Electronegativities of the Noble Gases Terry L. Meek University of the West Indies, Cave Hill, Barbados The electronegativities of the noble gas atoms were evaluated in 1980 by Allen and Huheey (1)by applying a variety of extrapolation procedures to four different electrouegativity scales: Allred-Rochow (21, Mulliken (31, Pauling (4), and Sanderson (5). Since then the Mulliken scale has been elaborated to allow the assessment of valence-state electronegativities for the main group elements (6). The Sanderson scale has been revised (71,and Allen has devised a new scale based on the average oue-electron energy of valence electrons (8).Thus, it may be useful to re-examine this topic. In this paper, the covalent radii of the noble gas atoms are estimated by extrapolation of those of other elements in the period and are used in the appropriate equations to calculate electronegativities on the Allred-Rochow and (revised) Sanderson scales. Values for krypton and xenon on the Pauling scale are recalculated using Pauling's original equation (4a). Finally, a new method is suggested for calculation of the Mulliken valence-state electronegativities of noble gas atoms in the "12.5% s" state proposed by Bratsch (6). Values obtained by these methods are listed in Table 1, along with those given in ref 1and elsewhere, and corresponding values for the halogens and hydrogen. Covalent radii extrapolated for the noble gas atoms are also listed.
where bond energies are in kJ mol-'and DAA= 0, to obtain the tabulated electronegativities. The other frequently cited equation
Allred-Rochow, Sanderson, and Allen (Spectroscopic) Scales In all of these, as noted by Allen and Huheey for the first two, there is a steady increase in eledronegativity across each period, and the trend continues through to the noble gases. In both the Allred-Rochow and Sanderson scales, the electronegativity calculated for helium is uncertain
gives negative values for the term in parentheses, defined by Pauling as ionic resonance energy, for krypton difluoride.
due to the difficulty of estimating a covalent radius. The Allred-Rochow relationship
gives XH* = 6.32 using r = 30 pm and 4.85 for r = 35 pm. Allen and Huheey extrapolated the helium radius to r = 32.5 pm. The Sanderson Equation Xr3= constant = 84,900 for hydrogen (and helium)
(2)
gives values of 3.14 (30 pm) and 5.43 (25 pm). Pauling Scale Bond-energy data are available only for krypton and xenon fluorides. These are used in Pauling's equation
Table 1. Electronegativities of the Noble Gases and Preceding Elements Atoms
Covalent Radiia I pm Aand R
AWRn
591155 (147)
S
Eiectronegativity Pauling
Allred-Rochow
Sanderson
Ref 4bl This work
Ref m i s work
Ref 7/Thiswork Ref 6
1.9012.05 (1.9012.05)
2.4412.49
I451144 2.201 (2.20)
Mulliken
2.8512.59 ( 12.12)
Allen /This work
12.78
~verage~
Ref 8
2.3512.44 (2.0512.1)
'Radii of haloaens calculated from Allred-Rochow eauation or taken fmm ref 7. Raa of nook gases ablalned by enrapalalaon of valJes tor e ements n same Peom 'For noDle gases. average ol v a l ~ e sin Ins *on and re1 8: for haogens rets 46 2. 7,6 8 All values in parentheses taken fmm ref 1 (noble gases) and ref lO(hal0gens and hydrogen).
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These calculated values are somewhat higher Table 2. Data Used in Calculation of Valence-State Electronegativities than those listed by Allen and Huheey, who use a fonn of Pauling's equation due to Fung ( 4 ~ ) . Element Orbital Ground-State Promotion Ground-State Ionization PotentialdeV EnergiedeV They are more in line with the other scales in that they are also substantially higher than the Second First p2' p electronegativities of bromine and iodine. He S 0 0 54.41 24.59 Mulliken Scale 40.96 21.56 Ne S (58.6) 0 Mulliken electronegativities, based on the avP 4.44 0 erage of ionization potential and electron aff~n- A, S (30.0) 0 27.62 15.76 ity, can be calculated in a variety of ways. The P 2.53 0 use of ground-state values invariably yields Kr S (29.9) 0 24.35 14.00 electronegativities for the noble gases that are P 2.58 0 21.20 12.13 lower than those of the halogen in the same pe- Xe S (25.0) 0 nod. Indeed, this decrease becomes more proP 2.96 0 S (27.9) 0 [I8.81 10.75 nounced down the group, to the extent that ra- Rn P 5.6 0 don has a lower value than polonium' 'Ien and Values in parentheses enidated Bratsch (mf 6): in brackets,estimated by using average ratio Huheey used the approximation that the elec- ,I S B W , , ~ : I ~ ~IPSfor ~ A,. K ~xe. , tronegativities of noble gases are proportional Mher energies obtained from ref 1 7 . Elearan canfigurations assumed for 2- cation: p2p2p2(s), s2pZp2(p),for neutral atom:s2p2p2pz to their ionization potentials, referenced to X = 4.10 for fluorine ( I ) because they estimated that the +2 ionization energy required for the atoms in electron volts, which are converted to Pauling Mulliken valence-state definition would yield unreasonably high values. units by The use of valence-state ionization potentials and electron afiiities, based on the removal of an electron from Xp= 1.35(xM)@1.37 (6) and addition of an electron to a s~ecific orbital. also Doses a problem: The valence shell s and p orbitals of the noble The method is seen to give quite reasonable agreement gas atoms are (6)assumes that the with other &ctronegativity scales, particularly when ratio of electronegativity to ionization potential for a given pared to the valence-state electronegativities of the haloorbital is the same for a noble gas atom as for the halogen -._. gans. in the same period. This gives-valence-state electronegaAlthough the electronegativity scales examined here tivities for the noble gases that are very similar to those of give different values for the noble gases, they all indicate the halogens or even lower in the case of radon. that the noble gases have higher electronegativities than A way around this difficulty is to regard the bonding in the halogens, with the magnitude of the difference denoble gas compounds as three-centered bonds, F - L F for number increasing down the m - o n. ~as ~. r i n c. i ~quantum .l e the difluorides. Such a molecule is equivalent to a combicreases. It is interesting to note that a recent investigation nation of F-L+ F and F- L+-F (9).The attraction of the (12)suggests that Mulliken valence-state electronegativicentral L atom for bonding electrons would be the average ties of argon, krypton, and xenon would be substa&ially of that exerted on the electrons in the two bondingregions. increased if d orbitals are included in the calculations. In one of these the electrons are shared by F and Lt, so the With the various extrapolation procedures described valence-state electronegativity of the L+cation is relevant. above, all of the traditional electronegativity scales--PaulIn the other there are no shared electrons, so the attraction ing, Sanderson, Allred and Rochow, and Mulliken-give is zero. Thus, the valence-state electronegativity of a noble values for the noble gas atoms (except He, Ne, Ar, and Rn gas atom with the (sZp6)conf~gurationcan be taken as half for Pauling) that explain the chemistry of these elements. that of its singly charged cation. However, in each case it was necessary to add a new ad hoc The s- and p-orbital electronegativities of the cations can interpretation or procedure to these definitions in order to be calculated by a modified Bratsch equation. The electron achieve acceptable values. In contrast, the new spectroaffinityof a cation is equal to the ionization potential of the scopic scale (8) yields reasonable values for them when neutral atom, so for a given orbital of the cation they are treated like the other atoms; no additional ad hoc assumptions are required,
by
Literature Cited
where IP, and EA, are the valence-state ionization potential and electron affinity of the cation; IP2and IP1are the second and first ground-state ionization potentials of the atom; and P2+ and PO are the valence-state promotion energies of the doubly charged cation and neutral atom. Data used in these calculations are given in Table 2. The orbital electronegativities thus obtained are combined to give valence-state electronegativities for the cations in the 12.5% s state proposed by Bratsch. These are halved to produce valence-state electronegativities for the neutral
18
Journal of Chemical Education
1. Allen, L. C.; Huheey J. E. J Inorg. N u c l Chem. 1960.42, 1523. 2. Allred, A. L.; Rachow E. 0. J Inarg NveC Cham. 1958,5,2M. 3. Mulliken, R. S. J C h m . Phys. 1934.2.780. 4. Is) Pauling, L. T h Nature of t h C h m v o l bond, 3rd ed.:Cornell, 1960: p 88. lb) AUred,A. L. J . h o g Nucl. Cham. 1961,17,215. (el Fung,B. M. J Phys. C h .
1966.69.596.
5. Sanderson. R.T.Inom. Cham. 1963.2.660. 6. Brauch, S. G J. C h m . Educ IW, 65.34. 7. Sandemon, R. T. Poior Couoknce;Academic, 1983: pp 1620. 8. Allen. L. C. J A m z C h m Sm. 1989. 111,9003. 9. (alMeWeeny R. Coulson$ Volmce, 3rd ed.:OxfordUniversity, 1979; pp373-376. (b) Smith, D. lnorgonic Substances; Camb"dge University 1990: pp 244.248. 10. Huhoey, J.E. Inorgenic Chsmidry, 3rd ed.:Harper and Raw, 1983:pp 146148. 11. Moore. C. E. Notiond Standard Referenn Do- Series, National Bureau of Standarda 35, Washington, DC,1971;Vals 1-111. 12. Meek, T L. J. Chem Educ m presa.
