Enthalpies of the Atoms

The group 14 M—M bond enthalpy may also be derived as one-half the enthalpy of the atomization process6... 

The heats of vaporization are measures of the work that must be done to overcome interatomic attractive forces. Since there are no ordinary electron-pair interactions between noble gas atoms, these weak forces (of the van der Waals or London type) are proportional to the polarizability and inversely proportional to the ionization enthalpies of the atoms they increase therefore as the size and diffuseness of the electron clouds increase. 

The stabilities of the Eu2+, Yb2+, and Sm2+ ions correlate with the third ionization enthalpies of the atoms and the sublimation enthalpies of the metals. The Eu2+(aq) ion is readily obtained by reducing Eu3+(aq) with Zn or Mg, while preparation of the others requires use of Na/Hg or electrolysis. The aqueous Eu2+ solutions are easily handled, but those of Sm2+ and Yb2+ are rapidly oxidized by air and by water itself. The Ln2+ ions show many resemblences to Ba2+, giving insoluble sulfates, for example, but soluble hydroxides. Europium can be easily separated from other lanthanides by Zn reduction followed by precipitation of the other Ln3+ hydroxides. 

By convention, the sign of A//° for exothermic reactions (those evolving heat) is negative. Endothermic reactions (those that absorb heat) have a positive A//°. The heat of reaction, A//°, measures the change in enthalpy of the atoms of the reactants as they are converted to products. For an exothermic reaction, the atoms have a smaller enthalpy as products than they do as reactants. For endothermic reactions, the reverse is true. 

Hence we obtain 430 kJ mole for the heat of formation of Br20(g) from atoms. By use of the values of the enthalpy of the atoms relative... 

Obviously sufficient energy is available to break the A1—Cl covalent bonds and to remove three electrons from the aluminium atom. Most of this energy comes from the very high hydration enthalpy of the AP (g) ion (p. 78). Indeed it is the very high hydration energy of the highly charged cation which is responsible for the reaction of other essentially covalent chlorides with water (for example. SnCl ). 

The very low bond dissociation enthalpy of fluorine is an important factor contributing to the greater reactivity of fluorine. (This low energy may be due to repulsion between non-bonding electrons on the two adjacent fluorine atoms.) The higher hydration and lattice enthalpies of the fluoride ion are due to the smaller size of this ion. 

Calculate the bond enthalpy of the C—C bond in ethane using only the enthalpies of atomization of methane and ethane. Compare this result with the accepted result. 

The approximate calculation of the surface energies of metals as a function of crystal structure described earlier uses the enthalpy of sublimation, s, and the co-ordination number to calculate the energy as a function of the atomic concentration on the surface. The atomic areas of the principal configurations are as follows ... 

All the elements have stable electronic configurations (Is or ns np ) and, under normal circumstances are colourless, odourless and tasteless monatomic gases. The non-polar, spherical nature of the atoms which this implies, leads to physical properties which vary regularly with atomic number. The only interatomic interactions are weak van der Waals forces. These increase in magnitude as the polarizabilities of the atoms increase and the ionization energies decrease, the effect of both factors therefore being to increase the interactions as the sizes of the atoms increase. This is shown most directly by the enthalpy of vaporization, which is a measure of the energy required to overcome the... 

As in the preceding transition-metal groups, the refractory behaviour and the relative stabilities of the different oxidation states can be explained by the role of the (n — l)d electrons. Compared to vanadium, chromium has a lower mp, bp and enthalpy of atomization which implies that the 3d electrons are now just beginning to enter the inert electron core of the atom, and so are less readily delocalized by the formation of metal bonds. This is reflected too in the fact that the most stable oxidation state has dropped to +3, while chromium(VI) is strongly oxidizing ... 

In a Born-Haber cycle, we imagine that we break apart the bulk elements into atoms, ionize the atoms, combine the gaseous ions to form the ionic solid, then form the elements again from the ionic solid (Fig. 6.32). Only the lattice enthalpy, the enthalpy of the step in which the ionic solid is formed from the gaseous ions, is unknown. The sum of the enthalpy changes for a complete Born-Haber cycle is zero, because the enthalpy of the system must be the same at the start and finish. 

The valence electron configuration of the atoms of the Group 2 elements is ns1. The second ionization energy is low enough to be recovered from the lattice enthalpy (Fig. 14.18). Flence, the Group 2 elements occur with an oxidation number of +2, as the cation M2+, in all their compounds. Apart from a tendency toward nonmetallic character in beryllium, the elements have all the chemical characteristics of metals, such as forming basic oxides and hydroxides. 

Some of the atomic properties of manganese differ markedly from its neighbors. For example, at constant pressure it takes 400 kj (2 sf) to atomize 1.0 mol Cr(s) and 420 kj to atomize 1.0 mol Fe(s), but only 280 kj to atomize 1.0 mol Mn(s). Propose an explanation, using the electron configurations of the gaseous atoms, for the lower enthalpy of atomization of manganese. 

The steric environment of the atoms in the vicinity of the reaction centre will change in the course of a chemical reaction, and consequently the potential energy due to non-bonded interactions will in general also change and contribute to the free energy of activation. The effect is mainly on the vibrational energy levels, and since they are usually widely spaced, the contribution is to the enthalpy rather than the entropy. When low vibrational frequencies or internal rotations are involved, however, effects on entropy might of course also be expected. In any case, the rather universal non-bonded effects will affect the rates of essentially all chemical reactions, and not only the rates of reactions that are subject to obvious steric effects in the classical sense. 

Molecular mechanics (also known diS force-field calculations) is a method for the calculation of conformational geometries. It is used to calculate bond angles and distances, as well as total potential energies, for each conformation of a molecule. Steric enthalpy can be calculated as well. Molecular orbital calculations (p. 34) can also give such information, but molecular mechanics is generally easier, cheaper (requires less computer time), and/or more accurate. In MO calculations, positions of the nuclei of the atoms are assumed, and the wave equations take account only of... 

Heats of atomization belong to the most important characteristics of ground states. Unfortunately, the number of conjugated radicals for which experimental data are available is very limited. A heat of atomization is defined as the enthalpy of the reaction... 

However, the rate of substitution of pyrrole is too high and that of benzene too low to be followed by standard techniques, and consequently a kinetic study was limited to furan, thiophene, selenophene, and tellurophene. Activation entropies are constant for all four members of the series, indicating that the arrangement of the atoms around the reaction center is similar, i.e., the transition states of all four rings occur at similar positions along the reaction coordinate. The relative rates for the formylation are thus controlled by the activation enthalpies. At 30UC relative rates are furan (107), thiophene (1), selenophene (3.64), and tellurophene (36.8).68... 

The enthalpy of the R02 + RH reaction is determined by the strengths of disrupted and newly formed bonds AH= Z>R H—Droo—h- For the values of O—H BDEs in hydroperoxides, see the earlier discussion on page 41. The dissociation energies of the C—H bonds of hydrocarbons depend on their structure and vary in the range 300 - 440 kJ mol-1 (see Chapter 7). The approximate linear dependence (Polany-Semenov relationship) between activation energy E and enthalpy of reaction AH was observed with different E0 values for hydrogen atom abstraction from aliphatic (R1 ), olefinic (R2H), and alkylaromatic (R3H) hydrocarbons [119] ... 

The ideal solution approximation is well suited for systems where the A and B atoms are of similar size and in general have similar properties. In such systems a given atom has nearly the same interaction with its neighbours, whether in a mixture or in the pure state. If the size and/or chemical nature of the atoms or molecules deviate sufficiently from each other, the deviation from the ideal model may be considerable and other models are needed which allow excess enthalpies and possibly excess entropies of mixing. 

Figure 11.7 shows schematically the resulting calculated variation of H with p for the NaCl-type and the CsCl-type phases of CaO. The NaCl-type structure, which is stable at low pressures, is the rock salt structure in which the Ca and O atoms are 6-coordinate. In the CsCl structure, stable at high pressures, both cation and anion are 8-coordinate. In the static limit where the entropy is set to zero, the thermodynamically most stable phase at any pressure is that with the lowest value of H at the thermodynamic transition pressure, ptrs, the enthalpies of the two phases are equal. For CaO the particular set of potentials used in Figure 11.7 indicates a transition pressure of 75 GPa between the NaCl-type and CsCl-type structures, which compares with experimental values in the range 60-70 GPa. 

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