Concept: The dipole moment ($\mu$) of a diatomic molecule is a measure of the polarity of the bond. It is defined as the product of the magnitude of the charge ($q$) and the distance between the charges (bond length, $r$). The fractional charge can be determined by comparing the observed dipole moment with the theoretical dipole moment if the bond were purely ionic (i.e., a full elementary charge).

Step 1: Convert units to SI.

Given dipole moment, ${\mu }_{observed}=1.20\text{ D}$.
1 Debye (D) = $3.33564\times 10^{-30}\text{ C m}$.
${\mu }_{observed}=1.20\times 3.33564\times 10^{-30}\text{ C m}=4.002768\times 10^{-30}\text{ C m}$.

Given bond length, $r=1.25\times 10^{-8}\text{ cm}$.
1 cm = $10^{-2}\text{ m}$.
$r=1.25\times 10^{-8}\times 10^{-2}\text{ m}=1.25\times 10^{-10}\text{ m}$.

Step 2: Calculate the theoretical dipole moment for a purely ionic bond.

For a purely ionic bond, the charge on each atom would be equal to the elementary charge, $e=1.602\times 10^{-19}\text{ C}$.

Theoretical dipole moment, ${\mu }_{ionic}=e\times r$.
${\mu }_{ionic}=1.602\times 10^{-19}\text{ C}\times 1.25\times 10^{-10}\text{ m}=2.0025\times 10^{-29}\text{ C m}$.

Step 3: Calculate the fraction of charge.

The fraction of charge ($f$) is the ratio of the observed dipole moment to the theoretical dipole moment for a purely ionic bond.

$f=\frac{{\mu }_{observed}}{{\mu }_{ionic}}=\frac{4.002768\times 10^{-30}\text{ C m}}{2.0025\times 10^{-29}\text{ C m}}$.

$f\approx 0.1999\approx 0.2$.

Option Analysis:

• A) 0.1: This value is too low.
• B) 0.2: This matches our calculated fraction of charge.
• C) 0.25: This value is too high.
• D) 0.3: This value is too high.

Correct Answer: (B)