Enthalpy indirect measurement

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. 

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. 

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... 

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... 

Measuring the emf of the cell at several different temperatures allows the calculation of the enthalpy change, giving another indirect measurement technique. 

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 enthalpy, entropy and free energy changes for an isothennal reaction near 0 K caimot be measured directly because of the impossibility of carrying out the reaction reversibly in a reasonable time. One can, however, by a suitable combination of measured values, calculate them indirectly. In particular, if the value of... 

The heat of mixing (excess enthalpy) and the excess Gibbs energy are also experimentally accessible, the heat of mixing by direcl measurement and G (or In Yi) indirectly as a prodiicl of the reduction of vapor/hqiiid eqiiihbriiim data. Knowledge of H and G allows calculation of by Eq. (4-13) written for excess properties. 

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 lattice enthalpy of a solid cannot be measured directly. However, we can obtain it indirectly by combining other measurements in an application of Hess s law. This approach takes advantage of the first law of thermodynamics and, in particular, the fact that enthalpy is a state function. The procedure uses a Born-Haber cycle, a closed path of steps, one of which is the formation of a solid lattice from the gaseous ions. The enthalpy change for this step is the negative of the lattice enthalpy. Table 6.6 lists some lattice enthalpies found in this way. 

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. 

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. 

Measurements based on the law of conservation of energy are of two main types. In phase change calorimetry the enthalpy of the reaction is exactly balanced by the enthalpy of a phase change of a contained compound surrounded by a larger reservoir of the same compound used to maintain isothermal conditions in the calorimeter. The latter enthalpy, the measurand, is often displayed indirectly through the change in the volumetric properties of the heat reservoir compound, e.g. ice/water. 

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. 

But what is the magnitude of the lattice enthalpy We cannot measure it directly experimentally, so we measure it indirectly, with a Hess s law energy cycle. The first scientists to determine lattice enthalpies this way were the German scientists Bom and Haber we construct a Born-Haber cycle, which is a form of Hess s-law cycle. 

It is quite difficult to measure an accurate enthalpy of solution A//( olutioni with a calorimeter, but we can measure it indirectly. Consider the example of sodium chloride, NaCl. The ions in solid NaCl are held together in a tight array by strong ionic bonds. While dissolving in water, the ionic bonds holding the constituent ions of Na+ and Cl- in place break, and new bonds form between the ions and molecules of water to yield hydrated species. Most simple ions are surrounded with six water molecules, like the [Na(H20)6]+ ion (VI). Exceptions include the proton with four water molecules (see p. 235) and lanthanide ions with eight. 

Enthalpy of Conformational Transition of a Protein from Indirect Calorimetric Measurements [8]... 

The enthalpy of complexation can be measured directly by reacting the metal and ligand in a calorimeter. It can also be determined indirectly by measuring log at different temperatures and applying the equation... 

Because of the compound s thermal instability, the enthalpy of fusion of peroxydode-canoic acid (perlauric acid) was indirectly determined from freezing point measurements in various solutions. The resulting value, 46.3 0.8 kJmol, is 10 kJmol larger than... 

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