Enthalpy cycles

Typical elements in Groups V. VI and VII would be expected to achieve a noble gas configuration more easily by gaining electrons rather than losing them. Electron affinity is a measure of the energy change when an atom accepts an extra electron. It is difficult to measure directly and this has only been achieved in a few cases more often it is obtained from enthalpy cycle calculations (p. 74). 

Fig. 2. Enthalpy cycle for formation of AB(solri from A(solv) + B(solv)...

Clearly, one should not use tabulated bond energy data for polyatomic molecules without knowing whether they are mean bond energies or bond dissociation energies. In any event, the relationship with the heat of formation of CH4 can be illustrated by an enthalpy cycle ... 

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. 

Radical heats of formation are defined in the usual way, that is, as enthalpy of formation of the radical in question from the elements in their standard states. The heats of formation and the bond dissociation energies are derivable from each other and are based on the same data. Thus, in Reaction 9.7, the heat of formation of R- is readily found from the bond dissociation energy by means of the enthalpy cycle shown in Scheme 3 if heats of formation of R—X and X are known conversely, D( R—X) may be found once heats of formation of RX, R-,... 

The effectiveness of xenon difluoride as an oxidative fluorinator in the presence of fluoride ion acceptors is probably due to the formation of [XeF]+ or [XejFj]. The electron affinity of the cation, E[XeF+fg)] is estimated from the following enthalpy cycle ... 

The polarographic behaviour of AgClO has been investigated in anhydrous DMSO, DMF, MeCN, PhCN, PhN02, and other solvents. The half-wave potential was observed to be related to the donicity of the solvents, unless specific cation-solvent interactions occur. A re-investigation of the thermal decomposition of the dioxan complex AgC104,3L has enabled the construction of an enthalpy cycle in which dioxan complexes are favoured only if the lattice energy of the complex exceeds that of the parent AgX salt plus the heat of vaporization of dioxan. ... 

We can calculate the enthalpy change of reaction by using the type of enthalpy cycle shown in Figure 6.8. 

Figure 6.8 An enthalpy cycle for calculating an enthalpy change of reaction. The dashed line shows the indirect (two-step) route.

We can illustrate Hess s law by drawing enthalpy cycles (Hess cycles). In Figure 6.7, the reactants A and B combine directly to form C. This is the direct route. 

Figure 6.9 The enthalpy cycle for the decomposition of sodium hydrogencarbonate. The dashed line shows the two-step route.

The enthalpy cycle for calculating the enthalpy of hydration of anhydrous sodium thiosulfate is shown in Figure 6.13. 

We can, however, use an enthalpy cycle to calculate this. We use the standard enthalpy changes of solution to complete the enthalpy cycle (Figure 6.12). 

We cannot usually find the value of bond energies directly so we have to use an enthalpy cycle. The average bond energy of the C—H bond in methane can be found using the enthalpy changes of atomisation of carbon and hydrogen and the enthalpy change of combustion or formation of methane. 

The enthalpy cycle for this reaction is shown in Figure 6.16. The relevant bond energies are ... 

We have seen how we can apply Hess s law in energy cycles to work out enthalpy changes (page 97). A Born-Haber cycle is a particular type of enthalpy cycle used to calculate lattice energy. In simple terms it can be represented by Figure 19.2. 

Taking lithium fluoride as an example, the relevant enthalpy cycle can be written to show these steps (Figure 19.3). 

Figure 19.10 An enthalpy cycle involving lattice energy, enthalpy change of hydration and enthalpy change of solution.

Draw an enthalpy cycle to calculate the enthalpy of hydration of magnesium ions when magnesium chloride dissolves in water. 

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