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Question 52

A diatomic molecule has a dipole moment of 1.2 D. If the bond distance is 1 $$\mathring{A}$$, then fractional charge on each atom is ______ $$\times 10^{-1}$$ esu. (Given 1D = $$10^{-18}$$ esu cm)


Correct Answer: 2.5

  • Experimental Dipole Moment ($$\mu_{\text{exp}}$$):
    $$\mu_{\text{exp}} = 1.2\text{ D} = 1.2 \times 10^{-18}\text{ esu}\cdot\text{cm}$$
  • Calculated Dipole Moment ($$\mu_{\text{cal}}$$ for $$100\%$$ ionic character):
    Assuming a full electronic charge ($$e = 4.8 \times 10^{-10}\text{ esu}$$) and bond distance ($$d = 1\text{ \AA} = 10^{-8}\text{ cm}$$):
    $$\mu_{\text{cal}} = q \times d = (4.8 \times 10^{-10}\text{ esu}) \times (10^{-8}\text{ cm}) = 4.8 \times 10^{-18}\text{ esu}\cdot\text{cm}$$
  • Fractional Charge:
    $$\text{Fractional charge} = \frac{\mu_{\text{exp}}}{\mu_{\text{cal}}} = \frac{1.2 \times 10^{-18}}{4.8 \times 10^{-18}} = \frac{1.2}{4.8} = 0.25 = 2.5 \times 10^{-1}$$

Conclusion:

Comparing our result with the required format ($$\text{Blank} \times 10^{-1}\text{ esu}$$), the numerical value for the blank space is $$2.5$$.

Answer: 2.5

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