Enthalpy and Entropy of Transformation

A value of 9.1 kcal/mol as calculated from data in [1] was criticized [2]. For a review, see 

For free energy, enthalpy, and entropy values related to solutions of Pb(C2H5)4, see Section 1.1.1.2.5. 

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If any solid-solid, solid-liquid, solid-gas, or liquid-gas transformation enters the calculation of the Gibbs energy of a particular reaction, the enthalpies and entropies of transformation must also be known. The following quantities are then tabulated to describe the thermodynamics of a particular chemical compound in full ... 

The solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 13 kJ mole-1 and 200 8 J K"1 mole-1) are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 7 kJ and 257 5 J K-1, respectively, referred to 1 mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, S02 and 02. Desorption occurs over an area equivalent to about 1.4% of the total exposed crystal surface. Other possible models are discussed. 

Table 1. Values of the parameters in equation (6) for PbZr,. Ti,03 where and c [2] are transformed from Celsius scale to Kelvin temperature. Due to the difficulty of finding the melting enthalpy and entropy of lead zirconate titanate PZT, mean values of PbO, TiOj and ZrOj be consisted of the compound [12] are utilized.

The total pressure of the vapour in equilibrium with (3-SnSe was measured in the temperature range 862 to 920 K using the Knudsen effusion technique. The enthalpy and entropy of sublimation according to the reaction a-SnSe SnSe(g) were calculated by the review from the reported vapour pressure expression and the selected heat capacities of SnSe(g) and a-SnSe, the enthalpy of transformation a-SnSe —> (3-SnSe being 1.28 kJ-mof (cf V.7.4.1.2), and a heat capacity expression of (3-SnSe being identical to that of a-SnSe, yielding (SnSe, a, 298.15 K) = (188.2 + 20.0) kJ-mol and... 

Transient, or time-resolved, teehniques measure the response of a substance after a rapid perturbation. A swift kiek ean be provided by any means that suddenly moves the system away from equilibrium—a ehange in reactant concentration, for instanee, or the photodissoeiation of a ehemical bond. Kinetic properties such as rate eonstants and amplitudes of chemieal reaetions or transformations of physical state taking place in a material are then determined by measuring the time eourse of relaxation to some, possibly new, equilibrium state. Determining how the kinetic rate constants vary with temperature ean further yield information about the thermodynamie properties (aetivation enthalpies and entropies) of transition states, the exceedingly ephemeral species that lie between reactants, intermediates and produets in a ehemieal reaetion. 

Relaxation-map analysis (RMA) n. A technique used on the results of a series of thermally stimulated current experiments in which the TSC data are transformed into relaxation times and plotted versus reciprocal absolute temperature to estimate enthalpy and entropy of activation for the molecular relaxations. 

Component activity is a direct measure of the slope of the Gibbs energy surfaces of the stable phases from the direction of the component reference state. The variation of the logarithm of activity with inverse temperature gives the partial molar enthalpy and entropy of mixing of the alloy component A, using the second-law method. A well-defined reference state that can be routinely measured is critical for activity measurements. In addition to these thermodynamic quantities, phase transformation temperatures can be determined from changes in the slopes of these plots. The extraction of the various thermodynamic properties from KEMS measurements is discussed later. 

Kubaschewski, Evans, and Alcock have tabulated many data of interest to metallurgists, including enthalpies of formation and standard entropies at 298.15 K, heat capacities, enthalpies and temperatures of transformation, melting and boiling temperatures, vapour pressures, and standard free energies of reaction. Some data on binary metallic systems are also given. 

For the determination of standard Gibbs energies of reaction, a wide variety of experimental methods have been devised. These may be subdivided into e.m.f. measurements, equilibria with a gaseous phase, and distribution equilibria. From the temperature coefficients of the Gibbs energies, enthalpies and entropies of reaction can be deduced, but experience has shown that these cannot be relied upon when one or more solid phase takes part in the reaction, and errors are very difficult to assess. In such cases, it is recommended that the enthalpies of reaction are measured caloriraetrically and combined with the standard Gibbs energies to yield standard entropies of reaction. Calorimetric methods are also used to determine heat capacities, enthalpies of transformation, and enthalpies of fusion. Only for the determination of enthalpies of evaporation may... 

Fig. 23. Variation of the solution enthalpy and entropy of H in the NdHj, system, for 0.32 < x < 0.95. The break near x = 0.65 indicates a phase transformation (cf. fig. 15b) (Ohki et al. 1989).

The change of the reference state has been made assuming that the enthalpies and entropies of fusion or of allotropic transformation do not vary with temperature. These values have been taken from Hultgren et al. (1973b) for the rare earths and from Getting et al. (1976) for the actinides. This choice was motivated by the fact that many authors have used these values to calculate the changes of the reference state (see for example Chiotti et al. 1981). 

Shiflet et al. (1979) combined the Kaufman approach with values of the enthalpies and entropies of melting and transformation of the pure rare earth metals and calculated the phase diagram for the Tb-Er system. The peritectic point in the... 

The assumption that the energy can be written as a sum of terms implies that the partition function can be written as a product of terms. As the enthalpy and entropy contributions involve taking the logarithm of q, the product thus transforms into sums of enthalpy and entropy contributions. 

When the free energies F of the two crystal structures are identical, the system is at a critical point. The identity of F does not imply identical fimctions (otherwise the two phases would be indistinguishable). Therefore, at the critical point first derivatives of F might differ and therefore enthalpy, volume, and entropy of the two phases would be different. These transformations are first-order phase transitions, according to Ehrenfest [105]. A discontinuous enthalpy imphes heat exchange at the transition temperature, which can easily be measured with DSC experiments. A discontinuous volume is evident under the microscope or, more precisely, with diffraction experiments on single crystals or powders. Some phase transitions are however characterized by continuous first derivatives of the free energy, whereas the second derivatives (specific heat, compressibility, or thermal expansivity, etc.) are discontinuous. These transformations are second-order transitions and are clearly softer. 

Transition enthalpy and entropy. For the Clapeyron equation we applied the transformation of pressure P to lateral pressure 7r and volume V to area a a- To get the molar transition enthalpies the equation has to be resolved with respect to AHc ... 

The terms on the right-hand sides of Eqs. (6.62) and (6.63) are readily associated with steps in a calculation path leading from an initial to a final state of a system. Thus, in Fig. 6.14, the actual path from state 1 to state 2 (dashed line) is replaced by a three-step calculational path. Step 1 - 1 represents a hypothetical process that transforms a real gas into an ideal gas at T, and Pi. The enthalpy and entropy changes for this process are... 

Samsonov [15] studied the direct sorption of ALA and other dipolar ions by SDV-3 ion exchanger resin at pH = 7. The enthalpy and entropy components of these sorptions were obtained from the isotherm dependence on temperature. It was found that the transformation of the resin from the hydrogen to the amino acid form was accompanied by a rise in the system s entropy. The thermodynamic-based description of the exchange of a-amino acids with hydrogen on three ion-exchange resins at pH < pK .co2 were determined as well. However, precise descriptions of the experimental measurements and the calculations program used were not given. 

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