Relative molar free energy

GA and Gg (later we will be using symbols Gi) are called partial molar free energies of A and B, respectively. These are also called chemical potentials (pi). GM is called relative molar free energy of the solution. A fuller discussion on these properties is given in Section 2.2.2. 

Fig. 6.2.1 Relative molar free energies of reactants and transition states for an assumed process of isomerisation and solvolysis at 25°C. Reference point is the molar free energy of trans- CoC 2(QV 2Y in DMA. Abbreviations is cw-[CoCl2(en)2r is trans-[CoC 2(en)2Y and are transition states for solvolysis of the trans and c/>cations, respectively and /f and cf are transition states for isomerisation.

These expressions comprise the nonideal terms in the previous equations for the chemical potential, Eqs. (30) and (31 ). They may therefore be regarded as the excess relative partial molar free energy, or chemical potential, frequently used in the treatment of solutions of nonelectrolytesi.e, the chemical potential in excess (algebraically) of the ideal contribution, which is —RTV2/M in dilute solutions. 

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

One must recognize that the partial molar free energy is not a measurable quantity because the absolute value of the free energy is not measurable. However, the relative partial molar free energy, AGa, defined as follows, is measurable... 

Besides the partial molar and the relative partial molar free energies of the components, some other important thermodynamic properties are the partial molar and the relative partial molar enthalpies and entropies. The partial molar enthalpy and entropy of the component A are defined by... 

The relative partial molar free energy of A is written in terms of the integral molar free energy of the solution as... 

The relationships presented thus far for partial, integral and relative partial molar free energies are applicable in a similar manner to entropy, enthalpy and also volume. 

As it follows from [14] in the field of the chains intertwining the molar free energy of the conformation is linear function of relative concentration of macromolecules and is described by the following expression in approximation by deformation of m-ball in real solution... 

Equating the molar free-energy terms in (12.24) and (12.25) affords an expression which relates the hydraulic pressure P required to force mercury into pores to the relative pressure, PJPq, exerted by the liquid with radius of curvature, r. That is. 

Figure 5.4 Relative partial molar free energy of oxygen. AGq, of Fei, 0 as a function of composition (log x). (Taken from the data given in S0rensen, 1981.)...

The second term on the right-hand side of Equation (86) arises from Equation (84) since chemical potential is the partial molar free energy. In this expression z, is the relative charge of the ith species and ip is the potential of the surface. 

On the basis of dissociative solution, i.e., hydrogen is absorbed as H atoms rather than H2 molecules, the relative partial molar free energy of absorption is related to the equilibrium constant via the equilibrium hydrogen pressure (Equation 3). Values of the relative partial molar enthalpy as a function of hy-... 

Although the partial molar Gibbs free energy (G<) or the chemical potential (pi) defined by the equation given below pertains to the individual components of the system, it is a property of the system as a whole. The value of the partial molar free energy depends not only the nature of the particular substance in question but also on the nature and relative amounts of the other components present as well. 

Gj -G° is the change in molar free energy of / due to the change in state from the standard state to the state of solution of a particular composition. This is called the partial molar free energy of mixing or relative partial molar free energy of i and is designated... 

This is called the relative integral molar free energy or the molar free energy of mixing. Hie method of tangential intercepts which we have applied for determination of partial molar quantities from the integral molar quantities can also apply to the relative quantities ... 

Calculate the relative integral molar free energy of the solution, Gv. 

Consider the relative partial molar free energy, G,w,... 

The free energy of mixing of the solution, or the relative integral molar free energy, G, for a A-B binary solutions given by... 

Activity — The absolute activity of a substance, A, is defined as A = exp(p/RT), where p is the molar free energy. The relative activity a, is defined as a = cxp[ (p -p" )/RT, where p" is the molar free energy of the material in some defined standard state for which the activity is taken as unity. Historically, the concept of activity arose out of an attempt, initially formulated by -> Lewis, to understand the behavior of mixtures. Ideal mixtures or solutions are those for which the -> chemical potential or molar free energy of any of the component species i can be written in the form p, = p + RT nx, where xt is the mole fraction of the ith component, defined as X =, n, is the number of moles of species i... 

The contribution to the partial molar free energy arising from the residual (enthalpic and non-conformational entropic) partial molar free energy of mixing of the two monomers is small relative to all other terms in the monomer droplet phase. 

At a given temperature T, this reaction has a hydrogen equilibrium pressure H. Consider now a solid solution of this metal with a non-hydride forming metal (B). The relative partial molar free energy of A in the alloy is AGa- If the resulting alloy AB reacts with hydrogen as... 

Pure acetone has a vapor pressure of 185.2 mm. and ether one of 443.5 mm. at 20 C. For a liquid mixture containing 0.457 mole fraction of the former, the respective partial vapor pressures are 105.2 and 281.8 mm., respectively. Assuming ideal behavior of the vapors, determine the partial molar free energy — F of each constituent of the mixture, relative to that of the pure liquid. 

Quantities that are determinable from experiments can be derived from Equation 12.28. For example, by differentiating the expression with respect to Ni, the number of solvent molecules, and multiplying the result by Avogadro s number, the relative partial molar free energy AG, is obtained ... 

We note for emphasis (also from Equation 12.43) that at the temperature T = 0 the excess, relative, partial molar-free energy, AG, due to polymer-solvent interactions is zero and deviations from ideahty vanish. 

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