Thermodynamic Consistency of Experimental Data

Values of isosteric sorption enthalpy, -AH, standard sorption entropy, AS°, and standard Gibbs free sorption energy, AG°, are calculated as dependences on n, cf., [4-8]. To calculate AG°, the boiling-point temperature of N2O is chosen as reference state. This choice provides a check for thermodynamic consistency of experimental data since dG°... 

In the three systems, AG° changes from negative values to zero as sorption-phase concentration increases and exceeds saturation capacities. This demonstrates thermodynamic consistency of experimental data. The larger negative values of AG° in cases of N2 sorption on Li,RE-LSX indicate a stronger exothermic sorption process compared to those of O2 and mixtures, whose AG° data amounts to only about half of that for N2 at initial concentration. 

Because experimental measurements are subject to systematic error, sets of values of In y and In yg determined by experiment may not satisfy, that is, may not be consistent with, the Gibbs/Duhem equation. Thus, Eq. (4-289) applied to sets of experimental values becomes a test of the thermodynamic consistency of the data, rather than a valid general relationship. 

C) In many experimental studies, all of the intensive variables are determined, giving a redundancy of experimental data. However, Equations (10.70) and (10.73) afford a means of checking the thermodynamic consistency of the data at each experimental point for the separate cases. Thus, for Equation (10.70), the required slope of the curve of P versus ylt consistent with the thermodynamic requirements of the Gibbs-Duhem equations, can be calculated at each experimental point from the measured values of P, xt, and at the experimental temperature. This slope must agree within the experimental error with the slope, at the same composition, of the best curve... 

Thus, when values of (A/if - A/if) are plotted as a function of xt, the area between the best smooth curve drawn through the points and the composition axis must be zero within the experimental accuracy. This test concerns the thermodynamic consistency of the data as a whole rather than that of each individual set of experimental values. It also applies strictly to the liquid solution at the arbitrary pressure P0 and only to the two-phase system at equilibrium through the calculation of A fi [ and A /if from the experimental data. 

THERMODYNAMIC CONSISTENCY OF EXPERIMENTAL VAPOR-LIQUID EQUILIBRIUM DATA 3.8... 

Recent papers deal mainly with the problems of testing the thermodynamic consistency of experimental vapour pressure data, and of calculating partial pressures and activity co-efficients of both components from measured total pressures. 

HER1 Herington, E.F.G. A thermodynamic test for the internal consistency of experimental data on volatility ratios. Nature (London) 160 (1947) 610-611. 

NONIDEAL LIQUID MIXTURES 3.5 K VALUE FOR IDEAL LIQUID PHASE, NONIDEAL VAPOR PHASE 3.7 K VALUE FOR IDEAL VAPOR PHASE, NONIDEAL LIQUID PHASE 3.8 THERMODYNAMIC CONSISTENCY OF EXPERIMENTAL VAPOR-LIQUID EQUILIBRIUM DATA 3.8 ESTIMATING INFINITE-DILUTION ACTIVITY COEFFICIENTS 3.10... 

This has the advantage that the expressions for the adsotbed-phase concentration ate simple and expHcit, and, as in the Langmuir expression, the effect of competition between sorbates is accounted for. However, the expression does not reduce to Henry s law in the low concentration limit and therefore violates the requirements of thermodynamic consistency. Whereas it may be useful as a basis for the correlation of experimental data, it should be treated with caution and should not be used as a basis for extrapolation beyond the experimental range. 

The estimation of f from Stokes law when the bead is similar in size to a solvent molecule represents a dubious application of a classical equation derived for a continuous medium to a molecular phenomenon. The value used for f above could be considerably in error. Hence the real test of whether or not it is justifiable to neglect the second term in Eq. (19) is to be sought in experiment. It should be remarked also that the Kirkwood-Riseman theory, including their theory of viscosity to be discussed below, has been developed on the assumption that the hydrodynamics of the molecule, like its thermodynamic interactions, are equivalent to those of a cloud distribution of independent beads. A better approximation to the actual molecule would consist of a cylinder of roughly uniform cross section bent irregularly into a random, tortuous configuration. The accuracy with which the cloud model represents the behavior of the real polymer chain can be decided at present only from analysis of experimental data. 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

The experimental determination of T, yu and xt is actually redundant. However, the equation corresponding to Equation (10.70) involves the partial molar entropies of the components in the two phases. In many cases the values of these quantities are not known. Therefore, a test of the thermodynamic consistency of each experimental point generally cannot be made, neither can the value of one of the three quantities T,yu and xt be calculated when the other two are measured. The test for the consistency of the overall data according to Equation (10.78) can be made when the isothermal values of both A i[T0, P, x] and Anf[T0> P> X1 have been determined. 

MD and MC simulations have provided data on layer spacings, thermodynamic properties, as well as interlayer water configurations, interlayer-species self-diffusion coefficients, and total radial distribution functions that are consistent with experimental data. Most of the clay surface is relatively... 

The parameterization of a force field can be based on any type of experimental data that is directly related to the results available from molecular mechanics calculations, i. e., structures, nuclear vibrations or strain energies. Most of the force fields available, and this certainly is true for force fields used in coordination chemistry, are, at least partially, based on structural data. The Consistent Force Field (CFF)197,106,1071 is an example of a parameterization scheme where experimentally derived thermodynamic data (e. g., heats of formation) have been used to tune the force field. Such data is not readily available for large organic compounds or for coordination complexes. Also, spectroscopic data have only rarely been used for tuning of inorganic force field parameters113,74,1081. 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

Tpo obtain vapor-liquid equilibrium data for binary systems, it is now well established that under certain circumstances it can be more accurate and less time consuming to measure the boiling point, the total pressure, and the liquid composition and then use the Gibbs-Duhem relationship to predict vapor composition (I) rather than to measure it. The disadvantage is that there is no way of checking the thermodynamic consistency of the experimental data. 

This paper is devoted to the verification of the quality of experimental data regarding the solubility of sparingly soluble solids, such as drugs, environmentally important substances, etc. in mixed solvents. A thermodynamic consistency test based on the Gibbs-Duhem equation for ternary mixtures is suggested. This test has the form of an equation, which connects the solubilities of the solid, and the activity coefficients of the constituents of the solute-free mixed solvent in two mixed solvents of close compositions. 

The main difficulties in this selection were the following 1) the total number of experimental data regarding the HOP in aqueous mixed solvents is small, much smaller that the number of experimental data regarding the solubilities of dmgs in aqueous mixed solvents (7). 2) There is no thermodynamic consistency test, such as those for vapor-liquid equilibrium (29), for checking the self-consistency of the data regarding the solubility of a solid in a mixed solvent. Therefore, it is difficult to evaluate whether the solubility data are accurate or contain errors. 

In summary, IGC is an experimentally attractive method for obtaining polymer-polymer interaction parameters in polymer blends at temperatures above Tm for a crystalline blend, and above Tg for an amorphous blend. This technique yields interaction parameters that are generally consistent with data obtained with other techniques such as vapor sorption, melting point depression, neutron scattering, and small-angle X-ray scattering (40). Advances in IGC of polymer blends will require increased experimental precision in order to improve the consistency of the data, as well as refinements of thermodynamic models to allow better interpretation of interactions in ternary solutions. 

The thermodynamic data compiled in the present review (see Chapters III and IV and Appendix E) refer to the reference temperature of 298.15 K and to standard conditions, cf. Section II.3. For the modelling of real systems it is, in general, necessary to recalculate the standard thermodynamic data to non-standard state conditions. For aqueous species a procedure for the calculation of the activity factors is thus required. This review uses the approximate specific ion interaction method (SIT) for the extrapolation of experimental data to the standard state in the data evaluation process, and in some cases this requires the re-evaluation of original experimental values (solubilities, emf data, etc.). For maximum consistency, this method, as described in Appendix B, should always be used in conjunction with the selected data presented in this review. However, some solubility data for highly soluble selenates were evaluated in the original papers by the Pitzer approach. No attempt was made to re-evaluate these data by the SIT method. 

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