Entropy calorimetric determination

Ulbrich and Waldbaum [14] pointed out that calorimetrically determined third law entropies for many geologically important minerals may be in error because site mixing among cations, magnetic spin disorder, and disorder among water molecules in the crystals is frozen in the samples used for calorimetric measurements. They have calculated corrections based on known crystallographic data for several minerals. 

In deahng with solutions, it frequently may be necessary to obtain values of AG for a process in solution for which only thermal data are available. If standard entropy data also could be obtained for solutions, then it would be possible to calculate AG° from a calorimetric determination of AH° and from Equation (7.26) ... 

Consideration of the effects of anharmonicity involved two empirical constants Z and vanh. Because only three quantities could be evaluated from the calorimetric data with any reliability, A was taken as 5.5 kcal mol"1 (cf. cyclohexane3). Fitting of the thermodynamic data then gave Z = 1.85 kcal mol", vanh = 750 cm 1 and AE = 0.57 kcal mol", favoring the Af-Heq conformer. Whereas A was found to be insensitive to the value of A , A was shown to be sensitive to the experimental error in the calorimetrically determined value of the entropy. 

Christensen, J. J., Wrathall, D. P., Oscarson, J. O., and Izatt, R. M. (1968). Theoretical evaluation of entropy titration method for calorimetric determination of equilibrium constants in aqueous solution. Anal. Chem. 40, 1713-1717. 

Gardner, W. L., Mitchell, R. E., and Cobble, J. W., 1969, The thermodynamic properties of high-temperature aqueous solutions. XI. Calorimetric determination of the stemdeird partial molar heat capacity and entropy of sodium chloride solutions from 100 to 200"C. J. Phys. Chem., 73 2025-32. 

CALORIMETRIC DETERMINATION OF ENTHALPIES,GIBBS ENERGIES,AND ENTROPIES OF INCLUSION OF SOME ALCOHOLS INTO a- AND B-CYCLODEXTRINS IN AQUEOUS SOLUTIONS+... 

Tabulated are single-ion entropies of about 110 diatomic and polyatomic ions in water Gibbs energies, enthalpies, and entropies of hydration of monatomic ions at 25 C partial molar volumes of about 120 common ions at 25 C ionic partial molar heat capacities of ions Gibbs energies of transfer of inorganic electrolytes from HjO to 020 and calorimetrically determined enthalpies of solution of salts in H2O and 020. 

The calorimetric determination of standard entropies of gaseous substances is briefly introduced in Section 9. 

The tables may be used to calculate barrier heights in cases where appropriate spectroscopic data are not available, but where experimental values of heat capacity or entropy are known at one or more temperatures. The calorimetrically determined value of the barrier height may then be used in conjunction with the tables to calculate internal rotation contributions to thermodynamic properties over an extended temperature range. Examples of this procedure include calculations for ethane," propene, acetaldehyde, buta-1,2-diene, acetic acid, hexafluoro-ethane, 3-methylthiophen, and 2-methylthiophen. Where spectroscopic values of the barrier height have subsequently been determined, satisfactory agreement has been obtained with the earlier calorimetric values. The agreement between calorimetric (8.16 kJ mol ) and subsequent micro-wave [(8.28 0.07) kJ mol ] values of the barrier height in propene... 

The absolute entropies are determined in turn from calorimetric measurements of the heat capacities of the monomer and polymer over a wide temperature range using the expression... 

The partial molar entropy of adsorption AI2 may be determined from q j or qsi through Eq. XVII-118, and hence is obtainable either from calorimetric heats plus an adsorption isotherm or from adsorption isotherms at more than one temperature. The integral entropy of adsorption can be obtained from isotherm data at more than one temperature, through Eqs. XVII-110 and XVII-119, in which case complete isotherms are needed. Alternatively, AS2 can be obtained from the calorimetric plus a single complete adsorption isotherm, using Eq. XVII-115. This last approach has been recommended by Jura and Hill [121] as giving more accurate integral entropy values (see also Ref. 124). 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

The chemical potential difference —ju may be resolved into its heat and entropy components in either of two ways the partial molar heat of dilution may be measured directly by calorimetric methods and the entropy of dilution calculated from the relationship A i = (AHi —AFi)/T where AFi=/xi —/x or the temperature coefficient of the activity (hence the temperature coefficient of the chemical potential) may be determined, and from it the heat and entropy of dilution can be calculated using the standard relationships... 

Papisov et al. (1974) performed calorimetric and potentiometric experiments to determine the thermodynamic parameters of the complex formation of PMAA and PAA with PEG. They investigated how temperature and the nature of the solvent affected the complex stability. They found that in aqueous media the enthalpy and entropy associated with the formation of the PMAA/PEG complex are positive while in an aqueous mixture of methanol both of the thermodynamic quantities become negative. The exact values are shown in Table II. The viscosities of aqueous solutions containing complexes of PMAA and PEG increase with decreasing temperature as a result of a breakdown of the complexes. 

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