P.A. Cox - Inorganic chemistry (793955), страница 21
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So in [Pb5]2− there are 22 valence electrons, 10 used in lone-pairs, hence 12 forskeletal bonding: a closo structure is expected, as found (4). In [Sn9]4− a similar count gives 22 skeletal bondingelectrons, corresponding to 2n+4 and hence the nido structure observed (7). It should be noted that there areexceptions. Extension to transition metal clusters needs to accommodate the d bonding electrons, and leads to theWade-Mingos rules.Section C—Structure and bonding in moleculesC8BOND STRENGTHSKey NotesBond enthalpiesMajor trendsPaulingelectronegativityUses and limitationsOther measuresRelated topicsMean bond enthalpies are defined as the enthalpy changes involved inbreaking bonds in molecules.
They may be determined fromthermochemical cycles using Hess’ Law, although assumptions oftransferability are sometimes required.Stronger bonds are generally formed with lighter elements in a group,when multiple bonding is present, and when there is a largeelectronegativity difference between the two elements. The‘anomalous’ weakness of single bonds involving N, O and F is oftenattributed to repulsion between nonbonding electrons. C, N and Oform especially strong multiple bonds.The Pauling electronegativity scale is derived using an empiricalrelationship from bond enthalpies.
For elements forming covalentbonds, it correlates fairly well with other scales.Quantitative uses of bond energies are of very limited accuracy, butqualitative comparisons can be useful in interpreting trends in thestructures and stability of covalent substances.Bond lengths, and spectroscopically measured stretching frequencies,are also useful comparative measures of bond strength.Electronegativity and bondIntroduction to nonmetalstype (B1)(F1)Methods of characterization(B7)Bond enthalpiesThe most straightforward measure of the strength of a bond is the energy required to break it.
Estimates of such bondenergies are normally obtained from thermochemical cycles using Hess’ Law (see Topic B3) and are called bondenthalpies. A bond dissociation enthalpy is the enthalpy change involved in breaking the bond to one atom in amolecule, and in a diatomic is by definition equal to the bond enthalpy.
Thus the enthalpy of dissociation of O2 givesdirectly the (double) bond enthalpy B(O=O).When a molecule contains several equal bonds, the enthalpy required to dissociate them successively is not the same.Instead of dealing with individual bond dissociation energies, it is normal to define the mean bond enthalpy. Thus B(O—H) is defined as half the enthalpy change in the process88SECTION C—STRUCTURE AND BONDING IN MOLECULESWhen several types of bonds are involved it is necessary to make assumptions about the energies of some of them.
Forexample, it is normal to assume that thevalue of B(O—H) obtained from H2O can also be applied to H2O2. Then forthe processwe havefrom which the (single) bond enthalpy B(O—O) can be obtained. This quantity is not the same as ΔH for thedissociation of H2O2 into 2OH, as it is argued that the bonding in the hydroxyl radical OH has changed from the‘normal’ situation where oxygen forms two bonds.
The assumption of transferability involved in this method ofdetermining bond enthalpies is, however, open to question (see below).Major trendsA selection of single bond enthalpies is shown in Table 1. Some important trends are summarized below.(i) Bond energies often become smaller on descending a main group (e.g. C—H >Si—H>Ge—H).
This is expectedas electrons in the overlap region of a bond are less strongly attracted to larger atoms. Some important exceptionsare noted in (v) and (vi) below, and the reverse trend is generally found in transition metal groups (see Topic H1).(ii) Bond energies increase with bond order, although the extent to which B(A=B) is larger than B(A—B) dependsgreatly on A and B, the largest differences occurring with elements from the set C, N, O (see Table 2). Strongmultiple bonding involving these elements may be attributed to the very efficient overlap of 2pπ orbitals comparedwith that of larger orbitals in lower periods.(iii) In compounds ABn with the same elements but different n values, B(A—B) decreases as n increases (e.g. in thesequence ClF>ClF3>ClF5).
The differences are generally less for larger A, and more electronegative B.(iv) Bonds are stronger between elements with a large electronegativity difference. This forms the basis for thePauling electronegativity scale (see below).(v) Single A—B bonds where A and B are both from the set N, O, F are weaker than expected from groupcomparisons. This is often attributed to a repulsion between nonbonding electrons, although as in othercases of ‘electron repulsion’ the effect may be attributed to the Pauli exclusion principle more than to electrostaticrepulsion (see Topic C2).(vi) Other exceptions to rule (i) above occur with A-O and A-X bonds (X being a halogen), which generally increase instrength between periods 2 and 3 (e.g.
C-O<Si-O). This may be partly due to the increased electronegativitydifference when A is period 3 (see (iv) above), but repulsion between lone-pairs electrons on nonbonded atomsmay also play a role (e.g. F-F repulsion in CF4, where the atoms are closer together than in SiF4).C8—BOND STRENGTHS89Table 1. A selection of single-bond AB enthalpies (kJ mol−1)Table 2. Variation in bond enthalpy (kJ mol−1) with bond orderPauling electronegativityPauling noted that B(A-B) is nearly always larger than the mean of the homonuclear A-A and B-B bond energies, andattributed this to the possibility of ionic-covalent resonance involving valence structures such as A+B− when B is themore electronegative atom. He related the bond strengths to the electronegativities xA and xB of the two elementsaccording to the formulawhere the constant C takes the value 96.5 if B values are in kj mol−1.
As this formula depends only on the difference ofelectronegativities, it is necessary to choose one value to start the scale; Pauling chose 4.0 for the electronegativity offluorine.Pauling’s formula should be regarded as purely empirical and without any rigorous theoretical foundation.Nevertheless, the electronegativity scale is widely used, and shows the same trends as ones based more directly on atomicquantities (see Topic B1). Pauling’s formula provides a useful rationalization of some bond-strength trends, and can beused as a semiquantitative guide for estimating unknown bond enthalpies.
It should not be used for solids with a highdegree of ionic character, as these are best interpreted using lattice energies (see Topic D6).90SECTION C—STRUCTURE AND BONDING IN MOLECULESUses and limitationsTabulated values of bond enthalpies can be used to estimate the enthalpy of formation of hypothetical compounds. Suchestimates should be regarded as rough and not quantitatively reliable, as the assumptions of additivity and transfer abilitythat underlie these calculations are not accurate.Trends in stability or structure of related compounds can often be usefully rationalized from bond strength trends.The decline in B(E-H) as a main group is descended leads to reduced thermodynamic stability of hydrides EHn (seeTopic F2).
Double-bonded structures are much commoner with the elements C, N and O than with others in the samegroup. The stability of O2 (double bonds) versus S8 (single bonds) can be rationalized from the fact that B(O=O) ismore than twice as large as B(O-O) but the same is not true of sulfur.
In a similar way we have CO2 (molecular withC=O) and SiO2 (polymeric with single Si-O). The formation of multiple bonds is one of the main factors leading todifferences in chemistry between 2p series elements and those in lower periods (see Topic F1).Changes with valence state are important in understanding the stability of ‘hypervalent’ compounds. Thus SH4 andSH6 are unknown, whereas they would be thermodynamically stable compounds if their S-H bonds were as strong as inH2S.
The common formation of fluorides in high valency states (e.g. SF6, IF7) can be understood from a combination offactors. The F-F bond is itself rather weak, E-F bonds are generally strong, and they decline less rapidly with increasingn in EFn molecules than in other compounds.Other measuresThermochemical bond energies may be hard to determine, either for experimental reasons or because of the limitationsin the assumption of transferability that is often required.
Alternative measures of comparative bond strength that areoften useful include the following:• the bond length, which for a given pair of elements decreases with increasing strength (e.g. with increasing bondorder, as in the sequence N-N 145 pm, N=N 125 pm, N≡N 110 pm); bond length measurements are often usefulfor showing the existence of metal-metal bonds in transition metal compounds (see Topic H5);• the bond stretching frequency measured by vibrational spectroscopy (e.g. IR, see Topic B7) is related to thestretching force constant and increases with bond strength; IR measurements have been particularly useful inthe study of CO as a ligand in transition metal carbonyl compounds (Topic H9).Section C—Structure and bonding in moleculesC9LEWIS ACIDS AND BASESKey NotesDefinition and scopeModels of interactionHard-soft classificationPolymerizationRelated topicsA Lewis acid (or acceptor) can accept an electron pair from a Lewisbase (or donor) to form a donor-acceptor complex.
The formation ofsolvated ions, complexes in solution and coordination compounds areexamples of this type of interaction.Contributions to the donor-acceptor interaction may come fromelectrostatic forces, and from the overlap between the highestoccupied MO (HOMO) of the donor and the lowest unoccupied MO(LUMO) of the acceptor.Hard donors interact more strongly with hard acceptors, soft donorswith soft acceptors. Harder acids tend to be more electropositive, andharder bases more electronegative. Softer donor and acceptor atomstend to be larger and more polarizable.Formation of dimers and polymeric structures is a manifestation ofdonor-acceptor interaction between molecules of the same kind.Solvent types and propertiesBrønsted acids and bases (E2)(E1)Complex formation (E3)Definition and scopeA Lewis acid is any species capable of accepting a pair of electrons, and a Lewis base is a species with a pair ofelectrons available for donation.
The terms acceptor and donor are also commonly used. Lewis acids include H+ andmetal cations, molecules such as BF3 with incomplete octets, and ones such as SiF4 where octet expansion is possible(see Topic C1). Any species with nonbonding electrons is potentially a Lewis base, including molecules such as NH3 andanions such as F−.
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