Enthalpy indirect method

There are many compounds in existence which have a considerable positive enthalpy of formation. They are not made by direct union of the constituent elements in their standard states, but by some process in which the necessary energy is provided indirectly. Many known covalent hydrides (Chapter 5) are made by indirect methods (for example from other hydrides) or by supplying energy (in the form of heat or an electric discharge) to the direct reaction to dissociate the hydrogen molecules and also possibly vaporise the other element. Other known endothermic compounds include nitrogen oxide and ethyne (acetylene) all these compounds have considerable kinetic stability. 

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... 

The chemistry of carbenes in solution hits been extensively studied over the past few decades.1-5 Although our understanding of their chemistry is often derived from product analyses, mechanistic details are often dependent on thermodynamic and kinetic data. Kinetic data can often be obtained either directly or indirectly from time-resolved spectroscopic methods however, thermochemical data is much less readily obtained. Reaction enthalpies are most commonly estimated from calculations, Benson group additivities,6 or other indirect methods. 

Solvation enthalpy data for neutral short-lived species, like radicals, are even more scant than for long-lived stable molecules. They can only be experimentally determined through indirect methods, namely, by comparing the enthalpies of reactions of those species in solution and in the gas phase. The former are obtained, for instance, by using the photoacoustic calorimetry technique (see chapter 13), and the latter by several gas-phase methods. 

After 1900 the direct determination of hydrate number was abandoned in favor of the second, indirect method. The indirect method is still in use today and is based on calculation of the enthalpies of formation of hydrate from gas and water, and from gas and ice. This method was originally proposed by de Forcrand (1902) who used the Clapeyron equation to obtain the heat of dissociation from three-phase, pressure-temperature data, as in the below paragraph. With this more accurate method many exceptions were found to Villard s Rule. The historical summary provided in Chapter 1 indicates that while the number of hydrated water molecules was commonly thought to be an integer, frequently that integer... 

Forster cycle Indirect method of determination of excited state equilibria, such as pK values, based on ground state thermodynamics and electronic transition energies. This cycle considers only the difference in molar enthalpy change (AAH) of reaction of ground and excited states, neglecting the difference in molar entropy change of reaction of those states (AAS). 

The donor number, DN, of a solvent, proposed by Gutmann, is a measure of the Lewis base donor power of the solvent.3 The DN is determined by measuring the negative enthalpy for the reaction of the standard Lewis acid, SbCl5, with solvent (Scheme 1), and reflects the ability of the solvent to solvate Lewis acids. The scale commences at zero for solvents with no Lewis basicity (1,2-dichloroethane is used as a reference), and extends to 38.8 kcalmol-1 for hexa-methylphosphoramide (HMPA). Certain solvents like alcohols and water solvolyse SbCl5 and the DN must be estimated by indirect methods. Sometimes values of DN are quoted as DNn, which corresponds to the DN/38.8 thereby giving a scale between 0 and l.4... 

The solution of the sample in a 2 1 mixture of concentrated hydrofluoric and nitric acids at Tref = 298 K was chosen as the reference state. The relative enthalpy, 7/rei(7m), was measured by indirect method of double calorimetry. This procedure enables us to determine Hiei(Tm) as the sum of enthalpy increase measured during the cooling of the system in a drop calorimeter (Acooi and during its dissolution in a solution calorimeter (Asoi//). Equation (4.34) can thus be written in the form... 

The above-described indirect method is not very accurate and can only be used in a qualitative sense. It also requires very sensitive enthalpy measurements (e.g., by using an LKB microcalorimeter). 

The Indirect Method. Many compounds cannot be directly synthesized from their elements. In some cases, the reaction proceeds too slowly, or side reactions produce substances other than the desired compound. In these cases AHf can be determined by an indirect approach, which is based on the law of heat summation (or simply Hess s law). Hess s law can be stated as follows When reactants are converted to products, the change in enthalpy is the same whether the reaction takes place in one step or in a series of steps, hi other words, if we can break down the reaction of interest into a series of reactions for which AH can be measured, we can calculate AT/ xn for the overall reaction. 

We have seen that the heat supplied to a system at constant pressure is equal to the enthalpy increase. For many chemical reactions it is possible to make a direct determination of the heat change at constant pressure for other reactions indirect methods (to be discussed later) can be used. In these ways it has proved possible to build a considerable body of data on the enthalpy changes of chemical processes of all kinds and these data have been of great value in an understanding of molecular structure and in various other ways, The study of enthalpy changes in chemical systems is known as thermochemistry. 

It does not matter that we cannot make this reaction occur cleanly and therefore cannot directly measure its enthalpy change. As seen above, indirect methods can be used. In such ways it is found that for this reaction is -17.9 kcal. Since we have arbitrarily taken the enthalpies of the reactants to be zero, it follows that on this basis the enthalpy of CH4 (g) is —17,9 kcal mol" h This is known as the enthalpy of formation, AHf, of methane. It.is important to use the term enthalpy of formation only for the formation of the compound from elements in their standard states. 

Correlation gas chromatography is an indirect method to determine the enthalpies of vaporization of both solids and liquids [99]. The quantity directly measured is the enthalpy of transference from the condensed state in the column to the gas state. The enthalpy of vaporization is obtained by using the equation obtained by regression analysis between the enthalpies of transference and the... 

There are direct and indirect methods to evaluate evaporation enthalpy. 

Indirect methods. These are specially used for the plasticizers and other less volatile substances. The application of the generalized expression of the first and the second laws of thermodynamics to heterogeneous equilibrium between condensed phase and vapor in isobaric conditions is given by the Clausius-Clapeyron equation. It links the enthalpy of vapor formation at the vapor pressure, P, and the temperature, T. In the case of a one-component system the Clausius-Clapeyron expression has the form ... 

Knowing the standard enthalpies of formation of reactants and products enables us to calculate the enthalpy of a reaction. We will discuss ways to determine these quantities either by the direct method from the elements or by the indirect method, which is based on Hess s law of heat summation. (6.6)... 

The A// values, obtained by indirect methods, of polymers that, except for minor exceptions, are not included in Table 11.1 or 11.2, are listed in Table 11.3. In general, the enthalpy of fusion is measured for a given sample and the level of crystallinity of the same specimen is determined, by one of the many methods that are available. The A//u value can then be calculated from these measurements. One problem associated with this procedure is that not all methods of measuring the level of crystallinity give exactly the same value. Small but significant differences are found between different techniques that reflect different sensitivities to the elements of phase structure [25]. A corollary to this procedure is to determine the enthalpy of fusion as a function of density for a sample that is crystallized in different ways. The results are then extrapolated to the density of the unit cell in order to obtain A//u. The density of the unit cell needs to be well established, and a long extrapolation is usually involved. 

The polymer bound fraction, p, can be directly determined using spectroscopic methods such as NMR. The method depends on the reduction in the mobility of the segments that are in close contact with the surface. By using a pulsed NMR technique, one can estimatep. An indirect method for estimation of p is to use microcalorimetry. Basically one compares the enthalpy of adsorption per molecule with that per segment [9]. The latter may be obtained by using small molecules of similar structure to a polymer segment. 

There are several indirect methods that also yield values of AH . They all require the determination of the enthalpy of fusion as well as the degree of crystallinity of the system. The degree of crystallinity can be obtained by different experimental techniques such as infra-red, wide-angle x-ray diffraction and density measurement among others. Quite often the enthalpy of fusion is measured as a fiinction of density and the data extrapolated to the value of the unit cell to yield AH . The directly measured enthalpy of fusion, as well as the methods used to determine the crystallinity level, are dependent on morphological and structural detail. Moreover, all of the methods usually have different sensitivities to the phase structures. In our... 

This volume consists of three chapters a hst of the references, and two indexes (Chemical Abstract Service Registry Number Index and Chemical Name Index). Chapter 1 describes the basic concepts of enthalpy of transition and fusion including their classification, temperature dependence, and applications. Chapter 2 is a brief review of the ejqrerimental methods used to determine the enthalpies of transition and fusion including both direct and indirect methods. Chapter 3 contains the tabulated original and evaluated values and auxiliary information including how these values were collected and evaluated (scope of the search, selection of the experimental data, and recommended data evaluation). 

An indirect method for arriving at the ced was from the corresponding enthalpies of vaporization AyH and surface tensions tr of 6 imidazolium RTILs, according to Jin et al. [204], noting the proportionafity between ced and and then... 

Indirect methods of evaluation of evaporation enthalpy Beeause the ealorimetric methods of measurement of enthalpy of vapor formation are very difficult, the irrdirect methods are used, especially for less volatile substances. The appli-eation of generalized expression of the first and second laws of thermodynarrrics to the heterogeneous eqrriUbrium between a condensed phase in isobaric-thermal conditiorrs is given by the Clausius-Clapeyron equation that relates enthalpy of a vapor formation at the vapor pressrrre, P, and temperatiu e, T. For one component system, the Clausius-Clapeyron eqrration has the following form ... 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

Equations 20.176 and 20.179 emphasise the essentially thermodynamic nature of the standard equilibrium e.m.f. of a cell or the standard equilibrium potential of a half-reaction E, which may be evaluated directly from e.m.f. meeisurements of a reversible cell or indirectly from AG , which in turn must be evaluated from the enthalpy of the reaction and the entropies of the species involved (see equation 20.147). Thus for the equilibrium Cu -)-2e Cu, the standard electrode potential u2+/cu> hence can be determined by an e.m.f. method by harnessing the reaction... 

Alternative negative ion-based methods for measuring carbene and diradical enthalpies of formation have been developed, which can give BDEs indirectly. A common approach for this involves the use of halide affinity measurements. The relationship between enthalpy of formation and halide affinity is illustrated by Eq. 5.14. 

In this section we deal with the first of the physical effects which impinge on reactivity — the influences which heats of reaction and bond dissociation energies have on the course of chemical reactions. Both heats of reaction and bond dissociation energies are enthalpy values that are experimentally determined by thermochemical methods, in the first case usually by direct calorimetric methods, in the second by more indirect techniques 22). 

Now, it is necessary to calibrate the calorimeter in order to analyze quantitatively the recorded thermograms and determine the amount of heat evolved by the interaction of a dose of gas with the adsorbent surface. The use of a standard substance or of a standard reaction is certainly the most simple and reliable method, though indirect, for calibrating a calorimeter, since it does not require any modification of the inner cell arrangement. [For a recent review on calibration procedures, see 72).3 No standard adsorbent-adsorbate system has been defined, however, and the direct electrical calibration must therefore be used. It should be remarked, moreover, that the comparison of the experimental heat of a catalytic reaction with the known change of enthalpy associated with the reaction at the same temperature provides, in some favorable cases, a direct control of the electrical calibration (see Section VII.C). 

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