Gibbs free energy values

The changes in free energy of formation of Reaction (1) are shown in Fig. 2.1 as a function of temperature. " The values of AG were calculated using Eq. (1) above for each temperature. The Gibbs free-energy values of the reactants and products were obtained from the JANAF Tables.1 Other sources of thermodynamic data are listed inRef 6. These sources are generally accurate and satisfactory forthe thermodynamic calculations of most CVD reactions they are often revised and expanded. 

The AG symbol refers to the nonstandard Gibbs free energy value, AG° is the standard value, R is the gas constant (8.314 J/mol-K), T is the temperature (K), and Q is the reaction quotient first seen in Chapter 14. At equilibrium, this equation becomes ... 

To begin the problem, we need the standard Gibbs free energy values for each of the reactants and products. These are the values we ll be using to complete this problem ... 

Entering the Gibbs free energy values into the relationship gives ... 

The method of Tardy and Garrels (1974) gives approximate estimates of Gibbs free energy values for mica compounds regardless of their chemical complexity. Nevertheless, the linearity of the method cannot account for the energy of mixing contributions. Experimental data on mica mixtures are also... 

Table 8.14 Standard potentials for various redox couples (aqueous cation-metal element-aqueous anion) arranged in order of decreasing E°. Valnes, expressed in volts, are consistent with standard partial molal Gibbs free energy values listed in table 8.13. valne for snlfur is from Nylen and Wigren (1971).

We can calculate the equilibrium constant of reaction 8.230 under any given P-T condition by computing the standard molal Gibbs free energy values of the various components at the P-T of interest—i.e.,... 

Knowing the standard molar Gibbs free energy values and giving an initial mole number vector the determination of the equilibrium composition consists of minimizing (2.72) subject to the linear constraints (2.73). The direct application of (2.69-2.70), however, would be rather complicated. In the... 

FIGLfRE 2. Calculated Gibbs free-energy values of unsolvated and solvated mixed complexes between a chiral lithium amido ether and methyllithium... 

Section 14.3 follows with the thermodynamic prescription for calculating the equilibrium constant from tabulated Gibbs free energy values for gas-phase, solution, and heterogeneous reactions, with specific examples for each. 

The electrochemical series tabulates standard electrode potentials. Some sources call the electrochemical series oxi-dation/reduction potentials, electromotive series, and so on. The reference state of electrochemical series is the hydrogen evolution reaction, or H+/H2 reaction. Its standard electrode potential has been universally assigned as 0 V. This electrode is the standard hydrogen electrode (SHE) against which all others are compared. For example, the standard electrode potential of the Fe/Fe2+ reaction is —0.440 V and that of Cu/Cu2+ reaction is +0.337 V. The standard electrode potentials are calculated from Gibbs free energy values by Eq. (8) that is applicable only in the above-mentioned standard state. 

At this point the program calculates a value of /cy that matches the excess Gibbs free-energy values from the EOS and from the UNIFAC model. Intermediate results will continuously be displayed on the screen in the form of an error bar. When the optimization is completed a message summarizing the results appears on the screen. Press RETURN to continue.)... 

Computer-based modeling on geochemical principles, using either the equilibrium constants or Gibbs free-energy values. Both approaches are subject to the conditions of equilibrium and mass balance. 

In order to have a standard Gibbs free energy value, G°, we set G, = G° when P, = P° = 1 bar, then we have... 

Determination of equilibrium constants from tables of Gibbs free energy values as described above is, in a sense, an indirect method, because the Gibbs energy values are themselves determined from other kinds of measurements, often calorimetric (measurements of quantities of heat involved in carefully controlled experiments). For the calcite reaction we have just considered, three separate free energy values are involved, and an error in any of them will result in an error in the equilibrium constant. 

Reference files containing the thermodynamic database used by most computer models are constructed from both experimental data and from data which have been estimated. Many rely heavily on extrapolation techniques for determining the equilibrium constants or Gibbs Free Energy values at higher temperatures. These estimation techniques are essential, but the error in the estimated constants is generally not reported and is large for extreme conditions of T and P. The... 

Many thermodynamic cycles contain anions, which often leads to a large error in the computational calculation of the Gibbs free energy of solvation of the anion. As a result, cycles with water molecules or additional acids [38,79,116,117,119,120] are often used to try and remove these sources ol error. If accurate Gibbs free energy values are used, pK calculations can be fairly accurate, but many papers report pK calculations with less accurate Gibbs free energy values for H+. These publications would need to be recalculated with more accepted values to produce reliable and accurate data. 

FIGURE 4.30 Relationships between the Gibbs free energy value (or melting temperature) and the amounts of unfrozen water bound to Si-60 or CS samples. 

Relative interaction Gibbs free energy values against water eomplex (58b)... 

Theoretical values of the diermodynamie parameters for alkyl substituted allyloxymethyl eation cyelizations indicate that the introduction of the substituent into the eation, irrespective of position, promotes formation of hydrogenated fuians (Fig. 8.1). So, the Gibbs free energy value of the non-substituted ion cyclization is 21.6 kJ/mol whereas reactions with y-alkyl substituted cations 2-5 proceed with AG° values equal to -15-30 kJ/mol. 

According to the Gibbs free energy values, a dioxane (ld-5d) formation is thermodynamically favorable it slightly increases while the number of alkyl substituents at the double bond grows. Thus, the Gibbs free energy value for ethylene amounts to -7.4 kJ/mol, whereas this value for butene-2 is -35.3 kJ/mol. 

According to the Gibbs free energy values, the reaction of hydropyran cations formation is thermodynamically favorable. 

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