Question

Calculate the electronegativity of fluorine from the following data:
\[{E_{H - H}} = 104.2{\text{ kcalmo}}{{\text{l}}^{ - 1}}\]
\[{E_{F - F}} = 36.6{\text{ kcalmo}}{{\text{l}}^{ - 1}}\]
\[{E_{H - F}} = 134.6{\text{ kcalmo}}{{\text{l}}^{ - 1}}\]
\[{X_H} = 2.1\]

Answer 1

Hint: Electronegativity is the measure of an atom's ability to attract the shared pair of electrons to itself. On the periodic table, electronegativity will generally increase as you move from left to right across a period and decrease as you move down a group. The most common scale used to measure electronegativity is the Pauling’s scale.

Complete answer:
Electronegativity can be found out by using the Pauling equation which relates the electronegativity difference of atoms to the bond energies.
The Pauling’s equation for the H-F molecule is given by:
\[ \Rightarrow {X_F} - {X_H} = 0.208\sqrt {{E_{H - F}} - \sqrt {{E_{H - H}} \times {E_{F - F}}} } \]
We are given the values of all of these quantities other than electronegativity of fluorine. So we can find out the unknown value by just substituting the given data into the above equation.
\[ \Rightarrow {X_F} - 2.1 = 0.208\sqrt {134.6 - \sqrt {104.2 \times 36.6} } \]
\[ \Rightarrow {X_F} - 2.1 = 0.208\sqrt {134.6 - 61.75} \]
\[ \Rightarrow {X_F} - 2.1 = 0.208 \times 8.534\]
\[ \Rightarrow {X_F} - 2.1 = 1.78\]
Now by rearranging the terms we can find out the value of electronegativity of fluorine.
\[ \Rightarrow {X_F} = 2.1 + 1.78\]
\[ \Rightarrow {X_F} = 3.88\]
Thus the electronegativity of fluorine from the following data is 3.88

Note:
There are many other scales and methods to find the electronegativity of an atom.
Mulliken scale is an electronegativity scale that considers the electronegativity of an element as the average of its ionization potential and the electron affinity of the given element.
Allred-Rochow’s Electronegativity is a measure of electronegativity that determines the values of the electrostatic force exerted by the effective nuclear charge on the valence electrons of the molecule in consideration. The value of the effective nuclear charges is estimated by using Slater's rules.
There are relations between these scales that will help in interconversion of electronegativity values into each other.