Cycle Bom Haber

The Bom-Haber cycle is also useful in examining the possibility of forming alkali-metal halides of stoichiometry MX2- The dominant term will clearly be the very large second-stage... 

Only AuF of the gold(I) halides is unknown in the solid state its stability can be examined by means of a Bom-Haber cycle, assuming that it would have an ionic lattice like AgF. (AuF has been generated in the gas phase from Au+ and CH3COF [22].)... 

EXAMPLE 6.13 Using a Bom-Haber cycle to calculate a lattice enthalpy... 

The strength of interaction between ions in a solid is measured by the lattice enthalpy, which can be determined by using a Bom-Haber cycle. 

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. 

The ionic model, developed by Bom, Lande, and Lennard-Jones, enables lattice energies (U) to be summed from inverse square law interactions between spherically symmetrical charge distributions and interactions following higher inverse power laws. Formation enthalpies are related to calculated lattice energies in the familiar Bom-Haber cycle. For an alkali fluoride... 

Extension of the method to nonisostructural metal halides, some of which yield erroneous AHf values via Bom-Haber cycles, is shown in Fig. 1. All curves are nonlinear with the bow increasing in the expected order T1(I) < Pb(II) < Bi(III) < Ag(I). For the first transition metal dihalides, however, straight lines can be drawn within the limits of enthalpy errors except for Zn(II) or Mn(II) salts. Thus heats of formation of the fluorides can be extrapolated linearly from the other three halides to a first approximation. 

P(NH3) at 0 K can be computed from other thermal data through consideration of an appropriate Bom-Haber cycle (aU substances except NH4CI... 

The volatilization process changes the contaminant from a sohd or hquid state, where the molecules are held together by intermolecular forces, into a vapor phase. The molar heats of fusion (A//p, volatilization (AH), and sublimation (AH) are related according to the Bom-Haber cycle by... 

Bom-Fajans-Haber cycle, 22 2, 6 Bom-Haber cycle, 5 6 account of, 1 158-162 Borofluorides, lattice energies of, 1 203 Borohydrides... 

Lattice energies can be related to the heats of formation AH of ionic solids through the Bom-Haber cycle, which is the counterpart of the thermochemical cycle for covalent compounds given in Section 2.7. 

Ion solvation is of vital importance in the dissolution of an electrolyte [2-7]. Figure 2.1 shows the Bom-Haber cycle for the dissolution of a crystalline electrolyte,... 

Thermochemical cycles extend to much less routine applications than those associated with (3.106). As an illustrative example, Sidebar 3.10 summarizes the Bom-Haber cycle, by which a key quantity of ionic lattice theory is obtained from fiendishly indirect thermochemical measurements. 

The initial step (S3.11-2a) is highly endothermic, corresponding to the cohesive energy of the crystal as evaluated by the Bom-Haber cycle (Sidebar 3.10) ... 

Most ot the enthalpies associated with steps in the cycle can be estimated, to a greater or less accuracy, by experimental methods. The lattice energy, however, is almost always obtained theoretically rather than from experimental measurement. It might be supposed that the "enthalpy of dissociation of a lattice coukl be measured in the same way as the enthalpy of atomization of the metal and nonmctal, that is, by heating the crystal and determining how much energy is necessary to dissociate it into ions. Unfortunately, this is experimentally very difficult When a crystal sublimes (AHj), the result is not isolated gaseous ions but ion pairs and other clusters. For this reason it is necessary to use Eq. 4.13 or some more accurate version of It. Wc can then use the Bom-Haber cycle to check the accuracy of our predictions if we can obtain accurate data on every other step in the cycle Values computed from the Bom-Haber cycle are compared with those predicted by Eq. 4.13 and its modifications in Table 4.3. 

In summary, in addition to allowing simple calculations of the energetics of ionic compounds, the Bom-Haber cycle provides insight into the energetic factors operating. Furthermore, it is an excellent example of the application of thermodynamic methods to inorganic chemistry and serves as a model for other, similar calculations not only for solids, but also for reactions in solution and in the gas phase. 

One additional term occurs ui this Bom-Haber cycle the formation of the tetra-fluoroborate ion in the gas phase ... 

Note that the proton affinity (PA) has the opposite sign from the enthalpy of reaction of Eq. 9.47 Proton affinities are always listed as positive numbers despite referring to exothermic reactions (recall the same convention with electron affinities. Chapter 3) Proton affinities may be obtained in a number of ways. The simplest, and most fundamental for defining an absolute scale of proton affinities, is to use a Bom-Haber cycle of the sort ... 

Show your understanding of the Bom-Haber cycle by calculating the heat oF Formation of potassium fluoride analogous to the one in the text for sodium chloride. 

Using any necessary data from appropriate sources, predict the enthalpy of formation of KCI by means of a Bom-Haber cycle. You can check your lattice energy against Table 4.3. 

II should be noted lhat the proton affimlies of aD of the irinegatrve and dinegative anions are calculated by means of a Bom-Haber cycle. They are not experimentally accessAle a nee these ions have no existence outside of a stabilizing crystal environment—they would exothermcally expel an electron (see Chapter 2). 

Using a Bom-Haber cycle. cleBtiy show all of the terms that one should evaluate in considering the energetics involved in transferring the competition fas given by the enthalpy of reaction) ... 

Using a Bom-Haber cycle employing the various energies contributing to the formation of M+, e(NHj)J species in ammonia solutions, explain why such solutions form only with the most active metals. 

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