Enthalpy calorimetric techniques

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... 

Drago and coworkers have also calculated the enthalpy values for the formation of many complexes or hydrogen bonds by NMR and calorimetric techniques. For example, in a series of phenols or t-BuOH, they observed the IR frequency shifts (Avqh) of the hydroxyl compounds and found that a linear relationship exists between bases and individual acids. In Table 7 shows some AH values calculated by equation 2, and Avqh values of t-BuOH" " while in Table 8 frequency data Avq of various substituted phenols and the AH values are given. 

The two sets of measurements of vE agree reasonably well with each other (cf. Fig. 3 of Ref. 25). The excess enthalpy has also been measured by Pool and Staveley26 by a calorimetric technique which seems somewhat less advanced than the one used by Lambert and Simon. Their results are in moderate agreement with (67). 

The enthalpies of ionization corresponding to Eqs. (4), (3"), and (11) can be determined by means of the temperature effect on the respective standard free energy changes (70MI3) or by calorimetric techniques. 

This relation is a direct consequence of the definition of enthalpy by Equation (I) and of the mathematical statement of the first law of thermodynamics, namely that the change in internal energy. AT. is equal to the heat adsorbed minus the work done q - PAY). It is clear that this thermodynamic relation does not define absolute values of enthalpy or internal energy. Changes in enthalpy, however, are readily measured by calorimetric techniques, and the relative enthalpy values nre sufficient for all therinochcmical calculations. 

Using a high temperature solution calorimetric technique, Hong and Kleppa ( ) measured a H (B C, cr, 1320 K) - -15.98 0. 4 kcal mol . We adopt this value and correct to 298.15 K using tabulated enthalpy data (2) to obtain A H (B C, cr, 298.15 K) > -14.98 1.5 kcal mol which is a correction to that reported by Hong and Kleppa (1 ). The uncertainty limit is that recommended by Hong and Kleppa. 

Clearly, it would be desirable if the area under the peak was a measure of the enthalpy associated with the transition. However, in the case of DTA, the heat path to the sample thermocouple includes the sample itself. The thermal properties of each sample will be different and uncontrolled. In order for the DTA signal to be a measure of heat flow, the thermal resistances between the furnace and both thermocouples must be carefully controlled and predictable so that it can be calibrated and then can remain the same in subsequent experiments. This is impossible in the case of DTA, so it cannot be a quantitative calorimetric technique. Note that the return to baseline of the peak takes a certain amount of time, and during this time the temperature increases thus the peak appears to have a certain width. In reality this width is a function of the calorimeter and not of the sample (the melting of a pure material occurs at a single temperature, not over a temperature interval). This distortion of peak shape is usually not a problem when interpreting DTA and DSC curves but should be borne in mind when studying sharp transitions. 

The enthalpy of transition between a- and P-zirconium has been measured by a number of workers using a variety of calorimetric techniques. A summary of the values obtained is given in Table V-6. There is reasonable agreement between the majority of values, with the exception of [31VOG/TON] and the average value is selected in the... 

The enthalpies of reaction of both ZrCl3(s) and ZrCl4(s) with 3 M HCl solution, and at 25°C, were measured using the calorimetric technique. From the resultant enthalpy changes of the reactions with HCl, the enthalpy change of the reaction ... 

The enthalpies of reaction ofZr(s), ZrCI. o9(s) and ZrCl4(s) with 1.0 M HF + 2.9 M HCl solution, and at 25"C were measured using a calorimetric technique. Enthalpy measurements were also carried out on HCl and H2O in the same medium and at the same temperature. On the basis of the measurements, values were determined for the... 

The thermochemical properties of the rare-earth orthophosphates [plus Sc(P04) and Y(P04)] have recently been investigated in detail by Ushakov et al. (2001). These workers obtained the formation enthalpies of 14 orthophosphates by using calorimetric techniques and found an almost linear dependence between the enthalpies of formation and the rare-earth radius, from La(P04) (-321.4 kJ/mol) to Lu(P04) (-236.9 kJ/mol) xenotime and pretulite were found to be consistent with this behavior as well. The structural transition from the xenotime structure to the monazite structure was not manifested in a significant discontinuity in the relatively linear trend in the enthalpies of formation. The complete results of these detailed thermochemical studies are tabulated in Ushakov et al. (2001). 

The values in this table were measured either by calorimetric techniques or by application of the Claperyon equation to the variation of vapor pressure with temperature. See Reference 1 for a discussion of the accuracy of different experimental techniques and methods of estimating enthalpy of vaporization at other temperatures. Several of the references present empirical techniques for correlating enthalpy of vaporization with molecular structure. 

When coupled to gas adsorption data, calorimetric data can be very useful for the textural characterization of carbons. The use of chemical probes with different molecular sizes allow determining the pore size distribution [288-295]. On the other hand, relevant information concerning chemical properties of the carbon surfaces and their influence on the sorption properties of carbons can be obtained when using the appropriate calorimetric technique. Immersion, flow adsorption and gas-adsorption calorimetry have been employed for the study of surface chemistry of carbons. For instance, immersion calorimetry provides a direct measurement of the energy involved in the interaction of vapor molecules of the immersion liquid with the surface of the solid. This energy depends on the chemical nature of the solid surfajoe and the probe molecules, i.e. the specific interaction between the solid and the liquid. Comparison between enthalpies of immersion into liquids with different polarities provides a picture of the surface chemistry of the solid. Although calorimetric techniques are not able to completely characterize the complex surface chemistry of carbons, they represent a valuable complement to other techniques. 

In DSC, differences in heat flow into a reference and sample are measured vs. the temperature of the sample. The difference in heat flow is a difference in energy DSC is a calorimetric technique, and results in more accurate measurement of changes in enthalpy and heat capacity than that obtained by DTA. 

Enthalpies of the dodecaborides MBi2 (M = 2Jro.eYo.4, Er, or U) were determined between 1300 and 2200 K by a drop-calorimetric technique. Data were all fitted to a function of the type ... 

Enthalpies of reaction can be measured by calorimetric techniques. Alternatively, the temperature dependence of equilibrium constants can be used to determine A/f° and A5° for these ligand substitution reactions by plotting In K versus /T. 

Two calorimetric techniques were used (drop calorimetry and differential scanning calorimetry DSC) to measure the temperatures and enthalpies of phase transitions (solid->solid and solid->liquid). Solution calorimetric determinations were also initiated. 

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