Transformation enthalpy

We would like to know the binding energy per mole of PALA and the enthalpy of the transformation T R, but we do not have enough information. Independent studies show that partial unfolding of ACTase occurs on binding of less PALA, in particular, 1.8 mol of PALA cause 43% unfolding and 4.8 mol... 

To confirm that the matrix is amorphous following primary solidification, isothermal dsc experiments can be performed. The character of the isothermal transformation kinetics makes it possible to distinguish a microcrystalline stmcture from an amorphous stmcture assuming that the rate of heat released, dH/dt in an exothermic transformation is proportional to the transformation rate, dxjdt where H is the enthalpy and x(t) is the transformed volume fraction at time t. If microcrystals do exist in a grain growth process, the isothermal calorimetric signal dUldt s proportional to, where ris... 

Equation 54 implies that U is a function of S and P, a choice of variables that is not always convenient. Alternative fundamental property relations may be formulated in which other pairs of variables appear. They are found systematically through Legendre transformations (1,2), which lead to the following definitions for the enthalpy, H, Hehnholt2 energy,, and Gibbs energy, G ... 

In the sohd state, uranium metal exists in three aHotropic modifications. The transformation temperatures and the enthalpies of transformation are given in Table 5. The thermodynamic properties of uranium metal have been deterrnined with great accuracy and have been discussed (50). 

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. 

The vibrational enthalpy consists of two parts, the first is a sum of hv/2 contributions, this is the zero-point energies. The second part depends on temperature, and is a contribution from molecules which are not in the vibrational ground state. This contribution goes toward zero as the temperature goes to zero when all molecules are in the ground state. Note also that the sum over vibrational frequencies runs over 3Ai — 6 for the reactant(s), but only 3A1 — 7 for the TS. At the TS, one of the normal vibrations has been transformed into the reaction coordinate, which formally has an imaginary frequency. 

These techniques help in providing the following information specific heat, enthalpy changes, heat of transformation, crystallinity, melting behavior, evaporation, sublimation, glass transition, thermal decomposition, depolymerization, thermal stability, content analysis, chemical reactions/polymerization linear expansion, coefficient, and Young s modulus, etc. 

Transition pressures were determined by equating enthalpies of different polymorphs via the common tangent construction. We found that ratile transforms to columbite structure at 11.8 GPa with a small volume change of 3%. These results agree well with experimental... 

A. Navrotsky and O.J. Kleppa, Enthalpy of the anatase-rutile transformation, J. Am. Ceram. Soc. 

Figure 2. The enthalpy, AH, of the phase transformation can be calculated from the variation of In P laleai] with reciprocical temperature in a van t Hoff plot.

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. 

The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

As already mentioned, the system ofEqs. (8.1-8.5) is supplemented by the Clausius-Clapeyron equation, as well as by the correlation that determines the dependence of enthalpy on temperature and describes the thermohydrodynamical characteristics of flow in a heated capillary. It is advantageous to analyze parameters of such flow to transform the system of governing equations to the form that is convenient for significant simplification of the problem. 

The heat of transformation is defined as the change in enthalpy that results when one mole of a substance undergoes a specific change of state such as melting, evaporation, or allotropic modification. 

The last term in the above equation, AH, refers to the enthalpies of transformation that the reactants and/or products may undergo in the temperature interval 298 to T. Enthalpies of transformations are added (the sign is + ) if products transform and subtracted (the sign is if reactants transform. Molar heat capacities of reactants and products do vary... 

The shaded areas represent the values of the different enthalpies of transformation. 

When the free enthalpy of reaction AG for the transformation of the structure of a compound to any other structure is positive, then this structure is thermodynamically stable. Since AG depends on the transition enthalpy AH and the transition entropy AS, and AH and AS in turn depend on pressure and temperature, a structure can be stable only within a certain range of pressures and temperatures. By variation of the pressure and/or the temperature, AG will eventually become negative relative to some other structure and a phase transition will occur. This may be a phase transition from a solid to another solid modification, or it may be a transition to another aggregate state. 

MnAs exhibits this behavior. It has the NiAs structure at temperatures exceeding 125 °C. When cooled, a second-order phase transition takes place at 125 °C, resulting in the MnP type (cf. Fig. 18.4, p. 218). This is a normal behavior, as shown by many other substances. Unusual, however, is the reappearance of the higher symmetrical NiAs structure at lower temperatures after a second phase transition has taken place at 45 °C. This second transformation is of first order, with a discontinuous volume change AV and with enthalpy of transformation AH. In addition, a reorientation of the electronic spins occurs from a low-spin to a high-spin state. The high-spin structure (< 45°C) is ferromagnetic,... 

Fig. 2.12. Enthalpy, entropy, and free energy differences for the ethane —> ethane zero-sum alchemical transformation in water. The molecular dynamics simulations are similar to those described in Fig. (2.7). 120 windows (thin lines) and 32 windows (thick lines) of uneven widths were utilized to switch between the alternate topologies, with, respectively, 20 and lOOps of equilibration and 100 and 500 ps of data collection, making a total of 14.4 and 19.2 ns. The enthalpy (dashed lines) and entropy (dotted lines) difference amount to, respectively, —0.1 and +1.1 kcalmol-1, and —0.5 and +4.1 calmol-1 K For comparison purposes, the free energy difference is equal to, respectively, +0.02 and —0.07kcalmol I, significantly closer to the target value. Inset Convergence of the different thermodynamic quantities...

An enormous number of phase transitions are known to occur in common solid compounds. For example, silver nitrate undergoes a displacive phase transition from an orthorhombic form to a hexagonal form at a temperature of approximately 162°C that has a enthalpy of 1.85 kj/mol. In many cases, the nature of these transitions are known, but in other cases there is some uncertainty. Moreover, there is frequently disagreement among the values reported for the transition temperatures and enthalpies. Even fewer phase transitions have been studied from the standpoint of kinetics, although it is known that a large number of these transformations follow an Avrami rate law. There is another complicating feature of phase transitions that we will now consider. 

Although there are other ways, one of the most convenient and rapid ways to measure AH is by differential scanning calorimetry. When the temperature is reached at which a phase transition occurs, heat is absorbed, so more heat must flow to the sample in order to keep the temperature equal to that of the reference. This produces a peak in the endothermic direction. If the transition is readily reversible, cooling the sample will result in heat being liberated as the sample is transformed into the original phase, and a peak in the exothermic direction will be observed. The area of the peak is proportional to the enthalpy change for transformation of the sample into the new phase. Before the sample is completely transformed into the new phase, the fraction transformed at a specific temperature can be determined by comparing the partial peak area up to that temperature to the total area. That fraction, a, determined as a function of temperature can be used as the variable for kinetic analysis of the transformation. 

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