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Page 94

86 Atomic Structure and Periodicity

such a scale has involved the powers of two Nobel Chemistry Prize
winners (Pauling in 1954, for valence bond theory, and Mulliken in 1966,
for molecular orbital theory), but, after many other efforts, there are still
doubts about the currently accepted values and about their usefulness.

4.4.1 The Pauling Scale of Electronegativity Coefficients
Pauling suggested that the bond
in a heteronuclear molecule, AB, Pauling’s scale of electronegativity was based on the observation that the
,would be stronger than that bond dissociation energy of a diatomic molecule, AB, was normally
expected for a purely covalent
bond owing to what he termed
as ionic-covalent resonance
energy. This is to be interpreted
by considering the bonding in AB
as some mixture of a covalent
bond, A-B, and an ionic form,
A*B (assuming that B is more
electronegative than A). This IS
the language of valence bond
theory.

_ _
greater than the average values for the diatomic molecules, A, and B,,
for any pair of elements, A and B. It is important to note thatihe three
molecules AB, A, and B, were those in which only single covalent bonds
existed.

He stipulated that the geometric mean of the bond dissociation
energies of the molecules A, and B, represented the strength of a pure-
ly covalent bond in the molecule AB, and that any extra strength of the
A-B bond was because of the of the difference in electronegativity of the
two atoms. This extra strength is represented by the equation:

A = D(A-B) - [D(A,) x D(B,)]1/2 (4.4)

Pauling found that there was a correlation between the square root of
A and the positive differences between values of the electronegativity
coefficients of the two elements concerned:

OC Ix, - XBl (4.5)
By assigning the value of 2.1 for the electronegativity coefficient of
hydrogen (this was done to ensure that all values of the coefficients would
be positive), Pauling was able to estimate values for a small number of
elements for which the thermochemical data were available. The scale
was limited by lack of data and by the perversity of the majority of
elements in not forming diatomic molecules.

4.4.2 Mulliken’s Scale of Electronegativity Coefficients

Mulliken’s scale was based on the logic that electronegativity is a
property of an element that can be related to the magnitude of its first
ionization energy, I , , and to that of its first electron attachment energy,
E l , both being indications of the effectiveness of the nucleus in attract-
ing electrons. Ionization energy is a measure of the effectiveness of a
nucleus in retaining electrons and electron attachment energy is a meas-
ure of the attraction of the neutral atom for an incoming electron. The
Mulliken coefficients were calculated as the average of the first ioniza-

Page 95

Periodicity I: Some Atomic Properties; Relativistic Effects 87

tion energy and the energy releused when the atom accepted an electron
( i . ~ the value of the first electron attachment energy with its sign
changed): % ( I , - E , ) , with a suitable modifying constant to ensure the
best correlation with the already established Pauling values.

An electronegative atom is expected to have a high first ionization
energy and to have a large negative value for its first electron attach-
ment energy, and to arrange for the two energies to work in the same
direction it is necessary to change the sign of the latter.

The scale was limited by the available accurate data, particularly the
values of the electron attachments energies. These latter are now well
established, but the up-dated Mulliken scale has not found general
acceptance. The correlation with the Allred-Rochow scale (Section 4.4.3,
below) is statistically highly significant, with a correlation coefficient of
0.9. The Mulliken values are, on average, 8% lower than the correspon-
ding Allred-Rochow values.

4.4.3 The Allred-Rochow Scale of Electronegativity
Coefficients

Of several at tempts at constructing an accurate scale of electronegativi-
ty, the one derived by Allred and Rochow4 is now generally accepted
and is known by their names. A discussion of its accuracy is included
below. The scale is based on the concept that the electronegativity of an
element is related to the force of attraction experienced by an electron
at a distance from the nucleus equal to the covalent radius of the par-
ticular atom. According to Coulomb’s law this force is given by:

(4.6)

where Zc,- is the effective atomic number and e is the electronic charge.
The effective atomic number is considered to be the difference between
the actual atomic number, 2, and a shielding factor, S, which is esti-
mated by the use of Slater’s rules. These represent an approximate
method of calculating the screening constant, S, such that the value of
the effective atomic number, Z,,.,., is given by 2 - S. The value of S is
obtained from the following rules:

1. The atomic orbitals are divided into groups: (Is); (2s, 2p); (3s, 3p);
( 3 4 ; (4s, 4p); (4d); (40; (5s, 5p); (5d); (50; and so on.

2. For an electron (principal quantum number n ) in a group of s and/or
p electrons, the value of S is given by the sum of the following con-
tributions:
( i ) Zero from electrons in groups further away from the nucleus than
the one considered.

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