Sodium chloride Born-Haber cycle

Let us consider the formation of sodium chloride from its elements. An energy (enthalpy) diagram (called a Born-Haber cycle) for the reaction of sodium and chlorine is given in Figure 3.7. (As in the energy diagram for the formation of hydrogen chloride, an upward arrow represents an endothermic process and a downward arrow an exothermic process.)... 

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 ... 

Figure 3.8 Born-Haber cycle constructed to obtain the lattice enthalpy A//(E, lce) of sodium chloride. All arrows pointing up represent endothermic processes and arrows pointing down represent exothermic processes (the figure is not drawn to scale)...

The electron affinities of elements (Chap, 7) that form negative ions may be calculated by considering the formations of compounds containing such negative ions. The formation of such a compound from the elements (the heat of such a reaction being directly measurable) may be broken down into a series of simpler steps. The treatment is again called a Born-Haber cycle and is analogous to the treatment of the conversion of an alkali metal to its hydrated ion (discussed in Chap. 6). Consider the formation of sodium chloride from the elements ... 

Experimental Born-Haber cycle for sodium chloride. The experimental binding energy AH = —8.0 eVis reasonably close to the Madelung energy Em= -8.923446 eV (after one adds to Em a relatively small ad hoc positive rep). 

The oxides of the alkaline earth metals crystallize in a sodium chloride lattice although in SrO and BaO the radius ratio is greater than 0 732. It has been proposed that the crystals are constructed from the ions M + and the electron affinity of the oxygen atom calculated on this assumption by the Born-Haber cycle for the different oxides give rather... 

In the sulphides, selenides, tellurides and arsenides, all types of bond, ionic, covalent and metallic occur. The compounds of the alkali metals with sulphur, selenium and tellurium form an ionic lattice with an anti-fluorite structure and the sulphides of the alkaline earth metals form ionic lattices with a sodium chloride structure. If in MgS, GaS, SrS and BaS, the bond is assumed to be entirely ionic, the lattice energies may be calculated from equation 13.18 and from these values the affinity of sulphur for two electrons obtained by the Born-Haber cycle. The values obtained vary from —- 71 to — 80 kcals and if van der Waal s forces are considered, from 83 to -- 102 kcals. 

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... 

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

The enthalpy changes described can be used to construct a Born-Haber cycle for sodium chloride (Figure 15.13). The Born-FIaber cycle can be used to calculate an individual enthalpy change if all the others are known. The unknown value is usually the lattice enthalpy. 

Using the data given below (all values are in kJ/mol) and Born-Haber cycles for the formation of both the hydride and the chloride of sodium, calculate the standard heats of formation in each case. Which type of compound is more stable Briefly discuss the principal reasons for the differences in stabilities as measured by the standard heat of formation. Would you expect differences in entropy of formation to change your conclusions ... 

M FIGURE 9.4 Born-Haber Cycle for Sodium Chloride The sum of the steps is the formation of NaCl from elemental Na and CI2. The enthalpy change of the last step is the lattice energy. 

The lattice energy may be determined experimentally from thermochemical data by considering a suitable cycle of changes (Born and Haber, 1919). The cycle for formation of sodium chloride is ... 

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