Calorimetric determination of entropy

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) ... 

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+... 

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

Calorimetric, electrochemical and vapour pressure methods are treated separately. The different techniques are to a large extent complementary. In general, enthalpy and entropy are measured most accurately by calorimetry, while electrochemical and vapour pressure techniques represent efficient direct methods for determination of activities and Gibbs energies. 

The relationship between the statistical expression (equation (5.6)) and the classical expression (equation (5.8)) for determination of the entropy can be explained by the statement that, due to the additional heat taken up, the system acquires more available microstates (Edsall and Gutfreund, 1983). Equation (5.8) introduces a procedure for the direct calorimetric measurement of the entropy change for a specific process such as the reversible formation of a new set of biopolymer interactions. 

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. 

The determination of standard transformed enthalpies of biochemical reactions at specified pH, either from temperature coefficients of apparent equilibrium constants or by calorimetric measurements, makes it possible to calculate the corresponding standard transformed entropy of reaction using... 

Thus Af G ° for a species in aqueous solution can be determined calorimetrically. The standard entropy of formation of a species at 298.15 K is related to its standard molar entropy at 298.15 K by... 

By way of illustrations we display in Fig. 1.17.2a plot of the molar heat capacity of oxygen under standard conditions. The plot of Cp vs. In T is then used to determine the entropy of oxygen from the area under the curves. Note that the element in the solid state exists in three distinct allotropic modifications, with transition temperatures close to 23.6 and 43.8 K the melting point occurs at 54.4 K, and the boiling point is at 90.1 K. All the enthalpies of transition at the various phase transformations are accurately known. An extrapolation procedure was employed below 14 K, which in 1929 was about the lower limit that could conveniently be reached in calorimetric measurements. 

Summarizing, an attempt has been made to provide a systematic account of the thermodynamic properties of the adsorbed phase. The Gibbs adsorption equation, as an extension of the Clausius-Clapeyron equation, has played a key role in linking experimental isotherm data to the determination of molar or differential entropies and enthalpies. Similarly, calorimetric measurements can be systematically applied to obtain the same type of information. 

---