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What is Pauling approach and mullikens approach and Allred Rochow scale


Solution

Linus Pauling ddescribed electronegativity as “the power of an atom in a molecule to attract electrons to itself.”1 Basically, the electronegativity of an atom is a relative value of that atom's ability to attract election density toward itself when it bonds to another atom. The higher the electronegative of an element, the more that atom will attempt to pull electrons towards itself and away from any atom it bonds to. The main properties of an atom dictate it's electronegativity are it's atomic number as well as its atomic radius. The trend for electronegativity is to increase as you move from left to right and bottom to top across the periodic table. This means that the most electronegative atom is Fluorine and the least electronegative is Francium.

There are a few different 'types' of electronegativity which differ only in their definitions and the system by which they assign values for electronegativity. For example, there is Mulliken electronegativity which is defined as "the average of the ionization energy and electron affinity of an atom"3, which as we will see, differs slightly from Pauling's definition of electronegativity.

Pauling Electronegativity

Linus Pauling was the original scientist to describe the phenomena of electronegativity. The best way to describe his method is to look at a hypothetical molecule that we will call XY. By comparing the measured X-Y bond energy with the theoretical X-Y bond energy (computed as the average of the X-X bond energy and the Y-Y bond energy), we can describe the relative affinities of these two atoms with respect to each other.

Δ Bond Energies = (X-Y)measured – (X-Y)expected

If the electonegativities of X and y are the same, then we would expect the measured bond energy to equal the theoretical (expected) bond energy and therefore the Δ bond energies would be zero. If the electronegativities of these atoms are not the same, we would see a polar molecule where one atom would start to pull electron density toward itself, causing it to become partially negative.

By doing some careful experiments and calculations, Pauling came up with a slightly more sophisticated equation for the relative electronegativities of two atoms in a molecule: EN(X) - EN(Y) = 0.102 (Δ1/2).1 In that equation, the factor 0.102 is simply a conversion factor between kJ and eV to keep the units consistent with bond energies.

By assigning a value of 4.0 to Fluorine (the most electronegative element), Pauling was able to set up relative values for all of the elements. This was when he first noticed the trend that the electronegativity of an atom was determined by it's position on the periodic table and that the electronegativity tended to increase as you moved left to right and bottom to top along the table. The range of values for Pauling's scale of electronegativity ranges from Fluorine (most electronegative = 4.0) to Francium (least electronegative = 0.7). 2 Furthermore, if the electronegativity difference between two atoms is very large, then the bond type tends to be more ionic, however if the difference in electronegativity is small then it is a nonpolar covalent bond.


 

A method for estimating electronegativity was developed by Robert Mulliken (1896–1986; Nobel Prize in Chemistry 1966) who noticed that elements with large first ionization energies tend to have very negative electron affinities and gain electrons in chemical reactions. Conversely, elements with small first ionization energies tend to have slightly negative (or even positive) electron affinities and lose electrons in chemical reactions. Mulliken recognized that an atom’s tendency to gain or lose electrons could therefore be described quantitatively by the average of the values of its first ionization energy and the absolute value of its electron affinity.

Mulliken

Robert S. Mulliken proposed that the arithmetic mean of the first ionisation energy(EI1EI1) and the electron negativity (EeaEea) should be a measure of the tendency of an atom to attract electrons. As this definition is not dependent on an arbitrary relative scale, it has also been termed absolute electronegativity. Using our definition of electron affinity, we can write Mulliken’s original expression for electronegativity as follows:Mulliken’s definition used the magnitude of the ionization energy and the electron affinity. By definition, the magnitude of a quantity is a positive number. Our definition of electron affinity produces negative values for the electron affinity for most elements, so vertical lines indicating absolute value are needed in Equation 1.11.1 to make sure that we are adding two positive numbers in the numerator.

χ=|EI1+Eea|2(1.1)(1.1)χ=|EI1+Eea|2

Elements with a large first ionization energy and a very negative electron affinity have a large positive value in the numerator of Equation 1.11.1, so their electronegativity is high. Elements with a small first ionization energy and a small electron affinity have a small positive value for the numerator in Equation 1.1, so they have a low electronegativity. Inserting the appropriate data into Equation 1.1 gives a Mulliken electronegativity value for fluorine of 1004.6 kJ/mol. To compare Mulliken’s electronegativity values with those obtained by Pauling, Mulliken’s values are divided by 252.4 kJ/mol, which gives Pauling’s value (3.98).

However, it is more usual to use a linear transformation to transform these absolute values into values that resemble the more familiar pauling values. For ionization energies and electron affinities in electronvolts:

χMulliken=0.187(EI1+Eea)+0.17(1.2)(1.2)χMulliken=0.187(EI1+Eea)+0.17

and for energies in kJ/mol,

χMulliken=(1.97×10−3)(EI1+Eea)+0.19(1.3)(1.3)χMulliken=(1.97×10−3)(EI1+Eea)+0.19

The Mulliken electronegativity can only be calculated for an element for which the electron affinity is known, fifty-seven elements as of 2006. The Mulliken electronegativity of an atom is sometimes said to be the negative of the chemical potential. By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i.e.,

μMulliken=−χMulliken=−EI1+Eea2(1.4)(1.4)μMulliken=−χMulliken=−EI1+Eea2

All electronegativity scales give essentially the same results for one element relative to another. Even though the Mulliken scale is based on the properties of individual atoms and the Pauling scale is based on the properties of atoms in molecules, they both apparently measure the same basic property of an element. In the following discussion, we will focus on the relationship between electronegativity and the tendency of atoms to form positive or negative ions. We will therefore be implicitly using the Mulliken definition of electronegativity. Because of the parallels between the Mulliken and Pauling definitions, however, the conclusions are likely to apply to atoms in molecules as well.

Significance

Despite being developed from a very different set of principles than Pauling electronegativity, which is based on bond dissociation energies, there is a good correlation between Mullikin and Pauling Electronegativities for the atoms, as shown in the plot below.

Allred-Rochow Electronegativity is a measure that determines the values of the electrostatic force exerted by the effective nuclear charge on the valence electrons. The value of the effective nuclear charges is estimated from slayer's rule. The higher charge, the more likely it will attract electrons. Although, Slater's rule are partly empirical. So the Allred-Rochow electronegativity is no more rigid than the Pauling Electronegativity

Electronegativity

Pauling established Electronegativity as the "power" of an atom in a molecule to attract electron to itself. It is a measure of the atom's ability to attract electron to itself while the electron is still attached to another atom. The higher the values, the more likely that atom can pull electron from another atom and into itself. Electronegativity correlates with bond polarity,ionization energy, electron affinity, effective nuclear charge, and atomic size.

Table 1: Pauling Electronegativity Values
H
2.1
                               
Li
1.0
Be
1.6
                    B
2.0
C
2.50
N
3.0
O
3.5
F
4.0
Na
0.9
Mg
1.3
                    Al
1.6
Si
1.9
P
2.2
S
2.5
Cl
3.0
K
0.8
Ca
1.3
Sc
1.4
Ti
1.5
V
1.6
Cr
1.7
Mn
1.6
Fe
1.8
Co
1.9
Ni
1.9
Cu
1.9
Zn
1.7
Ga
1.6
Ge
2.0
As
2.2
Se
2.6
Br
2.8
Rb
0.8
Sr
1.0
Y
1.2
Zr
1.3
Nb
1.6
Mo
2.2
Te
2.1
Ru
2.2
Rh
2.3
Pd
2.2
Ag
1.9
Cd
1.7
In
1.8
Sn
2.0
Sb
2.1
Te
2.1
I
2.7
Cs
0.8
Ba
0.9
La
1.1
Hf
1.3
Ta
1.5
W
1.7
Re
1.9
Os
2.2
Ir
2.2
Pt
2.2
Au
2.4
Hg
1.9
Tl
2.0
Pb
2.3
Bi
2.0
Po
2.0
At
2.2

The periodic trend for electronegativity generally increases from left to right and decreases as it go down the group. The exception are Hydrogen and the noble gases because the noble gases are content with their filled outermost shells, and hydrogen cannot bear to lose a valence electron unlike the rest of the group 1 metals. The elements in the halogen group usually have the highest electronegativity values because they only need to attract one valence electron to complete the octet in their outer shell. Whereas the group 1 elements except for Hydrogen, are willing to give up their only valence electron so they can fulfill having a complete, filled outer shell.

Slater's rules

Slater's rules are rules that provides the values for the effective nuclear charge concept, or ZeffZeff. These rules are based on experimental data for electron promotion and ionization energies, and ZeffZeff is determined from this equation:

Zeff=Z−S(1.1)(1.1)Zeff=Z−S

Where

  • ZZ is the nuclear charge,
  • ZeffZeff is the effective nuclear charge, and
  • SS is the shielding constant

Through this equation, this tells us that electron may get reduced nuclear charge due to high shielding. Allred and Rochow used ZeffZeff because it is accurate due to the involvement of shielding that prevents electron to reach its true nuclear charge: ZZ. When an atom with filled s-shell attracts electrons, those electrons will go to the unfilled p-orbital. Since the electrons have the same negative charge, they will not only repel each other, but also repel the electrons from the filled s-shell. This creates a shielding effect where the inner core electrons will shield the outer core electrons from the nucleus. Not only would the outer core electrons experience effective nuclear charge, but it will make them easily removed from the outer shell. Thus,  It is easier for outer electrons to penetrate the p shell, which has little likelihood of being near the nuclear, rather than the s shell. Consider this, each of the outer electron in the (ns, np) group contributes S = 0.35, S = 0.85 in the (n - 1) shell, and S = 1.00 in the (n - 2) or lower shells.

EXAMPLE 1: SLATER'S RULES

Let's consider this example of finding the ZeffZeff for 4s electrons in Ca. Since Ca has atomic number of 20, Z = 20.

Then, we find the electron configuration for Ca, which is 1s22s22p63s23p64s2.

Now we got that, we can use Slater's rule

Zeff=Z−S(1.2)(1.2)Zeff=Z−S =20−((8×0.85)+(10×1.00))(1.3)(1.3)=20−((8×0.85)+(10×1.00)) =3.2(1.4)(1.4)=3.2

So, Ca has a ZeffZeff of 3.2.

Allred-Rochow Electronegativity

Allred and Rochow were two chemists who came up with the Allred-Rochow Electronegativity values by taking the electrostatic force exerted by effective nuclear charge, Zeff, on the valence electron. To do so, they came up with an equation:

χAR=(3590×Zeffr2cov)+0.744(1.5)(1.5)χAR=(3590×Zeffrcov2)+0.744

At the time, the values for the covalent radius, rcovrcov, were inaccurate. Allred and Rochow added certain perimeters so that it would more closely correspond to Pauling's electronegativity scale.

Table 2: Allred-Rochow Electronegativity Values
H
2.20
                               
Li
0.97
Be
1.47
                    B
2.01
C
2.50
N
3.07
O
3.50
F
4.10
Na
1.01
Mg
1.23
                    Al
1.47
Si
1.74
P
2.06
S
2.44
Cl
2.83
K
0.91
Ca
1.04
Sc
1.20
Ti
1.32
V
1.45
Cr
1.56
Mn
1.60
Fe
1.64
Co
1.70
Ni
1.75
Cu
1.75
Zn
1.66
Ga
1.82
Ge
2.02
As
2.20
Se
2.48
Br
2.74
Rb
0.89
Sr
0.99
Y
1.11
Zr
1.22
Nb
1.23
Mo
1.30
Te
1.36
Ru
1.42
Rh
1.45
Pd
1.35
Ag
1.42
Cd
1.46
In
1.49
Sn
1.72
Sb
1.82
Te
2.01
I
2.21
Cs
0.86
Ba
0.97
La
1.08
Hf
1.23
Ta
1.33
W
1.40
Re
1.46
Os
1.52
Ir
1.55
Pt
1.44
Au
1.42
Hg
1.44
Tl
1.44
Pb
1.55
Bi
1.67
Po
1.76
At
1.90

In this table, the electronegativities increases from left to right just like Pauling's scale because the ZZ is increasing. As we go down the group, it decreases because of the larger atomic size that increases the distance between the electrons and nucleus.


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