Indirect measurement of enthalpy

Through a collection of indirect measurements, the enthalpy of formation of gaseous nitrosobenzene (40) has recently been reevaluated67 to be 210 8 kJ mol 1, in interesting comparison to those values reported earlier68. The need for indirect, i.e. not simple , combustion and phase-change measurements is unavoidable for this species because nitrosobenzene is normally dimeric. 

Indirect measurement of AH based on reactions with pyridine yields 10.4 0.8 kcal/mol, giving an average value of 10.8 1.0 kcal/mol that compares favorably with the AH of -9.4 0.9 kcal/mol for W(CO)3(PCy3)2.1,2 These values reflect the enthalpy for net reaction with H2 and do not incorporate enthalpies of tautomeriz-ation between tj2-H2 (1) and dihydride (2) species. The major species present in... 

As cited previously, one of the most successful methods for the indirect determination of enthalpies of sublimation is based on the Knudsen-cell mass-loss effusion methods. Recently equipment has been described with three [189] and nine [190] Knudsen cells used for simultaneous measurements. The torsion effusion method has been used recently to determine enthalpies of sublimation of uracil derivatives [191] and sublimation enthalpies have also been determined in drop calorimeters [192,193]. 

Because the calorimetric methods of measurement of enthalpy of vapor formation are very difficult, the indirect mefliods are used, especially for less volatile substances. The application of generalized expression of the first and second laws of thermodynamics to the heterogeneous equilibrium between a condensed phase in isobaric- thermal conditions is given in the Clausius-Clapeyron equation that relates enthalpy of a vapor formation at the vapor pressure, P, and temperature, T. For one component system, the Clausius-Clapeyron equation has the form ... 

Chickos, J. S. A protocol for correcting experimental fusion enthalpies to 298.15 K and its application in indirect measurements of sublimation enthalpy at 298.15 K, Thermoch. Acta 1998,313,19-26. 

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... 

Before proceeding further, we will take a closer look at the significance of enthalpy and internal energy, because these cannot be measured directly but are determined indirectly by measuring other properties such as temperature and pressure. 

The factors that affect the energetics of solid solutions and indirectly solid solubility are to a large extent the same as those that control the enthalpy of formation of compounds. Most often the differences between the atomic radii of the participating elements, in electronegativity and in valence electron density are considered for solutions of elements. For solid solutions of binary compounds, similar factors are used, but some measure of the volume of the compounds is often used instead of atomic radii. 

Finally, we look at indirect ways of measuring these energies. Both internal energy and enthalpy are state functions, so energy cycles may be constructed according to Hess s law we look also at Bom-Haber cycles for systems in which ionization processes occur. 

We obtained this value of AHr knowing the other enthalpies in the cycle, and remembering that enthalpy is a state function. Experimentally, the value of A Hr = 99 kJmol-1, so this indirect measurement with Hess s law provides relatively good data. 

An experimental measure of the interaction of a solute species with a given solvent medium is afforded by the partial molal heat of solution, AHs. For a stable species this is obtained directly by calorimetry or indirectly from the temperature coefficient of the Henry s law constant. The difference in the value of AHs between the two solvents is termed the enthalpy of transfer, denoted by 8AHtI. Combining enthalpies of transfer for the reactants, 8AHft, with transfer enthalpies of activation, 8AH t, using equation (1)... 

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 enthalpy of formation of H2Se03(cr) is obtained indirectly. Selivanova and Pakho-rukov [61SEL/PAK] measured the enthalpy changes of the reactions ... 

At that time the radical nature of solutions of "Cr(CO)3Cp was not yet proven. Hydrogenation of solutions of the dimer had been reported by Muetterties and coworkers,42 but the mechanism of oxidative addition was not known. In addition, the complex [Cr(CO)3Cp]2 is known to catalyze hydrogenation of dienes via H-Cr (CO)3Cp that is regenerated under catalytic conditions. Thermochemical data for reaction 10.54 were obtained by indirect thermochemical cycles, however direct measurement of the enthalpy of reaction of H2(g) and "Cr(CO)3Cp allowed the determination of H-Cr(CO)3Cp bond strength as 62.3 1 kcal/mol.74... 

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. 

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