Standard enthalpies, phase transition

ELDAR contains data for more than 2000 electrolytes in more than 750 different solvents with a total of 56,000 chemical systems, 15,000 hterature references, 45,730 data tables, and 595,000 data points. ELDAR contains data on physical properties such as densities, dielectric coefficients, thermal expansion, compressibihty, p-V-T data, state diagrams and critical data. The thermodynamic properties include solvation and dilution heats, phase transition values (enthalpies, entropies and Gibbs free energies), phase equilibrium data, solubilities, vapor pressures, solvation data, standard and reference values, activities and activity coefficients, excess values, osmotic coefficients, specific heats, partial molar values and apparent partial molar values. Transport properties such as electrical conductivities, transference numbers, single ion conductivities, viscosities, thermal conductivities, and diffusion coefficients are also included. 

Atrs m change in standard molar enthalpy of a phase transition... 

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 ... 

The types of values reported in the database standard enthalpies of formation at 298.15 K and 0 K, bond dissociation energies or enthalpies (D) at any temperature, standard enthalpy of phase transition—fusion, vaporization, or sublimation—at 298.15 K, standard entropy at 298.15 K, standard heat capacity at 298.15 K, standard enthalpy differences between T and 298.15 K, proton affinity, ionization energy, appearance energy, and electron affinity. The absence of a check mark indicates that the data are not provided. However, that does not necessarily mean that they cannot be calculated from other quantities tabulated in the database. 

If we want to calculate the entropy of a liquid, a gas, or a solid phase other than the most stable phase at T =0, we have to add in the entropy of all phase transitions between T = 0 and the temperature of interest (Fig. 7.11). Those entropies of transition are calculated from Eq. 5 or 6. For instance, if we wanted the entropy of water at 25°C, we would measure the heat capacity of ice from T = 0 (or as close to it as we can get), up to T = 273.15 K, determine the entropy of fusion at that temperature from the enthalpy of fusion, then measure the heat capacity of liquid water from T = 273.15 K up to T = 298.15 K. Table 7.3 gives selected values of the standard molar entropy, 5m°, the molar entropy of the pure substance at 1 bar. Note that all the values in the table refer to 298 K. They are all positive, which is consistent with all substances being more disordered at 298 K than at T = 0. 

Two remarks (1) The area change is negative because the area after the phase transition is lower than before. (2) The enthalpy of condensation is of the order of the standard enthalpies of vaporization of hydrocarbons. 

By combining the thermodynamic data with those on the structure of the equilibrium binary phase diagram, R. Pretorius et al 261,262 were able to improve the accuracy of predicting the sequence of compound-layer formation in the transition metal-aluminium systems. For this, they used the values of the standard enthalpies (heats) of formation of the compounds. 

Atrs H° A vapH° standard enthalpy of transition per mole (between phases) standard enthalpy of vaporisation per mole A trsH°... 

It is essential to realize that any thermodynamic evaluation of this solubility "maximum" with standard reference conditions in the form of the three pure components in liquid form is a futile exercise. The complete phase diagram. Fig. 2, shows the "maximum" of the solubility area to mark only a change in the structure of the phase in equilibrium with the solubility region. The maximum of the solubility is a reflection of the fact that the water as equilibrium body is replaced by a lamellar liquid crystalline phase. Since this phase.transition obviously is more. related to packing constraints — than enthalpy of formation — a view of the different phases as one continuous region such as in the short chain compounds water/ethanol/ethyl acetate. Fig. 3, is realistic. The three phases in the complete diagram. Fig. 2, may be perceived as a continuous solubility area with different packing conditions in different parts (Fig. 4). 

In another notation, we can understand Ep as the change in standard internal energy in going from one of the minima to the maximum, which is called the transition state or activated complex. We might designate it as the standard internal energy of activation, UsE. The standard enthalpy of activation, A//, would then be + A(PV) but A(PV) is usually negligible in a condensed-phase reaction, so that A// A . Thus, the Arrhenius equation could be recast as... 

Temperature calibration is achieved using standard reference materials whose transition temperatures are well characterized (Appendices 2.1 and 2.2) and in the same temperature range as the transition in the sample. The transition temperature can be determined by DTA, but the enthalpy of transition is difficult to measure because of non-uniform temperature gradients in the sample due to the strueture of the sample holder, which are difficult to quantify. This type of DTA instrument is rarely used as an independent apparatus and is generally coupled to another analytical instrument for simultaneous measurement of the phase transitions of metals and inorganic substances at temperatures greater than 1300 K. 

In Eqs. (127) and (128) /fa is the equilibrium constants of the chemical reaction and and are the activities at equilibrium concentrations of the reactants. Using the concept of standard reaction enthalpies, standard Gibbs reaction energies, and standard entropies (Section III), the quantities h (P T) can be calculated with the help of tabulated standard values (at 25°C and 1 atm) and Cp or U functions. Phase transitions on the path of integration must... 

Thermal phase transition temperatures (TJ and enthalpies (AH) were measured with a DuPont DSC 2910 at a heating rate of 2 C/min. A 10 mg sample was loaded in a sealed aluminum pan and pre-equllibrated at 5 X for 10 minutes prior to heating. The enthalpy of the transition was calculated from the area under the curve using an indium standard. 

Entropies calculated using Equ on S 21 (with phase transitions) are called third-law (or) entropies because these values are not measured relative to some reference state. Third-law entropies per mole of material measured at the standard pressure of 1 bar are referred to as standard molar entropies, denoted by S°. Table 8.2 lists standard molar entropies for a variety of inorganic and organic substances— values for many other substances are given in Appendix 2. The units of S° are J mol K , in contrast to A ff values, which are generally given in kJ mol". Entropies of elements and compounds are all positive (that is, 5° > 0) for all T > 0 K. By contrast, the standard enthalpy of formation (AHf) for elements in their stable form is arbitrarily set equal to zero, and for compounds it may be positive or negative. 

As noted previously, these considerations apply strictly to the steady state only - hence by no means to ordinary chemical or physical reactions that generate fast changes of the heat flow to the sample thus disturbing the steady state (a steady state develops, for example, when a long-lived radioactive material serves as the sample). The proportionality coefficients (calibration factor) that apply to the non-steady state must be determined in calibration tests. Under certain circumstances, they depend on the temperature course Ts(t) during the reaction (see Hbhne, Hemminger, and Flammersheim, 2003). It becomes obvious again that the temperature-time profile of these calibration experiments must match that of the sample reaction as closely as possible to ensure an accurate calibration for the particular non-steady state. Enthalpy standards with fast phase transitions may yield a different calibration factor to standards with slower delivery of heat. 

The standard molar quantities appearing in Eqs. 12.10.1 and 12.10.2 can be evaluated through a variety of experimental techniques. Reaction calorimetry can be used to evaluate AfH° for a reaction (Sec. 11.5). Calorimetric measurements of heat capacity and phase-transition enthalpies can be used to obtain the value of Sf for a solid or liquid (Sec. 6.2.1). For a gas, spectroscopic measurements can be used to evaluate S° (Sec. 6.2.2). Evaluation of a thermodynanuc equilibrium constant and its temperature derivative, for any of the kinds of equilibria discussed in this chapter (vapor pressure, solubility, chemical reaction, etc.), can provide values of ArG° and AfH° through the relations AfG° = —RTln K and ArH° = -Rd aK/d /T). 

Calculating the Heat of Phase Transition from Standard Enthalpies of Formation... 

Calculating the heat of phase transition from standard enthalpies of formation Given a table of standard enthalpies of formation, calculate the heat of phase transition. (EXAMPLE 6.8)... 

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