Gibbs function properties

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

The Clausius-Clapeyron equation provides a relationship between the thermodynamic properties for the relationship psat = psat(T) for a pure substance involving two-phase equilibrium. In its derivation it incorporates the Gibbs function (G), named after the nineteenth century scientist, Willard Gibbs. The Gibbs function per unit mass is defined... 

As the Gibbs function is a thermodynamic property, values of AG do not depend on the intermediate chemical reactions that have been used to transform a set of reactants, under specified conditions, to a series of products. Thus, one can add known values of a Gibbs function to obtain values for reactions for which direct data are not available. The most convenient values to use are the functions for the formation of a compound in its standard state from the elements in their standard states, as given in Tables 7.2... 

In this chapter, we shall consider the methods by which values of partial molar quantities and excess molar quantities can be obtained from experimental data. Most of the methods are applicable to any thermodynamic property J, but special emphasis will be placed on the partial molar volume and the partial molar enthalpy, which are needed to determine the pressure and temperature coefficients of the chemical potential, and on the excess molar volume and the excess molar enthalpy, which are needed to determine the pressure and temperature coefficients of the excess Gibbs function. Furthermore, the volume is tangible and easy to visualize hence, it serves well in an initial exposition of partial molar quantities and excess molar quantities. 

In our exposition of the properties of the Gibbs function G (Chapter 7), we examined systems with constraints on them in addition to the ambient pressure. We found that changes in Gibbs function are related to the maximum work obtainable from an isothermal transformation. In particular, for a reversible transformation at constant pressure and temperature [Equation (7.79)],... 

Interestingly, the standard entropies (and in turn heat capacities) of both phases were found to be rather similar [69,70]. Considering the difference in standard entropy between F2(gas) and the mixture 02(gas) + H2(gas) taken in their standard states (which can be extracted from general thermodynamic tables), the difference between the entropy terms of the Gibbs function relative to HA and FA, around room temperature, is about 6.5 times lower than the difference between enthalpy terms (close to 125 kJ/mol as estimated from Tacker and Stormer [69]). This indicates that FA higher stability is mostly due to the lower enthalpy of formation of FA (more exothermic than for HA), and that it is not greatly affected by entropic factors. Jemal et al. [71] have studied some of the thermodynamic properties of FA and HA with varying cationic substitutions, and these authors linked the lower enthalpy of formation of FA compared to HA to the decrease in lattice volume in FA. 

Gibbs functions for a real salt solution and the corresponding ideal salt solution containing m2 moles of salt in a kilogram of solvent. GE can be calculated for many aqueous salt solutions from published values of 0 and y . In the same way, the corresponding excess enthalpy HE can be defined and this equals the apparent partial molar enthalpy. Thus the properties of salt solutions can be examined in plots of GE, HE, and T SE against m2, where SE is the... 

Considerable information concerning structural effects on aqueous salt solutions has been provided by studies of the properties of mixed solutions (Anderson and Wood, 1973). In a mixed salt solution prepared by mixing YAm moles of a salt MX (molality m) with Yhm moles of a salt NX (molality m) to yield m moles of mixture in 1 kg of solvent, if W is the weight of solvent, the excess Gibbs function of mixing Am GE is given by (19) where GE is the excess function for... 

A theoretical treatment emphasizing the above feature is found in scaling properties. Under ordinary circumstances we impose the homogeneity requirement on the extensive variables that occur in the Gibbs function G as expressed by (see Section 1.3)... 

The macroscopic state of any one-component fluid system in equilibrium can be described by just three properties, of which at least one is extensive. All other properties of the state of the same system are necessarily specified by the chosen three properties. For instance, if for a single component gas in equilibrium, pressure, temperature, and volume are known, all other properties which describe the state of that gas (such as number of moles, internal energy, enthalpy, entropy, and Gibbs energy) must have a specific single value. Since the state of a system can be described exactly by specific properties, it is not necessary to know how the state was formed or what reaction pathway brought a state into being. Such properties that describe the state of a system are called slate functions. Properties that do not describe the state of a system, but depend upon the pathway used to achieve any state, are called path functions. Work and heat are examples of path functions. 

The coefficients of this formula were found to vary with time, however (Kremling and WUhelm, 1997). The computation of thermodynamic properties from the new Gibbs function using the absolute salinity (20.2) rather than (20.1) will be more accurate since it properly accounts for first-order corrections with respect to the chemical compositions anomaly (Millero et al., 2008). 

The following values are given by Rossini et al. ( Sdected values of diemical thermodynamic properties , U.S.Nat. Bureau Stand. 1952) for the standard Gibbs function (Gibbs free energy) of formation at 25 C. 

State functions—properties relating to changes in a system which are dependent only on its initial and final states. Many of the important system properties discussed in the next sub-sections such as internal energy, enthalpy, entropy, and Gibbs free energy are called state functions. 

Table 5.4.3. Thermodynamic properties of the liquid mixtures used as cosolvents of PMMA. Excess Gibbs function G, and excess entropy S, of the binary mixtures at equimolecular composition (at 25°C). From Prolongo et al. (Copyright by Butterworth-Heineman Ltd., used with permission)...

Mairs, T. E. Swinton, F. L. The thermodynamic properties of binary mixtures containing an octane. II. Excess Gibbs functions J. Chem. Thermodyn. 1980,12, 575-580... 

Garrett, P. R. Pollock, J. M. Morcom, K. W. Thermodynamic properties of mixtures of benzene with pyridines. 2.Excess volume and excess Gibbs function of benzene + pyridine J. Chem. Thermodyn. 1973,5, 569-575... 

Basic to the thermodynamic description is the heat capacity which is defined as the partial differential Cp = (dH/dT)n,p, where H is the enthalpy and T the temperature. The partial differential is taken at constant pressure and composition, as indicated by the subscripts p and n, respectively A close link between microscopic and macroscopic description is possible for this fundamental property. The integral thermodynamic functions include enthalpy H entropy S, and free enthalpy G (Gibbs function). In addition, information on pressure p, volume V, and temperature T is of importance (PVT properties). The transition parameters of pure, one-component systems are seen as first-order and glass transitions. Mesophase transitions, in general, were reviewed (12) and the effect of specific interest to polymers, the conformational disorder, was described in more detail (13). The broad field of multicomponent systems is particularly troubled by nonequilibrium behavior. Polymerization thermodynamics relies on the properties of the monomers and does not have as many problems with nonequilibrium. 

The Wong-Sandler mixing rules extend the use of cubic equations of state to mixtures that were previously only correlated with activity-coefficient models. For many mixtures, the Gibbs-function model parameters in the equation of state could be taken to be independent of temperature, thereby allowing extrapolation of phase behaviour over wide ranges of temperature and pressure. For example, for (ethanol-h water) the activity-coefficient model reported in DECHEMA is at a pressure of 0.4 MPa and this model provides reasonable predictions of the phase boundaries at pressures up to 20 MPa. This means the method can be used with UNIversal Functional Activity Coefficient (known by the acronym UNIFAQ and other group-contribution methods to predict properties at elevated pressure. 

At the end of this part, we would like to emphasize two important facts First, because the F-H theory is a theory of regular polymer solutions and the crossinteraction term can be expressed as a geometric average of homo-interactions, the Gibbs function of mixing can be decomposed into parts corresponding to the pure components and to the entropy of mixing. Consequently, it is possible to predict the properties of polymer solutions at a semiquantitative level on the basis of the... 

Another less frequently used equation which can represent gas-phase properties is a reduced Gibbs function. This was successfully used by Craven etal. (1989) to correlate the gas-phase data for methanol. 

---