Thermodynamics, of dilute solutions

The steel will be considered to be an ideal ternary solution, and therefore at all temperatures a, = 0-18, Ani = 0-08 and flpc = 0-74. Owing to the Y-phase stabilisation of iron by the nickel addition it will be assumed that the steel, at equilibrium, is austenitic at all temperatures, and the thermodynamics of dilute solutions of carbon in y iron only are considered. 

Defect thermodynamics, as outlined in this chapter, is to a large extent thermodynamics of dilute solutions. In this situation, the theoretical calculation of individual defect energies and defect entropies can be helpful. Numerical methods for their calculation are available, see [A. R. Allnatt, A. B. Lidiard (1993)]. If point defects interact, idealized models are necessary in order to find the relations between defect concentrations and thermodynamic variables, in particular the component potentials. We have briefly discussed the ideal pair (cluster) approach and its phenomenological extension by a series expansion formalism, which corresponds to the virial coefficient expansion for gases. 

G. Jancso and D. V. Fenby Thermodynamics of Dilute Solutions, J. Chem. Educ. 60, 382 (1983). [172] M. D. Zeidler Struktur einfacher molekularer Fliissigkeiten, Angew. Chem. 92, 700... 

Thermodynamics of High Polymer Solutions, Part 13, 453 (1945). Thermodynamics of Dilute Solutions of High... 

There are some who question the usefulness of the Flory-Huggins solubility parameter for problems related to the solubilization of polymers, although it is agreed that it is useful for study of the thermodynamics of dilute solutions. Barton (1975) has referred to literature that cites its shortcomings as a practical criterion of solubility. Some of these are ... 

The pertinence of the Flory-Huggins theory (18) has been discussed in detail elsewhere (2), It continues to be used and is valuable in the study of thermodynamics of dilute solutions. It is of relatively little help in solving engineering and formulation problems. 

In some treatments of the thermodynamics of dilute solutions BaovM s law is taken as the fundamental datum, and the other relations concerning change in equilibrium temperatures are derived... 

GLA Gladkova, E.A., Pavlova, S.-S.A., Dirbrovina, L.V., arrd Korshak, V.V., Thermodynamics of dilute solutions of polyarylates (Russ.), Vysokomol. Soed., Ser. 

As we have learned in Section 1.8, there are a few concentration regimes in the polymer solution. Chapter 2 will primarily focus on the thermodynamics of dilute solutions, that is, below the overlap concentration, although we will also look at how the thermodynamics of the solution deviates from that of the ideal solution with an increasing concentration. Properties characteristic of nondilute solutions will be examined in detail in Chapter 4. 

FLO Floiy, P.J., Thermodynamics of dilute solutions of high polymers, J. Chem. Phys., 11, 453, 1945. 

G. A. Krestov, Proc. 1st Intern. Conf. Calorimetry and Thermodynamics, Warsaw, August 31-Sept. 4, 1969, p. 949. Thermodynamics of dilute solutions. 

Pourbaix, M. J. N., Thermodynamics of Dilute Aqueous Solutions (Trans, by J. N. Agar), Edward Arnold, London (1949)... 

Vapour Pressures of Dilute Solutions Thermodynamic Theory. 

If we glance back over the various branches of application of thermodynamics to chemical problems detailed in the preceding sections of this book, looking more especially at the historical sequence, we shall find that the physical chemists have, until recently, focussed their attention on the theory of dilute solutions. This preference is due to the great stimulus given by the... 

The statistical distribution of r values for long polymer chains and the influence of chain structure and hindrance to rotation about chain bonds on its root-mean-square value will be the topics of primary concern in the present chapter. We thus enter upon the second major application of statistical methods to polymer problems, the first of these having been discussed in the two chapters preceding. Quite apart from whatever intrinsic interest may be attached to the polymer chain configuration problem, its analysis is essential for the interpretation of rubberlike elasticity and of dilute solution properties, both hydrodynamic and thermodynamic, of polymers. These problems will be dealt with in following chapters. The content of the present... 

W. H. Stockmayer, Problems of the statistical thermodynamics of dilute polymer solutions, Makromol. Chem. 35, 54 (1960). 

Such an electrochemical arrangement can also be used to transport oxygen from one electrode to the other by the imposition of an externally applied potential. This technique, known as coulometric titration , has been used to prepare flowing gas mixtures of oxygen/argon with a controlled oxygen partial pressure, to vary the non-stoichiometry of oxides, to study the thermodynamics of dilute oxygen solutions in metals, and to measure the kinetics of metal oxidation, as examples. 

As the laws of dilute solution are limiting laws, they may not provide an adequate approximation at finite concentrations. For a more satisfactory treatment of solutions of finite concentrations, for which deviations from the limiting laws become appreciable, the use of new functions, the activity function and excess thermodynamic functions, is described in the following chapters. 

In the preceding chapters we considered Raoult s law and Henry s law, which are laws that describe the thermodynamic behavior of dilute solutions of nonelectrolytes these laws are strictly valid only in the limit of infinite dilution. They led to a simple linear dependence of the chemical potential on the logarithm of the mole fraction of solvent and solute, as in Equations (14.6) (Raoult s law) and (15.5) (Heiuy s law) or on the logarithm of the molality of the solute, as in Equation (15.11) (Hemy s law). These equations are of the same form as the equation derived for the dependence of the chemical potential of an ideal gas on the pressure [Equation (10.15)]. 

Andon, R.J.E., Counsell, J.F., Tees, E.B., Martin, J.F., and Mash, MJ. Thermodynamic properties of organic oxygen compounds. Part 17. Tow-temperature heat capacity and entropy of the cresols, Trans. Faraday Soc., 63 1115-1121,1967. Andon, R.J.E., Cox, J.D., and Herington, E.F.G. Phase relationships in the pyridine series. Part V. The thermodynamic properties of dilute solutions of pyridine bases in water at 25 °C and 40 °C, J. Chem. Soc. (London), pp. 3188-3196, 1954. Andrades, M.S., Sanchez-Martin, M.J., and Sanchez-Camazano, M. Significance of soil properties in the adsorption and mobility of the fungicide metalaxyl in vineyard soils, J. Agric. Food Chem., 49(5) 2363-2369, 2001. 

Both modifications affect the analysis of dilute solution behavior, and it is difficult to judge how much the e/e0 term is actually needed. In any case, as the authors themselves point out (41), the e/e0 term makes an entirely negligible contribution to solvent activity in concentrated solutions. For example, simple calculations yield a contribution of approximately l%ina 10% solution of natural rubber in benzene at 30° C (M = 500000, [t/]g = 250, y=0.4). It is therefore clear that thermodynamic measurements can furnish no evidence for or against continued collapse in concentrated solutions. 

Pourbaix, M., Thermodynamics of Dilute Aqueous Solutions, E. Arnold, London, 1949. 

Walkley s research interests over the years have focused on the thermodynamics and statistical mechanics of dilute solutions,248 intermolecular potential calculations, and Monte Carlo calculations. 

Thermodynamic properties in dilute aqueous solutions are taken to be functions of ionic strength so that concentrations of reactants, rather than their activities can be used. This also means that pHc = — log[H+] has to be used in calculations, rather than pHa = — log a(H + ). When the ionic strength is different from zero, this means that pH values obtained in the laboratory using a glass electrode need to be adjusted for the ionic strength and temperature to obtain the pH that is used to discuss the thermodynamics of dilute aqueous solutions. Since pHa = — log-/(H + ) + pHc, the use of the extended Debye-Hiickel theory yields... 

The classification of chemical elements into major and minor or trace element categories is somewhat arbitrary. Thermodynamically, a minor element may be defined as one that is partitioned between coexisting phases in compliance with laws of dilute solutions, such as Henry s law, eq. (7.2b). In geochemical parlance, however, trace elements are usually categorized on the basis of abundance data. In this context, the mineral, rock or environment containing the chemical elements must be defined as well as the concentration boundary separating a major and trace element. 

Horton, J. C., Harding, S. E., Mitchell, J. R., and Morton-Holmes, D. F. (1991). Thermodynamic non-ideality of dilute solutions of sodium alginate studied by sedimentation equilibrium ultracentrifugation. Food Hydrocoll. 5 125-127. 

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