Question

Dipole moment of HCl = \(1.03\,D\), HI = \(0.38\,D\). Bond length of HCl = \(1.3\,\AA\) and HI = \(1.6\,\AA\). The ratio of fraction of electric charge \(\delta\) existing on each atom in HCl and HI is

• A. \(1.2:1\)
• B. \(2.7:1\)
• C. \(3.3:1\)
• D. \(1.3:1\)

Hint:

Fractional charge \(\delta\) is proportional to \(\mu/r\). So compare dipole moments divided by bond lengths.

Answer 1

The Correct Option is C

Step 1: Use dipole moment formula.
\[ \mu = \delta \times e \times r \]
Thus:
\[ \delta \propto \frac{\mu}{r} \]
Step 2: Compute ratio \(\delta_{HCl}:\delta_{HI}\).
\[ \frac{\delta_{HCl}}{\delta_{HI}} = \frac{\mu_{HCl}/r_{HCl}}{\mu_{HI}/r_{HI}} = \frac{\mu_{HCl}\,r_{HI}}{\mu_{HI}\,r_{HCl}} \]
Substitute values:
\[ = \frac{1.03 \times 1.6}{0.38 \times 1.3} \]
\[ = \frac{1.648}{0.494} \approx 3.33 \]
So:
\[ \delta_{HCl}:\delta_{HI} = 3.3:1 \]
Final Answer:
\[ \boxed{3.3:1} \]