an electrically-charged phase, this quantity is termed the electrochemical potential of the ith component... 

Thus, (6.11c) shows that chemical potential ixt could also be described as partial molar Gibbs energy ... 

One word about the Gibbs energies of adsorption. In equilibrium the molar Gibbs energy of adsorption is zero AadGm = /P — pT 0. The reason is simple. In equilibrium and for constant P and T the chemical potential of the molecules in the gas phase n9 is equal to the chemical potential of adsorbed molecules /P. What is not zero is the standard Gibbs energy of adsorption... 

The molar Gibbs energy of micelle formation is the Gibbs energy difference between a mole of monomers in micelles and the standard chemical potential in dilute solution ... 

The quantity gk T) in Equation (7.67) is again a molar quantity, characteristic of the individual gas, and a function of the temperature. It can be related to the molar Gibbs energy of the fcth substance by the use of Equation (7.67). The first two terms on the right-hand side of this equation are zero when the gas is pure and ideal and the pressure is 1 bar. Then gk(T) is the chemical potential or molar Gibbs energy for the pure fcth substance in the ideal gas state at 1 bar pressure. We define this state to be the standard state of the fcth substance and use the symbol 1 bar, yk = 1] for the... 

The relation between the standard molar Gibbs energy of hydrogen ion and that of hydronium ion is obtained by two methods that differ only in the assumption used. The result is the same. In the first method we choose to define the acid species either as hydrogen ion or as hydronium ion, and we do not consider an equilibrium between the two species and the solvent. In this case the chemical potential of the hydrogen ion is related to that of the hydronium ion in aqueous solution by... 

Once the species present in a solution have been chosen and the values of the various equilibrium constants have been determined to give the best fit to the experimental data, other thermodynamic quantities can be evaluated by use of the usual relations. Thus, the excess molar Gibbs energies can be calculated when the values of the excess chemical potentials have been determined. The molar change of enthalpy on mixing and excess molar entropy can be calculated by the appropriate differentiation of the excess Gibbs energy with respect to temperature. These functions depend upon the temperature dependence of the equilibrium constants. 

Here, M, may represent the partial molar internal energy Uit the partial molar enthalpy H(, the partial molar entropy Sif the partial molar Gibbs energy Gt, etc. Comparison of Eq. (10.1) with Eq. (11.2) written for the Gibbs energy shows that the chemical potential and the partial molar Gibbs energy are identical, that... 

For a species in solution, we recall that the chemical potential is identical with the partial molar Gibbs energy. Therefore, we write Eq. (10.9) for an ideal... 

A quantity whose magnitude is additive for subsystems is called extensive examples are mass m, volume V9 Gibbs energy G. A quantity whose magnitude is independent of the extent of the system is called intensive examples are temperature 7, pressure p, chemical potential (partial molar Gibbs energy) p. 

Equation 11.20 can be rewritten using the chemical potential in place of the partial molar Gibbs energy. Doing so, while also allowing for nonstandard state conditions gives ... 

In Eq. 11.21, /ta is equivalent to the partial molar Gibbs energy Ga and (jla is the chemical potential of the pure component A. If both components have low vapor pressures, the chemical potential of the ith component in solution relative to the pure component is approximately equal to ... 

Since the chemical potential fi and the partial molar Gibbs energy are identic Bq. (10.14) gives the partial molar Gibbs energy for species i in an ideal solutioi... 

The chemical potential fn can be identified with the molar Gibbs energy Gi at the standard- ate temp aturc and pressure or with the molar Helmholtz energy Ai (= Gi-pVi Ui-TSi) at the standard-state temperature and molar volume. The first alternative is usual in thermodynamic tables it gives the relations... 

Sometimes the question is asked how it is possible that the surface tension of pure water increases by the addition of electrolytes that are depleted from the surface. The answer must be found in the excess nature of molar Gibbs energies (or chemical potentials) in the Interface, as compared with those in the bulk. If, by adding a substance to the solution decreases more than, the surface tension should rise. In formulas, such as -i-0RTln(l- x), see [1.2.18.5], where 0 is... 

The partial molar Gibbs energy or chemical potential of species i in an ideal gas mixture is given by Eq. (4-195), written as... 

The chemical potential of a substance corresponds at 298 K and 100 kPa (1 bar) to its molar Gibbs energy of formation if the zero points of the potential scales are appropriately chosen. Therefore, when looking for the chemical potential, tables in which this quantity is listed can be used. 

The chemical potential defined in (A.8) is the partial molar Gibbs energy. 

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