Question

When the polarity of bond $A-B$ is expressed in “ $\mathrm{\Delta }$” expressed in SI units, the relationship between their electronegativity difference is:
A.$x_A-x_B=0.1071\mathrm{\Delta }$
B.$x_A-x_B=\mathrm{\Delta }\sqrt{0.208}$
C.$x_A-x_B=0.2071\sqrt{\mathrm{\Delta }}$
D.$x_A-x_B=0.1071\sqrt{\mathrm{\Delta }}$

Answer 1

Hint: We know that $1eV/atom=96.4KJ/mol$. The polarity of a bond is the separation of electric charge along with a bond which results in a dipole moment. In $C^{\delta +}-C{l}^{\delta -}$ , the Chlorine is more electronegative than Carbon, so we could see that chlorine pulls the electrons and acquires a partial negative charge. Therefore, on finding the electronegativity difference between the atoms, we can determine the polarity of the bond.

Complete step by step answer:
We know that in a molecule with a difference in electronegativity in its atoms, the electrons are shifted to the more electronegative atom.
The greater the electronegativity, the more will be the partial charge as we saw in $C^{\delta +}-C{l}^{\delta -}$
If the electronegativity of both the atoms is equal, then it is a nonpolar molecule.
It is given that the polarity of the bond $A-B$ is $\mathrm{\Delta }$.
As we mentioned above the difference in electronegativity of both the atoms can give the polarity.
$x_A$ be the electronegativity of A and let $x_B$ be the electronegativity of B.
According to Pauling Scale, We know that electronegativity difference can be written as $x_A-x_B=(eV{)}^{{\displaystyle \frac{-1}{2}}}\sqrt{E_{A-B}-{\displaystyle \frac{E_{A-A}+E_{B-B}}{2}}}$ where $E_{A-B}$ is the bond energy of $A-B$ where $E_{A-A}and{E}_{B-B}$ are the bond dissociation energies. Here the bond energy Is $\mathrm{\Delta }$
So $x_A-x_B=(eV{)}^{{\displaystyle \frac{-1}{2}}}\sqrt{\mathrm{\Delta }}$
$1eV/atom=96.4KJ/mol$
So, ${(eV)}^{{\displaystyle \frac{-1}{2}}}={\displaystyle \frac{1}{\sqrt{96.49}}}$ So $eV=0.1071$
Now, we can say that $x_A-x_B=0.1071\sqrt{\mathrm{\Delta }}$ where $\mathrm{\Delta }$ is the polarity.
Polarity is measured by the dipole moment of $A-B$
The polarity can be measured as bond energy, as the difference in experimental and calculated. Therefore when its SI unit is $KJ/mol$ and the difference in electronegativity is $x_A-x_B=0.1071\sqrt{\mathrm{\Delta }}$
Therefore, the correct answer is an option (D).

Note:
 $1eV/atom=23.06Kcal/mol$ . When bond energy is calculated in $Kcal/mol$ , the answer will be $x_A-x_B=0.208\sqrt{\mathrm{\Delta }}$ . We have come across a term dipole moment, it is used to measure the polarity of bond within a molecule, and is found in molecules having separation of positive and negative charges.