The determination of thermodynamic functions

Calorimetry is not always practicable, especially for biochemically Important reactions, but in some cases their thermodynamic properties can be measured electrochemically. 

A special case of the Nernst equation has great importance in chemistry. Suppose the reaction has reached equilibrium then Q = K, where K is the equiHbrium constant of the cell reaction. However, because a chemical reaction at equilibrium cannot do work, it generates zero potential difference between the electrodes. Setting Q = K and = 0 in the Nernst equation gives 

The equilibrium constant in terms of the standard cell potential 

This very important equation—which is simply eqn 4.10 expressed electrochemic-ally—lets us predict equilibrium constants from the standard potential of an electrochemical cell. Note that 

Because the standard potential of the DanieU cell is +1.10 V, the equilibrium constant for the cell reaction (reaction A) is 

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In the determinations of thermodynamic functions of solution equilibria, the position is different. Values obtained by NMR are generally similar to those obtained in other ways, but are seldom the same. 

Hammers and de Ligny [25—28] have pointed out the information that the determination of thermodynamic functions of solute vaporization from the stationary state can supply. 

Rather few papers have dealt with the computation of thermodynamic functions from the results of ab initio calculations, but for H2, where the latter are of spectroscopic accuracy, Kosloff, Levine, and Bernstein have computed the thermodynamic properties of Ha, Da, and HD, using the best theoretical results.75 This work represents the first example of an accurate determination of a bulk, macroscopic property from first principles. 

In chapter 2, computational methods used for the determination of thermodynamic data of the compound, and the kinetic calculations performed in this work are presented. We give a brief review of the computational methods ab initio, and Density Functional Theory, Statistical Mechanics methods. Group Additivity method, and multifrequency Quantum Rice-Ramsperger-Kassel (QRRK). 

Phase equilibria data are extremely important not only because this is information about the state of the phases in the system rmder study, but also these data themselves provide the experimental basis of several physicochemical methods. It is a somce of thermodynamic information that permits us to calculate the thermodynamic functions both for chemical equilibria and reactions, and for individual substances and aqueous species. Although methods of thermodynamic characteristic are not the subject of our review, some experimental methods to study phase equilibria and later determination of thermodynamic functions are so deeply intertwined that they should be mentioned in it. 

The use of thermodynamic functions corrected for the electronic excitation of RQ determined from the excitation energy of the free R ion leads to smaller deviations from the experimental data (Sapegin, 1984) not only in calculations according to the third law but also for those made according to the second law. 

This makes it possible to measure electronic excitation energies, which is of utmost importance for increasing the reliability of thermodynamic functions. Actually, these parameters and measurements of the low-temperature heat capacity are the main factors that determine the accuracy of the sought for values. 

The information system of the Moscow Power Institute, as well as AIST, can calculate the values of thermodynamic functions at different combinations of the independent variables. It can determine also the analytic dependencies as explicit functions of these variables. The initial data for conqiiling such functions ate formed inside the computer with the help of the basic set of equations. Therefore, the system gives information on the thermodynamic properties of substances in the form of tables or equations, approximating part of the thermodynamic surface in terms of given independent variables (Sychev Spiridonov 1984 Sychev et al 1985b). 

The lattiee model, also called the cell model, takes its origin in statistical mechanics and has a prolonged history [74]. It was first applied to the thermodynamical and statistical mechanical description of binary mixtures and the determination of activity functions in the bulk phase [75]. It was later used for the description of the surface tension of binary mixtures [76]. 

The observed emf dtrring the titration provides fundamental information on the thermodynamics of the system in addition to the phase eqtrilibria. The knowledge of the emf as a function of stoichiometry allows the determination of thermodynamic data with high resolution as a function of the composition of the sample. 

Mini-probes (Figure 6) have been developed for the determination of thermodynamic properties of MIEC as a function of composition Zirconia- or thoria-based tubes, a few mm in diameter, have been used. A metal-metal oxide system serves as a reference. Such cells have been used for the measurement of oxygen potential in urania-based solid solutions or for continuous control of oxygen redistribution in UO2+X under a thermal gradient [Ducroux et al, 1980 Une Oguma, 1982]. 

M. Bacci, M. Bini, A. Checcucci, A. Ignesfi, L. Millanta, N. Rubino, R. Vanni, Microwave heating for the rapid determination of thermodynamic functions of chemical reactions, J. Chem. Soc. Faraday Trans. 1 (77) (1981) 1503-1509. 

This experiment describes the determination of the stability (cumulative formation) constant for the formation of Pb(OH)3 by measuring the shift in the half-wave potential for the reduction of Pb + as a function of the concentration of OH . The influence of ionic strength is also considered, and results are extrapolated to zero ionic strength to determine the thermodynamic formation constant. 

On the experimental side, one may expect most progress from thermodynamic measurements designed to elucidate the non-configurational aspects of solution. The determination of the change in heat capacity and the change in thermal expansion coefficient, both as a function of temperature, will aid in the distinction between changes in the harmonic and the anharmonic characteristics of the vibrations. Measurement of the variation of heat capacity and of compressibility with pressure of both pure metals and their solutions should give some information on the... 

The selectivity of ion exchange Ks can easily be determined experimentally for the simplest systems of exchange between monovalent ions. The value of Ks may be used for analysis of thermodynamic functions AG°, AH0 and AS0, of sorption selectivity... 

The chemical constants may therefore be determined directly by the measurement of vapour pressures, especially at low temperatures. Equation (9), which is more general, shows that the chemical constant is determined for a. homogeneous gas as soon as we know A, and C, as functions of temperature, and the vapour pressure at one temperature. These data, especially vapour pressures at very low temperatures, are not very well known at present, and some other method must therefore be used in the determination of the chemical constant. Several such methods have been proposed by Nernst (loc. cit. cf. also Haber, Thermodynamics of Technical Gas Reactions, pp. 88—96 Weinstein, Thermodynamik and Kinetik III., 2, pp. 1064—1074). 

Another useful application of DSC is the determination of the specific heat (Cp) of substances as a function of temperature [71]. The specific heat is an important parameter in many thermodynamic and process design calculations. 

The determination of the heat capacity of a substance as a function of the temperature is by itself a very important application of DSC, because it may lead to values of the thermodynamic functions S%, //-" — //q, and Gy, mentioned in chapter 2. An example is the study of C6o carried out by Wunderlich and co-workers [271], The application of DSC in the area of molecular thermochemistry has been particularly important to investigate trends in transition metal-ligand bond dissociation enthalpies. The typical approach used in these studies, and its limitations, can be illustrated through the analysis of the reaction 12.27, carried out by Mortimer and co-workers [272] ... 

Fluorescence quantum yield and emission maximum determinations as a function of peptide concentration may also permit the detection of peptide self-aggregation at concentrations below 10-4 M, because the peptide fluorophore is likely to be located in a different environment in the peptide aggregate. For example, the concentration-dependent changes in the tryptophan fluorescence emission maximum of mellitin were monitored to determine the equilibrium dissociation constant and thermodynamic parameters of the monomer-tetramer self-association reaction of this peptide. 25 Similarly, measurement of the changes in the tryptophan fluorescence intensity of gramicidin A as a function of its concentration permitted the determination of an average monomer-dimer equilibrium con-stant. 26 ... 

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