Thermodynamic criteria

In earlier chapters an unperturbed coil referred to molecular dimensions as predicted by random flight statistics. We saw in the last chapter that this thermodynamic criterion is met under 0 conditions. 

We have shown that the steam reforming of propane may be adequately described by LH mechanism involving different adsorption sites for steam and hydrocarbon. The associated model satisfied both statistical compliance and the BMV thermodynamic criterion. 

The interaction between the adsorbed molecules and a chemical species present in the opposite side of the interface is clearly seen in the effect of the counterion species on the HTMA adsorption. Electrocapillary curves in Fig. 6 show that the interfacial tension at a given potential in the presence of the HTMA ion adsorption depends on the anionic species in the aqueous side of the interface and decreases in the order, F, CP, and Br [40]. By changing the counterions from F to CP or Br, the adsorption free energy of HTMA increase by 1.2 or 4.6 kJmoP. This greater effect of Br ions is in harmony with the results obtained at the air-water interface [43]. We note that this effect of the counterion species from the opposite side of the interface does not necessarily mean the interfacial ion-pair formation, which seems to suppose the presence of salt formation at the boundary layer [44-46]. A thermodynamic criterion of the interfacial ion-pair formation has been discussed in detail [40]. 

The equation above is called the thermodynamic criterion of flotation . Its only strict interpretation is that the more negative the value of AG, the more is the probability of mineral nonwetting (AG = 0 for 0 = 0°, and AG < 0 for 0 > 0°). 

The thermodynamic criterion for spontaneity (feasibility) of a chemical and electrochemical reaction is that the change in free energy, AG have a negative value. Free-energy change in an oxidation-reduction reaction can be calculated from knowledge of the cell voltage ... 

Structural and molecular biologists often study the temperature dependence of the equilibrium position of a reaction or process. The Gibbs free energy undoubtedly provides the correct thermodynamic criterion of equilibrium. An understanding of this parameter can be achieved from either a macroscopic level (classical thermodynamics) or a molecular level (statistical thermodynamics). Ultimately, one seeks to understand the factors influencing AG° for a specific reaction. 

It is apparent that CMC values can be expressed in a variety of different concentration units. The measured value of cCMC and hence of AG c for a particular system depends on the units chosen, so some uniformity must be established. The issue is ultimately a question of defining the standard state to which the superscript on AG C refers. When mole fractions are used for concentrations, AG c directly measures the free energy difference per mole between surfactant molecules in micelles and in water. To see how this comes about, it is instructive to examine Reaction (A) —this focuses attention on the surfactant and ignores bound counterions — from the point of view of a phase equilibrium. The thermodynamic criterion for a phase equilibrium is that the chemical potential of the surfactant (subscript 5) be the same in the micelle (superscript mic) and in water (superscript W) n = n. In general, pt, = + RTIn ah in which... 

E. Jouguet also proved in a general form that this thermodynamic criterion of the possibility of compressive shock waves... 

Thermodynamics is used to predict whether reactants have a spontaneous tendency to change into products. This tendency is associated with a decrease in the free energy or Gibbs energy of the system (G) to a minimum. As a consequence, the thermodynamic criterion for spontaneous change at constant temperature and pressure is AG < 0. Under standard conditions (concentrations = 1 M, and P = 1 atm), the standard Gibbs energy variation (AG°) is related with the equilibrium constant (A) by equation 11 ... 

At equilibrium, the fugacity of a component in the gas is equal to the fugacity of the same component in the liquid. This thermodynamic criterion defines the relationship between the equilibrium concentration of a component in the gas and its concentration in the liquid. The quantity of gas dissolved in a given quantity of solvent at equilibrium conditions is often referred to as the gas solubility. 

It emerges from thermodynamics that the overall thermodynamic criterion for spontaneity is vested in a quantity defined as the Gibbs (free) energy change, AG which, for an isothermal (Frame 1) process, is defined by the equation ... 

The thermodynamic criterion for the equilibria CaCO, ) = Ca0(,) + C02 (,) is AG ° = -RT n Kp, where AG° is the change in Gibbs free energy of the reactants and products in their standard state, R is the gas constant, and Kp is the equilibrium constant. For this equilibria, A p = pco, for pressure in units of atmospheres. Values for AG are tabulated in the form AG° = a+ bT combining these expressions yields an exponential relationship between the partial pressure of CO2 and temperature for the above equilibria. Complete derivations and discussion of these equations may be found in physical chemistry textbooks such as references [13] and [14]. 

Hence, the correct thermodynamic criterion of the kinetic irreversibility at any step in the chemical transformation chain is a considerable (against quantity RT) change in the chemical potential of the reaction groups related to this step—that is, A j > RT. Note that the criterion is valid for both elementary and stepwise reaction, although in the latter case, one must consider the affinity for the stepwise transformation A,2 > RT. 

The specific examples in Section 14.5 demonstrate that when 1C > 1 the reaction has progressed far toward products, and when K 1 the reaction has remained near reactants. The empirical discussion in Section 14.6 shows how the reaction quotient Q and the principle of Te Chatelier can predict the direction of spontaneous reaction and the response of an equilibrium state to an external perturbation. Here, we use the thermodynamic description of K from Section 14.3 to provide the thermodynamic basis for these results obtained empirically in Sections 14.5 and 14.6. We identify those thermodynamic factors that determine the magnitude of K. We also provide a thermodynamic criterion for predicting the direction in which a reaction proceeds from a given initial condition. 

Qiao et al. (1996) defined the thermodynamic criterion forjudging the symmetry of the ternary systems and its application. Based upon the previous significant studies and the enlightening analysis made by works of Toop (1965), Ansara (1979), Hillert (1980), Lukas (1982), and taking into account interactions among components, the thermodynamic criterion for defining the symmetry of ternary systems from the energetic point of view, was explicitly proposed as follows ... 

The other two possible explanations of increased reaction rate under the simultaneous presence of radiation and solid, short-lived catal3d ic sites, and radiolysis affected by the solid, cannot always be distinguished with certainty. A thermodynamic criterion can be used in a few cases, and in some others an enhancement can be observed after cessation of irradiation. 

The thermodynamic criterion establishes radiolysis as the mechanism in the cases to which it is applicable. If irradiation of substrate and solid yields products that must arise from a nonspontaneous reaction, for example the dissociation of water at room temperature, then the process must originate in radiolysis. Unusual ratios of products are not a sufficient criterion, since they can arise from either radiolysis or catalysis provided the partial reactions concerned are spontaneous. 

If a liquid mixture at temperature T and pressure P is in equilibrium with a vapor mixture at the same temperature and pressure, therefore at an equilibrium condition, the thermodynamic criterion will be... 

Or, again, take the case of pure benzene on the one hand and a saturated solution of benzene in water on the other, both systems being at the same temperature A saturated solution of benzene is necessarily in equilibrium with pure liquid benzene itself because of the fact of saturation The conclusion to he drawn from the thermodynamic criterion considered is, that under these conditions, (8A)TV = o, and therefore, if we imagine one mole of benzene transferred from the pure benzene to the saturated solution, the work must be zero That is, there must be the same vapour pressure over the pure benzene as there is over its saturated solution in water, the vapour in each case being benzene vapour In the case of a hydrated salt on the one hand and the saturated solution of the salt on the other, the conditions are more complex We shall consider this point in Chap X in connection with the application of the Phase Rule to two component systems... 

Chemyakov, A. V. and Kazenin, D. A., Thermodynamic criterion for nonbreaking flow-down of a film, Rus. Chem. Industry, No. 8,1997. 

Since Ecell is defined to be positive for a spontaneous reaction, this equation correctly expresses a decrease in Gibbs function, which is the thermodynamic criterion for a spontaneous reaction at constant T and P. It is evident that if AGreact can be calculated from AG j- data, the potential of a cell arranged for reversible operation can be determined conversely, experimental measurements of Ecen permit calculation of AGreact. Both types of calculations are useful in electrochemical work and, thus, in the analysis of corrosion. 

Use of the thermodynamic criterion of equilibrium in the derivation of the algebraic form of the equilibrium constant... 

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