Lattice Energy Thermodynamic Cycles

We would like to compare the preceding calculated values of lattice energies with those derived from experiment. Unfortunately, the lattice energy corresponding to the forward reaction shown in Equation (8.12) cannot be directly measured because it is not possible to produce isolated gaseous ions. 

The vaporization of an ionic solid results in ion pairs and other more complicated aggregates. If a direct measurement of lattice energy is not possible, how can we confirm or disprove the results of the Born-Lande (or the Kapustinskii) equation The answer lies in thermodynamic cycles. 

The Born-Haber cycle for an alkali-metal halide. 

Equation (8.13) corresponds to the standard enthalpy of formation of MX(s). The equations in the box represent a second pathway for the formation of MX(s) from its constituent elements. Equation (8.14) represents Hess s law of summation for these two pathways. 

IE = ionization energy of M AHg = enthalpy of formation of gaseous X EA = electron affinity of X f/B = lattice energy of MX 

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Born-Haber cycle A thermodynamic cycle derived by application of Hess s law. Commonly used to calculate lattice energies of ionic solids and average bond energies of covalent compounds. E.g. NaCl ... 

An important property of an ionic crystal is the energy required to break the crystal apart into individual ions, this is the crystal lattice energy. It can be measured by a thermodynamic cycle, called the Born-Haber cycle. 

One problem which is of great interest and which has not been tackled directly because of the great instability of the obvious substrate is the electron affinity of the hydroxyl radical. Lattice energy calculations, and thermodynamic cycles, can be made consistent with any value between 40 and 70 kcal., as can the electron transfer spectra. Some years ago the author interpreted a number of microwave studies of flames as indicating an electron affinity of hydroxyl of 62... 

Quite apart from its theoretical calculation, by the use of one of the expressions developed above, it is possible to relate the lattice energy of an ionic crystal to various measurable thermodynamic quantities by means of a simple Hess s law cycle. This cycle was first proposed and used by Bom 15) and represented in its familiar graphical form by Haber (45). It is now usually referred to as the Born-Haber cycle. The cycle is given below for a uni-univalent salt in terms of enthalpies. 

Ionic lattice energies are measured experimentally by means of a thermodynamic cycle developed by Max Born and Fritz Haber. The Born-Haber cycle is an application of Hess s law (the first law of thermodynamics). It is illustrated by a determination of the lattice energy of sodium chloride, which is A for the reaction... 

Lattice energies may be estimated from a thermodynamic cycle known as a Born-Haber cycle, which makes use of Hess Law (see Topic B3Y Strictly speaking, the quantities involved are enthalpy rather than energy changes and one should write HL for the lattice enthalpy. From Fig. 1. 

The heats of formation of various ionic compounds show tremendous variations. In a general way, we know that many factors contribute to the over-all heat of formation, namely, the ionization potentials, electron affinities, heats of vaporization and dissociation of the elements, and the lattice energy of the compound. The Born-Haber cycle is a thermodynamic cycle that shows the interrelation of these quantities and enables us to see how variations in heats of formation can be attributed to the variations in these individual quantities. In order to construct the Born-Haber cycle we consider the following thermochemical equations, using NaCl as an example... 

The thermodynamic cycle shown in Eqn. 59 allows a discussion of the solubilities of ionic salts, where AG and AG are the free energy changes associated with the sublimation of the lattice into the separate gaseous ions at a standard state and the... 

Born-Haber cycle - A thermodynamic cycle in which a crystalline solid is converted to gaseous ions and then reconverted to the solid. The cycle permits calculation of the lattice energy of the crystal. 

The Born-Haber (Born, 1919 Haber, 1919) cycle shows the relationship between lattice energy and other thermodynamic quantities. It also allows the lattice energy to be calculated. The background of the Born-Haber cycle is Hess s law, which states that the enthalpy of a reaction is the same whether the reaction proceeds in one or several steps. The Born-Haber cycle for the formation of an ionic compound is shown in Figure 4.6. It is a necessary condition that... 

As an example of using the Born-Haber cycle we will calculate the lattice energy of MgO. The values of the various thermodynamic parameters can be found in Kubaschewski et al. (1993), Johnson (1982), and in the NIST-JANAF tables (Chase, 1998). 

Born-Haber cycle A thermodynamic cycle based on Hess s law that relates the lattice energy of an ionic substance to its entha y of formation and to other measurable quantities. (Section 8.2)... 

For metals exhibiting variable oxidation states, the relative thermodynamic stabilities of two ionic halides that contain a common halide ion but differ in the oxidation state of the metal (e.g. AgF and AgF2) can be assessed using Bom Haber cycles. In such a reaction as 17.19, if the increase in ionization energies (e.g. M — M versus M— M +) is approximately offset by the difference in lattice energies of the compounds, the two metal halides will be of about equal stability. This commonly happens with block metal halides. 

The lattice energies for a variety of mineral and syntetic complex compounds that can be classified as double salts, were calculated by summing the lattice energies of the constituent simple salts [268]. A comparison with the lattice energies obtained from the Born-Haber or other thermodynamic cycles using the Madelung constant or... 

Lattice energy is the amount of energy required to convert a mole of ionic solid to its constituent ions in the gas phase. Lattice energy cannot be measured directly, but is determined using the Bom-Haber cycle and thermodynamic quantities that can be measured directly. 

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