Ionisation enthalpies,

The sign of the RT term is opposite to that in the corresponding equation which converts ionisation energies into enthalpies. In a thermochemical analysis involving ionisation enthalpies, electron attachment enthalpies are sure to occur also, unless electrons are to appear in the overall... 

The first of these involves the removal of two electrons from zinc atoms in the gas phase, and A/f° for the process will be equal to the sum of the first and second ionisation enthalpies of Zn(g), designated /, and /2 respectively. For the second process, AH° will be equal to twice the electron attachment enthalpy of H+(g) (which is the same as —21, where / is the ionisation enthalpy of atomic hydrogen). Obviously, we could use ionisation and electron attachment energies (instead of enthalpies), without correction for the RT terms which cancel out when we sum up the enthalpy changes for all the steps in the analysis. Thus for the process ... 

The Principle of Hard and Soft Acids and Bases states that hard acids form more stable complexes with hard bases and soft bases form more stable complexes with soft acids. In orbital terms hard molecules have a large gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and soft molecules have a small HOMO-LUMO gap. In recent years it has been possible to correlate the hardness with the electronic properties of the atoms involved. Thus, if the enthalpy of ionisation (I) and the electron affinity (A) are known the so-called absolute hardness (t ) and absolute electronegativity (%) can be found from r = (I - A) / 2 and % = (I + A) / 2. For example, the first and second ionisation enthalpies of sodium are 5.14 and 47.29 eV. Thus for Na+, I = + 47.29 and A = + 5.14, so r = (47.29 - 5.14) / 2 = 21.1. Similarly for silver the first and second ionisation enthalpies are 7.58 and 21.49eV, so for Ag+ we have, n = (21.49 - 7.58) 12 = 6.9. 

Table Properties of alkali metals melting and boiling points, atomisation and ionisation enthalpies, ionic and standard electrode potentials...

To date there is no evidence that sodium forms any chloride other than NaCl indeed the electronic theory of valency predicts that Na" and CU, with their noble gas configurations, are likely to be the most stable ionic species. However, since some noble gas atoms can lose electrons to form cations (p. 354) we cannot rely fully on this theory. We therefore need to examine the evidence provided by energetic data. Let us consider the formation of a number of possible ionic compounds and first, the formation of sodium dichloride , NaCl2. The energy diagram for the formation of this hypothetical compound follows the pattern of that for NaCl but an additional endothermic step is added for the second ionisation energy of sodium. The lattice energy is calculated on the assumption that the compound is ionic and that Na is comparable in size with Mg ". The data are summarised below (standard enthalpies in kJ) ... 

Ah second ionisation energy for sodium (additional) +4561 A/13 enthalpy of atomisation of chlorine, x 2 (since two... 

This is an exothermic process, due largely to the large hydration enthalpy of the proton. However, unlike the metallic elements, non-metallic elements do not usually form hydrated cations when their compounds dissolve in water the process of hydrolysis occurs instead. The reason is probably to be found in the difference in ionisation energies. Compare boron and aluminium in Group III ... 

The enthalpy changes AH involved in this equilibrium are (a) the heat of atomisation of the metal, (b) the ionisation energy of the metal and (c) the hydration enthalpy of the metal ion (Chapter 3). 

Heat of atomisation Sum of 1st and 2nd ionisation energies Hydration enthalpy AH... 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

Potzinger and coworkers determined ionisation and appearance energies for the molecular and major fragment ions of several dialkylsulfoxides, R SOR (R =Me R = Me, Et, i-Pr, and i-pentyland R = R = Et or i-Pr). In addition to the evaluation of dissociation energies in the ions and their enthalpies of formation, a value of 280 + 30kJmol" for the C—S dissociation energy in neutral dialkyl sulfoxides was derived. 

Because strong acids and strong alkalis are almost completely ionised, the standard enthalpy of neutralisation is the enthalpy change for the reaction ... 

If a weak acid or weak alkali is used (or both are weak), the standard enthalpy of neutralisation is generally less exothermic. This is because heat energy is required to ionise a weak acid or base. 

The second-order rate-constants kp and kA for polymerisations in solution which we consider reliable are summarised in Table 12. The initiators used by the various investigators have not been listed, because by definition kp and Ep must be independent of these and there are insufficient data to permit any firm conclusions about the effects of the nature of the anion on and E. When considering the rate-constants in this Table it must be remembered that all of them, except those for isobutene, probably comprise a contribution from the polymer-complexed cation, p+p, greater or smaller according to circumstances (see Section 2.3), and correspondingly the activation energies would contain a term Ep+P and an enthalpy of complexation further, for the reason explained in Section 4.1.9, the kp from ionising radiation experiments are minimum values. 

One advantage of ionisation energy as opposed to ionisation potential is its applicability in thermochemical arguments, where we may be performing an energetic analysis of some reaction. Here, we are dealing with substances and the appropriate unit is kJ mol-1. Usually, however, we want enthalpy changes AH° at 25 °C, rather than AU° at absolute zero. For the process ... 

The RT term amounts to 6.2n kJ mol-1 at 25 °C. This is small in relation to ionisation energies/enthalpies but is often far from trivial in thermodynamic arguments. However, it is rarely necessary to convert ionisation energies into enthalpies because, as we shall presently see, the RT terms ultimately cancel out. A number of tabulations of thermochemical data give enthalpies (or heats) of formation for ions in the gas phase these include the RT correction. 

AH° is equal to the sum of the appropriate ionisation and electron attachment energies and the corresponding enthalpies need not be explicitly considered. Throughout this book, ionisation and electron attachment energies may, where appropriate, masquerade as enthalpies on the understanding that the RT corrections which ought to have been made ultimately cancel. 

The atomisation enthalpy of elemental sodium Afl%tom, the first ionisation energy of atomic sodium Iu the dissociation enthalpy D of gaseous chlorine, the electron attachment energy Ex of atomic chlorine and the enthalpy of formation A//)1 of crystalline sodium chloride can all be taken from standard tabulations of experimental data. An experimental lattice energy UL is thus given by ... 

Evidently the most - practically the only - stable oxidation state of La in ionic compounds is III. Does this hold for the later members of the lanthanide series Fig. 5.1 suggests that the I oxidation state has little prospect of stability, given the high atomisation enthalpies and the relatively low second and third ionisation energies. The II oxidation state has better prospects, however. Consider the disproportionation ... 

Thus the higher I3 of Eu is mainly responsible for the limited stability of its II oxidation state, although the lower atomisation enthalpy helps as well. As shown on Fig. 5.2, the third ionisation energy follows the sequence ... 

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