Born-Haber cycle A thermodynamic

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 ... 

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. 

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)... 

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. 

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 Born-Haber cycle and thermodynamic quantities that can be measured directly. 

The enthalpy of formation of a compound is a so-called thermodynamic state function, which means that the value depends only on the initial and final states of the system. When the formation of crystalline NaCl from the elements is considered, it is possible to consider the process as if it occurred in a series of steps that can be summarized in a thermochemical cycle known as a Born-Haber cycle. In this cycle, the overall heat change is the same regardless of the pathway that is followed between the initial and final states. Although the rate of a reaction depends on the pathway, the enthalpy change is a function of initial and final states only, not the pathway between them. The Born-Haber cycle for the formation of sodium chloride is shown as follows ... 

Before considering further the thermodynamic nature of particular macrocyclic effects, it is necessary to consider the various components of a typical complexation reaction. These are best illustrated by the Born-Haber cycle illustrated in Figure 6.1. Each of the steps 1-5 has a AG, AH and a A5 term associated with it and the overall values of these parameters reflect the respective sums of the individual components. To understand fully the nature of a particular macrocyclic effect, it is necessary to have data available for each of these steps for both the macrocyclic system and open-chain (reference) system. Although some progress has been made... 

The initiation of the cationic polymerisation of alkenes is examined in detail by means of simple thermodynamic concepts. From a consideration of the kinetic requirements it is shown that the ideal initiator will yield a stable, singly charged anion and a cation with a high reactivity towards the monomer by simple, well defined reactions. It must also be adequately soluble in the solvent of choice and for the experimental method to be used. The calculations are applied to carbocation salts as initiators and a method of predicting their relative solubilities is described. From established and predicted data for a variety of carbocation salts the position of their ion molecule equilibria and their reactivity towards alkenes are examined by means of Born-Haber cycles. This treatment established the relative stabilities of a number of anions and the reason for dityl, but not trityl salts initiating the polymerisation of isobutene. 

In principle, we can use the Born-Haber cycle to predict whether a particular ionic compound should be thermodynamically stable, on the basis of calculated values of U, and so proceed to explain all of the chemistry of ionic solids. The relevant quantity is actually the free energy of formation, AGf, and this is calculable if an entropy cycle is set up to complement the Born-Haber enthalpy cycle. However, in practice AHf dominates the energetics of formation of ionic compounds. 

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. 

Hess s law states that the enthalpy of a reaction is the same whether the reaction takes place in one or several steps it is a necessary consequence of the first law of thermodynamics concerning the conservation of energy. If this were not true, one could manufacture energy by an appropriate cyclic la-ocess. Bom and Haber applied Hess s law to the enthalpy of formation of an ionic soHd. For the formation of an ionic crystal from the elements, the Born-Haber cycle may most simply be depicted as... 

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. 

A further example considers the possible formation of CaF (in contrast to the more usual Cap2). Here, a simple Born-Haber cycle is not helpful since CaF is not thermodynamically unstable with respect to decomposition into its constituent elements, but is unstable with respect to disproportionation (equation 5.24). 

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 Born-Haber cycles. In such a reaction as 16.16, if the... 

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... 

An alternate method is to make use of the first law of thermodynamics, namely, that energy can be neither created nor destroyed. If a cycle can be devised where all the energies are known except -Fiatt, then it can be easily calculated. For such a cycle, known as the Born-Haber cycle, shown in Fig. 2.6, it is necessary that... 

Born-Haber cycles have been used by Passmore et al. to rationalize the thermodynamic stability of a large number of AsF6 salts of cluster cations. The calculations correctly predict the stability of most characterized compounds and also give indications that some compounds, which never have been synthesized in spite of great efforts eg. AsFe salts of monoatomic halogen cations), are unstable. This success confirms the argument that the formation of sub-valent cations is mainly enthalpy driven and that a Coulombic treatment of their solid compounds often is a reasonable approximation. 

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... 

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... 

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