Gibbs energy equation

Guffey and Wehe (1972) used excess Gibbs energy equations proposed by Renon (1968a, 1968b) and Blac)c (1959) to calculate multicomponent LLE. They concluded that prediction of ternary data from binary data is not reliable, but that quarternary LLE can be predicted from accurate ternary representations. Here, we carry these results a step further we outline a systematic procedure for determining binary parameters which are suitable for multicomponent LLE. 

Table 6.6. Linear Gibbs energy equations for some non-transition elements that include a pressure term taken (Kaufman and Bernstein 1970). Values are applicable only at temperatures >300 K...

These equations are based on the integration of the partial molar Gibbs energy equation dG = —SdT + VkdP for component k at constant T and volume Vk of pure component. Substituting Eq. (10.2) into Eq. (10.1), we have the equilibrium condition... 

Such relationships are useful in two ways. The first application is in the study of reaction mechanisms. The correlation of data for a new reaction series by means of a linear Gibbs energy relationship establishes a similarity between the new series and the reference series. The second use of linear Gibbs energy equations is in the prediction of reaction rates or equilibrium constants dependent on substituent or solvent changes. Let us consider a reaction between a substrate and a reagent in a medium M, which leads, via an activated complex, to the products . ... 

Of particular interest is the partial molar excess Gibbs energy. Equation (4-202) may be written as... 

By using the relationships in equations 25.34 and 25.35, we can write equation 25.60 in terms of Gibbs energies (equation 25.61). 

Thermodynamic data of high accuracy and reliability for the Ni - NiO system at high temperatures were obtained from electrochemical cells with yttria- or calcia-stabilised zirconia electrolytes. The experimental results are in excellent agreement with available calorimetric data as well as emf measurements of previous publications. The recommended Gibbs energy equation for the reaction ... 

The behavior of polymers in solution and their phase transition at different temperatures can also be described thermodynamically. Three types of interactions can occur once a polymer is dissolved in water water-polymer, water-water, and polymer-polymer (Klouda and Mikos 2008 Solis et al. 2005), and they can be analyzed using the free Gibbs energy equation given below ... 

The simplest form of excess Gibbs energy (Equation 10.44) is illustrated in Figure 10.13. This is a completely symmetrical The ideal A ,j G curve from Figure 7.4 is shown as a dashed line. The real curve is the sum of this and and is therefore also symmetrical. Of course in real solutions both A i,jG and G will generally have more complicated shapes, but we can... 

Flemr V (1976) A note on excess Gibbs energy equations based on local composition concept. Coll Czech Chem Commun 41 3347-3349... 

The differential of the electrical energy in Equation 6.56 implies a corresponding term in the differential of the Gibbs energy. Equation 4.12 ... 

Thermodynamic and Spectroscopic Scales of Halogen-Bond Basicity and Affinity 285 Table 5.24 Summary of linear Gibbs energy Equation 5.17 results. 

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