Equations gibbs free energy

When we consider a measurable change in the Gibbs free energy, the equation we have derived becomes... 

Plan Calculate A7/fxn and ASfxn, then use the Gibbs free energy change equation, AG = AH - TAS, to... 

Recall Gibbs free energy change equation AG = AH -TAS... 

Plan Evaluate A7/KI1 and AS. To assess the temperature range over which the reaction is spontaneous, use the signs of AH and AS and the Gibbs free energy change equation, AG = AH - TAS. Assume that AH and AS are independent of temperature. 

The Hammett equation is the best-known example of a linear free-energy relationship (LEER), that is an equation which implies a linear relationship between free energies (Gibbs energies) of reaction or activation for two related processes71. It describes the influence of polar meta- or para-substituents on reactivity for side-chain reactions of benzene derivatives. 

Equation (46), one form of the Gibbs equation, is an important result because it supplies the connection between the surface excess of solute and the surface tension of an interface. For systems in which y can be determined, this measurement provides a method for evaluating the surface excess. It might be noted that the finite time required to establish equilibrium adsorption is why dynamic methods (e.g., drop detachment) are not favored for the determination of 7 for solutions. At solid interfaces, 7 is not directly measurable however, if the amount of adsorbed material can be determined, this may be related to the reduction of surface free energy through Equation (46). To understand and apply this equation, therefore, it is imperative that the significance of r2 be appreciated. 

The glass transition is a second-order transition, that is, the second derivative of the free energy function. In comparison, a first-order transition, such as the melting of a material, is the first derivative of Gibbs free energy. The equation used to determine the glass transition is ... 

Such relationships are usually referred to as linear free energy relationships (LFER). The appropriateness of this term may easily be seen. For equilibria, equation (1) applies, where is the standard free energy (Gibbs energy) of reaction. 

For chemical rate processes, equation (2) applies, where AG is the standard free energy (Gibbs energy) of activation. 

Abrams and Prausnitz (1975) combined Guggenheim s quasi-chemical tiieory with the concept of local compositions to develop the Universal Quasi-Chemical (UNIQUAC) expression for the excess Gibbs free energy. [The equation can be also developed from the two-fluid theory (Maurer and Prausnitz, 1978).]... 

Gibbs-Helmholtz equation This equation relates the heats and free energy changes which occur during a chemical reaction. For a reaction carried out at constant pressure... 

Helmholtz free energy The maximum amount of energy available to do work resulting from changes in a system at constant volume. See free energy and Gibbs-Helmholtz equation. 

Equation ( A2.1.39) is the generalized Gibbs-Diihem equation previously presented (equation (A2.1.27)). Note that the Gibbs free energy is just the sum over the chemical potentials. 

We have seen that equilibrium in an isolated system (dt/= 0, dF= 0) requires that the entropy Sbe a maximum, i.e. tliat dS di )jjy = 0. Examination of the first equation above shows that this can only be true if. p. vanishes. Exactly the same conclusion applies for equilibrium under the other constraints. Thus, for constant teinperamre and pressure, minimization of the Gibbs free energy requires that dGId Qj, =. p. =... 

Figure A2.5.15. The molar Gibbs free energy of mixing versus mole fraetionxfor a simple mixture at several temperatures. Beeause of the synuuetry of equation (A2.5.15) the tangent lines indieating two-phase equilibrium are horizontal. The dashed and dotted eiirves have the same signifieanee as in previous figures.

Since equation (A3.6.4) is equal to the difference between the Gibbs free energy of... 

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

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