Born-Haber cycle applications. 197-8

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 ... 

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. 

In fact, it may be impossible to measure the heat associated with an atom gaining two electrons, so the only way to obtain a value for the second electron affinity is to calculate it. As a result, the Born-Haber cycle is often used in this way, and this application of a Born-Haber cycle will be illustrated later in this chapter. In fact, electron affinities for some atoms are available only as values calculated by this procedure, and they have not been determined experimentally. 

A Born-Haber cycle is the application of Hess s Law to the enthalpy of formation of an ionic solid at 298 K. Hess s law states that the enthalpy of a reaction is the same whether the reaction takes place in one step or in several. A Born-Haber cycle for a metal chloride (MCI) is depicted in Figure 1.56 the metal chloride is formed from the constituent elements in their standard state in the equation at the bottom, and by the clockwise series of steps above. From Hess s law, the sum of the enthalpy changes for each step around the cycle can be equated with the standard enthalpy of formation, and we get that ... 

The knowledge of the relative stability of oxidation states, i.e., redox potentials, is very important for a chemical application. Trends in the stability of various oxidation states of the very heavy elements were predicted earlier on the basis of atomic relativistic DF and DS calculations in combination with some models based on a Born-Haber cycle (see [12]). The conclusions were, however, not always unanimous and varied depending on the model. Later, this topic received a more detailed consideration... 

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... 

By considering the definition of lattice energy, it is easy to see why these quantities are not measured directly. However, an associated lattice enthalpy of a salt can be related to several other quantities by a thermochemical cycle called the Born-Haber cycle. If the anion in the salt is a haUde, then all the other quantities in the cycle have been determined independently the reason for this statement will become clearer when we look at applications of lattice energies in Section 5.16. 

Worked example 5.5 Application of the Born-Haber cycle... 

Thermodynamic cycles are applications of Hess s law, which states that the total enthalpy change for (or heat of) a reaction is independent of the pathway followed from reactants to products. Max Born and Fritz Haber applied Hess s law to an ionic solid in 1917. The Born-Haber cycle for a general alkali-metal halide (M X) is shown in Figure 8.5. Equation (8.13) at the top of the cycle shows the formation of MX(j) from its constituent elements in their standard states and therefore corresponds to the standard enthalpy of formation. The reactions in the box of the figure... 

Also listed in the table is the lattice energy, f/pop obtained from the application of the Born - Fajans - Haber cycle (BHFC) described below, using the Standard Thermochemical Properties of Chemical Substances table in Section 5 of this Handbook, References 1 through 4, and certain otha- data which are given in Table 3 below. 

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