Thermodynamic interpretation

Equation (5-43) has the practical advantage over Eq. (5-40) that the partition functions in (5-40) are difficult or impossible to evaluate, whereas the presence of the equilibrium constant in (5-43) permits us to introduce the well-developed ideas of thermodynamics into the kinetic problem. We define the quantities AG, A//, and A5 as, respectively, the standard free energy of activation, enthalpy of activation, and entropy of activation from thermodynamics we now can write 

These quantities (which are standard molar quantities) describe the process initial state transition state 

The numerical values of AG and A5 depend upon the choice of standard states in solution kinetics the molar concentration scale is usually used. Notice (Eq. 5-43) that in transition state theory the temperature dependence of the rate constant is accounted for principally by the temperature dependence of an equilibrium constant. 

By combining Eqs. (5-43)—(5.45) we can express the rate constant in these alternative forms  

The evaluation of the activation parameters AG, A//, and AS proceeds as follows. From the Arrhenius equation, Eq. (5-1), we have 

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In addition to the thermodynamic interpretation of 0 conditions that we discussed in Chap. 8, we have now established the hydrodynamic significance of these conditions as the point at which [r ] . Summarizing in terms of the... 

Shikazono, N. (1976) Thermodynamic interpretation of Na-K-Ca geothermometer in the natural water system. Geochem. J., 10, 47-50. 

The dissolution rate, according to the theory, does not depend on the mineral s saturation state. The precipitation rate, on the other hand, varies strongly with saturation, exceeding the dissolution rate only when the mineral is supersaturated. At the point of equilibrium, the dissolution rate matches the rate of precipitation so that the net rate of reaction is zero. There is, therefore, a strong conceptual link between the kinetic and thermodynamic interpretations equilibrium is the state in which the forward and reverse rates of a reaction balance. 

Electro Capillarity and the dropping Mercury Electrode. The term electro capillarity derives from the early application of measurements of interfacial tension at the Hg-electrolyte interface. The interfacial tension, y, can be measured readily with a dropping mercury electrode. E.g., the life time of a drop, tmax. is directly proportional to the interfacial tension y. Thus, y is measured as a function of y in presence and absence of a solute that is adsorbed at the Hg-water interface this kind of data is amenable to thermodynamic interpretation of the surface chemical properties of the electrode-water interface. 

Cognet and Renon (25) Thermodynamic interpretation of Cu(II) extraction by LIX 64 organic reagent. 

For the four typical variations in ionic conductivity with composition illustrated in Fig. 4.2, thermodynamic interpretations and predictions have been advanced. 

The thermodynamic interpretation of kjC follows also from definitions (2.2.6),... 

The probabilistic and thermodynamic interpretations of follow directly from the definition. By substituting the various binding constants, one can rewrite the GPF as well as the BI in terms of the conditional constant. Particularly simple are the expressions for the individual Bis. For instance. 

SAP produces a set of virtual excitations from the fully occupied to the unoccupied Kohn-Sham orbitals thus producing a fictitious statistical ensemble. A thermodynamic interpretation of SAP is presented in [50] (see [51,52] as well), where two main observations are given. First, the redistribution of single particle states in the smoothing procedure leads to... 

The key role of electron microscopy is illustrated by Merritt and Hyde (1973) in studies of rutile. In the studies, the coexistence of (121) and (132) CS planes revealed only by TEM, is shown to lead to more correct thermodynamical interpretations. However, thermodynamic treatments in the literature tend to be incomplete as they have not included the reaction mechanism or the nature of the CS defect formation. 

As functional properties of soy proteins, viscosity and solubility are alike in that they are non-equilibrium properties of the system. In the case of solubility, there is at least evidence of steady state equilibrium which allows for the possibility of some qualitative thermodynamic interpretation. In the case of viscosity, steady state equilibrium is not reached. Thus, thermodynamic interpretation is impossible. Molecular dynamics data are needed. 

As mentioned above, the primary focus of this chapter is on osmotic pressure and its basis in solution thermodynamics. We consider both classical and statistical thermodynamic interpretations of osmotic pressure. The next three sections are devoted to this. The last two sections describe osmotic effects in charged systems and a few applications of osmotic phenomena. 

Despite the complexities introduced by metastable solid and liquid phases, topological features of the phase diagram can be thermodynamically interpreted in a standard manner from Clapeyron-type equations. Thus, from the forward slopes of a-fi, /3-liquid (stable), and a-liquid (metastable) phase boundaries, we can infer from (7.32) that... 

An idealized equilibrium model in which the essential features (pressure, temperature, predominant phases, major solution components, etc.) of the real system are accounted for is amenable to rigorous thermodynamic interpretation. 

Thus the selectivity a has a thermodynamic interpretation as the ratio of two distribution constants. Consequently a is itself a constant, independently from the injected concentrations of the analyte and the interferent, respectively. 

Forty years later Meyer [1], and at the same time Overton [2], observed a linear relationship between the activity of narcotics and their oil-water partition coefficient. An 40 years after that, a thermodynamic interpretation of this relationship was provided by Ferguson [3], which also explained cut-off of biological activity that is sometimes observed after a certain lipophilicity range has been passed. 

Quantitative Thermodynamic Interpretation of Le Chatelier s Principle. Temperature Change... 

Kawai and collaborators have extensively studied copolymers of styrene and isoprene. They have synthetized and studied SI copolymers63,169, SIS copolymers64, and ternary polymer blends of SI block copolymers with polystyrene and polyisoprene170-171 and proposed a thermodynamic interpretation of the domain structure in solvent-cast films of SI, SIS, and blends of these copolymers with their homopoly-mers63 64,172. ... 

Development of the "flow" MEIS with the form reminding the models of nonequilibrium thermodynamics seems to be a very promising direction in equilibrium modeling of physical and chemical systems. Application of these models opens prospects for simpler analysis and solution of many complex problems related to the calculations of processes considered to be irreversible in principle. Certainly the flows in MEIS are interpreted statically as the coordinates of states. Thermodynamic interpretations are naturally extended to the kinetic coefficients that relate these flows with forces. Correctness of such interpretations is confirmed by the application of MP, being the theory of equilibrium states, as the terms for MEIS description. 

It must be emphasized that the conditions of chemical equilibrium can be derived and explained most exactly on the basis of thermodynamics, that is without involving reaction rates at all. Textbooks of physical chemistry will of course contain the thermodynamical interpretation (cf. W. J. Moore s Physical Chemistry. 4th edn., Longman 1966, p. 167 et f.)... 

Extended nonequilibrium thermodynamics is not based on the local equilibrium hypothesis, and uses the conserved variables and nonconserved dissipative fluxes as the independent variables to establish evolution equations for the dissipative fluxes satisfying the second law of thermodynamics. For conservation laws in hydrodynamic systems, the independent variables are the mass density, p, velocity, v, and specific internal energy, u, while the nonconserved variables are the heat flux, shear and bulk viscous pressure, diffusion flux, and electrical flux. For the generalized entropy with the properties of additivity and convex function considered, extended nonequilibrium thermodynamics formulations provide a more complete formulation of transport and rate processes beyond local equilibrium. The formulations can relate microscopic phenomena to a macroscopic thermodynamic interpretation by deriving the generalized transport laws expressed in terms of the generalized frequency and wave-vector-dependent transport coefficients. 

Inoue T, Soen T (1969) Thermodynamic interpretation of domain structure in solvent-cast films of A-B type block copolymers of styrene and isoprene. J Polym Sci B Polym Phys 7 1283-1301... 

Karim, K. A. Bonner, D. C., "Thermodynamic Interpretation of Solute-Polymer Interactions at Infinite Dilution," J. Appl. Polym. Sci., 22, 1277 (1978). 

Gritti, F. and Guiochon, G. Peak shapes of acids and bases under overloaded conditions in reversed phase liquid chromatography, with weakly buffered mobile phases of various pH a thermodynamic interpretation. J. Chromatogr. A. 2009, 1216, 63-78. 

A thermodynamic interpretation of this relation is that the left side is inversely proportional to the system volume V. This relation then says that the fluctuations... 

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