Gibbs free energy standard-state

Integration of this requires a limit to be defined. The limit is taken simply as follows. We define a standard pressure p at which the Gibbs free energy has a standard value G. We have thereby defined a standard state for this component of the system a standard temperature too, is implicit in this since the above equations are treated for constant temperature. 

G° = standard state Gibbs free energy R = gas content T = absolute temperature... 

A note on good practice Always write Eq. 8 with the standard state sign. Note too that, for the units to match on both sides, we have to use the molar convention for the standard Gibbs free energy. 

The standard Gibbs free energy change per mole accompanying vaporization (the conversion of a substance from the liquid state into the vapor state), standard hydrogen electrode (SHE) A hydrogen... 

The Gibbs free energy (computed in the harmonic approximation) were converted from the 1 atm standard state into the standard state of molar concentration (ideal mixture at 1 molL-1 and 1 atm). 

AG° = the molar standard state Gibbs free energy (the change in free energy of a reaction when the products and reactants are maintained at standard conditions)... 

Once the standard states for the various species have been established, one can proceed to calculate a number of standard energy changes for processes involving a change from reactants, all in their respective standard states, to products, all in their respective standard states. For example, the Gibbs free energy change for this process is... 

In order to have a consistent basis for comparing different reactions and to permit the tabulation of thermochemical data for various reaction systems, it is convenient to define enthalpy and Gibbs free energy changes for standard reaction conditions. These conditions involve the use of stoichiometric amounts of the various reactants (each in its standard state at some temperature T). The reaction proceeds by some unspecified path to end up with complete conversion of reactants to the various products (each in its standard state at the same temperature T). 

When an element enters into a reaction, its standard Gibbs free energy and standard enthalpy of formation are taken as zero if its state of aggregation is that selected as the basis for... 

The standard Gibbs free energy change for a reaction refers to the process wherein the reaction proceeds isothermally, starting with stoichiometric quantities of reactants each in its standard state of unit activity and ending with products each at unit activity. In general it is nonzero and given by... 

As equation 2.4.8 indicates, the equilibrium constant for a reaction is determined by the temperature and the standard Gibbs free energy change (AG°) for the process. The latter quantity in turn depends on temperature, the definitions of the standard states of the various components, and the stoichiometric coefficients of these species. Consequently, in assigning a numerical value to an equilibrium constant, one must be careful to specify the three parameters mentioned above in order to give meaning to this value. Once one has thus specified the point of reference, this value may be used to calculate the equilibrium composition of the mixture in the manner described in Sections 2.6 to 2.9. 

As a thermodynamicist working at the Lower Slobbovian Research Institute, you have been asked to determine the standard Gibbs free energy of formation and the standard enthalpy of formation of the compounds ds-butene-2 and trans-butene-2. Your boss has informed you that the standard enthalpy of formation of butene-1 is 1.172 kJ/mole while the standard Gibbs free energy of formation is 72.10 kJ/mole where the standard state is taken as the pure component at 25 °C and 101.3 kPa. 

The Gibbs Free Energy change accompanying the transfer of dnB moles of B from a reservoir in which it is present in its standard state to the equilibrium mixtures is... 

Here AGr° is the Gibbs free energy change in the ideal gas phase reaction system when all the gases are in their respective standard states. The equilibrium constant Kp is given in terms of the partial pressures at equilibrium by... 

We have seen in chapter 2 that the heat capacity at constant P is of fundamental importance in the calculation of the Gibbs free energy, performed by starting from the standard state enthalpy and entropy values... 

Figure 3.9 Conformation of Gibbs free energy curve in various types of binary mixtures. (A) Ideal mixture of components A and B. Standard state adopted is that of pure component at T and P of interest. (B) Regular mixture with complete configurational disorder kJ/mole for 500 < r(K) < 1500. (C) Simple mixture IF = 10 - 0.01 X r(K) (kJ/ mole). (D) Subregular mixture Aq = 10 — 0.01 X T (kJ/mole) = 5 — 0.01 X F (kJ/ mole). Adopting corresponding Margules notation, an equivalent interaction is obtained with IFba = 15 - 0.02 X r(kJ/mole) Bab = 5 (kJ/mole).

It is evident from equation 5.204 that the intrinsic significance of equation 5.206 is closely connected with the choice of standard state of reference. If the adopted standard state is that of the pure component at the P and T of interest, then AG%i is the Gibbs free energy of reaction between pure components at the P and T of interest. Deriving in P the equilibrium constant, we obtain... 

The first step in the model is a normative calculation (table 6.12) to establish the molar amounts of the various melt components. For each component, the molar Gibbs free energy at the standard state of pure component at T and P of interest is given by... 

Once the standard state potentials at the P and T of interest have been calculated (ix° = Gf for a pure single-component phase), the ideal and excess Gibbs free energy of mixing terms are easily obtained on the basis of the molar fractions of the various melt components and the binary interaction parameters listed in table 6.15 (cf eq. 6.78). 

We can then derive the calculated Gibbs free energy of mixing with respect to the molar amount of the component of interest, thus obtaining the difference between the chemical potential of the component in the mixture and its chemical potential at standard state ... 

The Gibbs free energy of phase y is represented by a straight line connecting the standard state potentials of the two end-members in the mixture. Because we use the term mixture, it is evident that the standard state of both end-members is the same and is that of pure component. The two components are totally immiscible in any proportion and the aggregate is a mechanical mixture of the two components crystallized in form y ... 

At Ty, the Gibbs free energy of phase a (i.e., melt) at all compositions is lower than that of mechanical mixture y + y" phase a is then stable over the whole compositional range. At T2, the chemical potential of component 1 in a is identical to the chemical potential of the same component in y . Moreover, the equahty condition is reached at the standard state condition of the pure component T2 is thus the temperature of incipient crystallization of y. At T, the Gibbs free energy of a intersects mechanical mixture y + y" on the component 1-rich side of the diagram and touches it at the condition of pure component 2. Applying the prin-... 

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