Transition enthalpies of

If, in going from 0 K to T, a substance undergoes phase changes (fusion, vaporization, etc) at and Tg with molar enthalpies of transition AHy, one can write... 

AHt, enthalpy of transition (at temperature specified, superscript, measured in degrees Celsius) in kJ mol ... 

In a procedure similar to that described earlier for N , the entropy at T = 49.44 K point (a) can be calculated from the heat capacities and the enthalpies of transition, by following two different paths. Sm 49 44 was found to be 34.06 J-K-1 mol-1 following the solid III— solid II path and Sm.49.44 = 34.02 JK 1 mol l following the (solid V— solid IV—>solid II) path. The two results agree well within experimental error, which requires that the entropy of solid III and solid V be the same at 0 K, an occurrence that is unlikely unless Sm 0 = 0 for both forms. 

When one polymorph can be thermally converted to another, differential scanning calorimetry (DSC) analysis cannot be used to deduce the heat of transition between the two forms, and so solution calorimetry represents an alternative methodology. This situation was encountered when evaluating the polymorphs of losartan [140], Enthalpies of transition were obtained in water (A(A//sol) = 1.723 kcal/mol) and in A A-dimethylformarnide (A(A//S0 ) = 1.757 kcal/mol), with the equivalence in results demonstrating the quality of the results. Although enthalpy does not indicate stability, the authors deduced from solution calorimetry that form I was more stable than form II at ambient temperature. 

The enthalpy that accompanies a change of physical state at standard conditions is called the standard enthalpy of transition and is denoted A trsH°. Enthalpy changes accompanying chemical reactions at standard conditions are in general termed standard enthalpies of reaction and denoted A r H0. Two simple examples are given in Table 1.3. In general, from the first law, the standard enthalpy of a reaction is given by... 

Whereas the enthalpy of formation of A12Si(>5 from the elements is large and negative, the enthalpy of formation from the binary oxides is much less so. Af ox m is furthermore comparable to the enthalpy of transition between the different polymorphs, as shown for A SiOs in Table 1.5 [3], The enthalpy of fusion is also of similar magnitude. 

It follows that the standard molar entropy of the transition can be derived from the measured standard molar enthalpy of transition through the relationship... 

Figure 6.19 The enthalpy of transition of y-A C to a-Al203 as a function of the surface area of the nanocrystalline particles [25],...

Figure 7.9 Thermodynamic data (b)-(d) needed in analysis of the enthalpy of formation of the binary transition metal compounds given in (a), (b) Atomization enthalpy of first series transition metals (c) sum of first and second ionization enthalpies of first series transition metals (d) derived lattice enthalpy of transition metal dihalides.

Figure 7.19 Enthalpy of transition from the stable polymorph versus volume correlations for micro- and mesoporous SiC>2 and AIPO4 materials [29, 34],...

Table 10.5 Selected experimental determinations of the enthalpy of transition of Agl (a-Agl = j8-Agl).

Considerable spread is also observed in reported enthalpies of transition in single-component systems. As an example, the reported enthalpy of the first-order transition giving the fast ionic conductor phase of Agl at 420 K are compared in Table 10.5. In general, the agreement between the results obtained by adiabatic or... 

Experimental Methods Measurements of specific heat and enthalpies of transition are now usually carried out on quite small samples in a Differential scanning calorimeter (DSC). DSC is applied to two different moles of analysis, of these the one is more closely related to traditional calorimetry and is described here. In DSC an average-temperature circuit measures and controls the temperature of sample and reference holders to conform to a Organisation and Qualities... 

The standard enthalpy of transition of a substance A from a phase a to a phase P (AtrsH°) is the enthalpy associated with the process ... 

Calculation of the enthalpy of transition in the solid state from the enthalpy of combustion is particularly important when changes of reference state from one allotrope to another are necessary. Carbon is illustrated as an example [7] ... 

The different transitions for which calorimetric data have been obtained and the relationships of the experimental A//m values to the enthalpy of transition, A//tji(T R), and to the enthalpy of binding of PALA, A// ,pala. are shown in Figure 4.1, which is a thermodynamic cycle that permits calculation of A// , for one step if all others are known. Each enthalpy AH to A//mv, in principle, contains some contribution from the enthalpy of binding and some from the enthalpy of conformational transition. It has been assumed that the enthalpy of binding per mole of ligand, AH aPALA, is identical for each of the six PALA molecules taken up sequentially by the enzyme. Thus,... 

Steele et al. [28] have measured the standard enthalpy of combustion of buckminsterfullerene Ceo with bomb calorimetry of solid samples at 298.15 K. They have found a value of 26,033 + 14kJ mol Calculate the standard enthalpy of formation of Ceo and the standard enthalpy of transition from graphite to Cgo-... 

Any change from one phase to another—for example, from ice to water—can be carried out reversibly and at a constant temperature. Under these conditions. Equation (6.71) is applicable. Generally, equilibiium phase transitions also are carried out at a fixed pressure. As no work is expended in these transitions except against the atmosphere, Q is given by the enthalpy of transition, and... 

Methylammonium chloride exits in several crystalline forms, as is evident from Figure 11.3. The thermodynamic properties of the (3 and 7 forms have been investigated by Aston and Ziemer [10] down to temperatures near 0 K. Some of their data are listed below. From the information given, calculate the enthalpy of transition from the (3 to the 7 form at 220.4 K. 

Two different crystalline forms of benzothiophene have been described [18]. The one that is the stable form at low temperatures is labeled I and the other II. Calorimetric measurements down to 12 K have been made with each crystalline form. At the normal transition temperature, 261.6 K, the molar enthalpy of transition (I = II) is 3010 J moI . Some additional thermodynamic data obtained by these investigators are given in Table 11.6. Is Crystal II a perfect crystal at 0 K ... 

The area of a DSC peak can be used to estimate the enthalpy of transition, AH, provided the thermal history of the sample is considered [29]. Calibration with respect to enthalpy requires an area that corresponds to a well-defined enthalpy change—a heat of fusion AH(Tm) is commonly used, especially that of indium [3]. 

The values chosen for the various enthalpies of transition have been obtained by drawing the respective values for pure AP and typical fuels from the indicated references and converting them to their equivalent values for a typical propellant containing 70% AP—i.e., for pure AP, we assumed,... 

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