G, Gibbs function

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 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. 

For large departures from T, we have to fall back on eqn. (5.21) in order to work out Wf. Thermodynamics people soon got fed up with writing H - TS all the time and invented a new term, the Gibbs function G, defined by... 

Fig. 5.6. Plot of the Gibbs functions for ice and water os functions of temperature. Below the melting point Tn, > Gjjj and ice is the stable state of HjO above T , G...

Note that eq. (3.16) involves the Helmholtz function, A, rather than the Gibbs function G, but the difference between A A and AG is negligible in solutions and we will use AG in this book. 

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... 

In the following sections, we introduce the concept of a thermodynamic universe (i.e. a system plus its surroundings). For a reaction to occur spontaneously in a system, we require the change in Gibbs function G to be negative. We then explore the thermodynamic behaviour of G as a function of pressure, temperature and reaction composition. 

The Gibbs function G is named after Josiah Willard Gibbs (1839-1903), a humble American who contributed to most areas of physical chemistry. He also had a delightful sense of humour A mathematician may say anything he pleases, but a physicist must be at least partially sane. ... 

As well as calling G the Gibbs function, it is often called the Gibbs energy or (incorrectly) free energy. ... 

This compound variable occurs so often in chemistry that we will give it a symbol of its own G, which we call the Gibbs function. Accordingly, a spontaneous process in a system is characterized by saying,... 

Or, more conveniently, if G2 is the final value of G and G the initial value of G, then the change in Gibbs function is... 

From an equation like Equation (4.43), G = G + RT n(p/p ), so each G term in Equation (4.50) may be converted to a standard Gibbs function by inserting a term like Equation (4.43) ... 

Writing the equation in this way tells us that if we know the enthalpy of the system, we also know the temperature dependence of G -i-T. Separating the variables and defining Gj as the Gibbs function change at Ti and similarly as the value of G2 at T2, yields... 

Figure 5.19 The chemical potential /j, (the partial molar Gibbs function) of a species in a mixture is obtained as the slope of a graph of Gibbs function G as a function of composition...

Figure 6.2 Graph of Gibbs function G (as y ) against the extent of reaction f (as V). The minimum of the graph corresponds to the position of equilibrium the position of equilibrium for a weak acid, such as ethanoic acid, lies near the un-ionized reactants the position of equilibrium for a strong acid, like sulphuric acid, lies near the ionized products...

Thermodynamic stability. Let us consider a liquid binary mixture of two species, a and b, crystallizing to a solid solution. Let G be the free enthalpy (Gibbs) function of each phase, either solid or liquid. Calculate the change AG in molar free enthalpy when a liquid of molar composition XUqb crystallizes to a solid of molar composition... 

The function in parentheses in Equation (7.15) is a state function and is called the Gibbs function, or Gibbs free energy, symbolized by G [2] Relationships for G are... 

The letter F previously has been associated with the Gibbs function, particularly in the United States. Some older tabulations of chemical thermodynamic data use F for the function of Equation (7.17). The term free energy is most commonly assigned to G, but we have adopted the name Gibbs function to be consistent with Helmholtz function for A and Planck function for Y. 

As the procedure is the same for both the Gibbs function and the Helmholtz function, we shall consider in detail only the derivation for the Gibbs function G. After Equation (7.14), we obtained the differential of the function, which was later to be defined as G, as... 

Figure 9.3. A graph of the Gibbs function G as a function of the progress variable which shows equilibrium at the minimum.

In this situation, the Gibbs function G may be a function of h, the height above ground level, as well as of T, P, and... 

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