Total Gibbs free energy

An isothermal reaction can proceed spontaneously only if the total Gibbs free energy of the system decreases, i.e. the free energy of the reactants must be greater than the free energy of the products. For a reaction... 

Equation (5.21) is especially important in that it indicates that p, the chemical potential of the ith component in the mixture is the contribution (per mole) of that component to the total Gibbs free energy/... 

Naslain, R., Thebault, J., Hagenmuller, P., and Bernard, C., The Thermodynamic Approach to Boron CVD Based on the Minimization of the Total Gibbs Free Energy, J. Less Common Metals, 67(1) 85-100 (1979)... 

G is the total Gibbs free energy of the crystal. The condition for equilibrium is that the Gibbs free energy is a minimum,... 

If the temperature T and pressure P of a closed system are kept constant, the total Gibbs free energy is minimum in equilibrium. For an ideal gas mixture of NS species the Gibbs free energy is given by... 

Chemical Equilibrium The chemical equilibrium approach is more complex computationally than applying the assumption of an infinitely fast reaction. The equilibrium composition of a multicomponent system is estimated by minimizing the Gibbs free energy of the system. For a gas-phase system with K chemical species, the total Gibbs free energy may be written as... 

By using equation (18.72), equations can be obtained for relating the other thermodynamic properties to m. The total Gibbs free energy G of the surfactant solution is the sum of the contributions from the solvent, the monomer, and the micelle. That is,... 

When the system is subjected to an external pressure pcxi, the undulations of the membranes occur in such a manna- to minimize the total Gibbs free energy of the system, which is the sum between the enthalpy of the system and the entropic contribution provided by Eq. (10) (see Appendix B) ... 

Let us now assume that the functional form for the entropic contribution, Eq. (B.12), holds even when the membrane is subjected to an arbitrary potential, f (it). The total Gibbs free energy of the membrane at a constant external pressure pexl is given by ... 

As an example, the values of [—AG ], [—AG P] and total Gibbs free energy, [—AGa], of the polar probes studied for the untreated high-strength carbon fiber (namely T-300) measured at 54.5°C, are listed in the Table 8 obtained from the results of the Fig. 7 [64]. 

Write equations for minimization of total Gibbs free energy. This step employs the method of Lagrange undetermined multipliers for minimization under constraint for a discussion of this method, refer to mathematics handbooks. As for its application to minimization of total Gibbs free energy, see Perry and Chilton [7] and Smith and Van Ness [11]. 

Let us finally assume that each of the c components of the system is encountered in every one of the p phases removal of this constraint is considered in Exercise 2.1.1. Thus, let the total Gibbs free energy be written as... 

An excellent discussion of the thermodynamics of LLE systems has been given by Sorensen and Arlt (1979,1980) and Sorensen et al. (1979). The following section is adapted from these references. Consider a binary liquid mixture of + n2 moles at fixed temperature and pressure. The necessary and sufficient condition for equilibrium is that the total Gibbs free energy of mixing, AG, for the mixture is a minimum with respect to all possible changes... 

According to the Flory-Huggins theory, the reduced total Gibbs free energy of mixing for a binary mixture is given by... 

Consider a physical property (such as the total Gibbs free energy G) of a continuous mixture, the value of which depends on the composition of the mixture. Because the latter is a function of, say, the mole distribution n(x), one has a mapping from a function to (in this case) a scalar quantity G, which is expressed by saying that G is given by afunctional of n(x). [One could equally well consider the mass distribution function m(x), and consequently one would have partial mass properties rather than partial molar ones.] We use z for the label x when in-... 

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