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When the polarity of bond ${{A - B}}$ is expressed in “ $\Delta $” expressed in SI units, the relationship between their electronegativity difference is:
A.${{{x}}_{{A}}}{{ - }}{{{x}}_{{B}}}{{ = 0}}{{.1071 }}\Delta $
B.${{{x}}_{{A}}}{{ - }}{{{x}}_{{B}}}{{ = }}\Delta \sqrt {0.208} $
C.${{{x}}_{{A}}}{{ - }}{{{x}}_{{B}}}{{ = 0}}{{.2071 }}\sqrt {{\Delta }} $
D.${{{x}}_{{A}}}{{ - }}{{{x}}_{{B}}}{{ = 0}}{{.1071 }}\sqrt {{\Delta }} $

Last updated date: 23rd Jun 2024
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Hint: We know that ${{1 eV/atom = 96}}{{.4 KJ/mol}}$. 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 $\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}}{{{)}}^{\dfrac{{{{ - 1}}}}{{{2}}}}}\sqrt {{{{E}}_{{{A - B}}}}{{ - }}\dfrac{{{{{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 $\Delta $
So ${{{x}}_{{A}}}{{ - }}{{{x}}_{{B}}}{{ = (eV}}{{{)}}^{\dfrac{{{{ - 1}}}}{{{2}}}}}{{ }}\sqrt {{\Delta }} $
${{1 eV/atom = 96}}{{.4 KJ/mol}}$
So, ${{{(eV)}}^{\dfrac{{{{ - 1}}}}{{{2}}}}}{{ = }}\dfrac{{{1}}}{{\sqrt {{{96}}{{.49}}} }}$ So ${{eV = 0}}{{.1071}}$
Now, we can say that ${{{x}}_{{A}}}{{ - }}{{{x}}_{{B}}}{{ = 0}}{{.1071 }}\sqrt {{\Delta }} $ where $\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 {{\Delta }} $
Therefore, the correct answer is an option (D).

 ${{1 eV/atom = 23}}{{.06 Kcal/mol}}$ . When bond energy is calculated in ${{Kcal/mol}}$ , the answer will be ${{{x}}_{{A}}}{{ - }}{{{x}}_{{B}}}{{ = 0}}{{.208}}\sqrt {{\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.