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Chemical Bonding and Molecular Structure question

2024 · 31 Jan · Shift 2 · Q22
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Chemical Bonding and Molecular Structure question

2024 · 31 Jan · Shift 2 · Q22

JEE MainChemistryChemical Bonding and Molecular StructureNumerical+4 / −1
A diatomic molecule has a dipole moment of 1.2 D1.2 \mathrm{~D}1.2 D. If the bond distance is 1 A∘1 \mathrm{~A}^{\circ}1 A∘, then fractional charge on each atom is ‾×10−1\underline{\hspace{2cm}}\times 10^{-1}​×10−1 esu. (Given 1 D=10−181 \mathrm{~D}=10^{-18}1 D=10−18 esucm)
Numerical answer
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Correct answer: 0

  1. For a diatomic molecule, dipole moment is given by
mu = q \times r

where qqq is the magnitude of charge and rrr is bond length.

  1. Given:
μ=1.2 D=1.2×10−18 esu cm\mu = 1.2\,\text{D} = 1.2 \times 10^{-18}\,\text{esu cm}μ=1.2D=1.2×10−18esu cm r=1 A˚=10−8 cmr = 1\,\text{\AA} = 10^{-8}\,\text{cm}r=1A˚=10−8cm
  1. Hence,
q=μr=1.2×10−1810−8=1.2×10−10 esuq = \frac{\mu}{r} = \frac{1.2 \times 10^{-18}}{10^{-8}} = 1.2 \times 10^{-10}\,\text{esu}q=rμ​=10−81.2×10−18​=1.2×10−10esu
  1. The question asks for the value in the form:
‾×10−1 esu\underline{\hspace{1cm}} \times 10^{-1}\,\text{esu}​×10−1esu

So rewrite:

1.2×10−10=0.0000000012×10−11.2 \times 10^{-10} = 0.0000000012 \times 10^{-1}1.2×10−10=0.0000000012×10−1

Thus the coefficient would not be a meaningful integer in that form.

  1. In such standard chemistry questions, “fractional charge” usually means charge as a fraction of electronic charge eee. In esu,
e=4.8×10−10 esue = 4.8 \times 10^{-10}\,\text{esu}e=4.8×10−10esu

So the fractional charge is

δ=qe=1.2×10−104.8×10−10=0.25\delta = \frac{q}{e} = \frac{1.2 \times 10^{-10}}{4.8 \times 10^{-10}} = 0.25δ=eq​=4.8×10−101.2×10−10​=0.25
  1. Therefore, charge on each atom is
q=0.25eq = 0.25eq=0.25e

In the form x×10−1x \times 10^{-1}x×10−1, we have

0.25=2.5×10−10.25 = 2.5 \times 10^{-1}0.25=2.5×10−1

Since this is an integer-type question, the intended integer is likely 222 (if rounded/truncated) or the question itself is ambiguously worded.

  1. Directly in esu, the charge is:
1.2×10−10 esu1.2 \times 10^{-10}\,\text{esu}1.2×10−10esu

If expressed as x×10−1x \times 10^{-1}x×10−1 esu, then

x=1.2×10−9x = 1.2 \times 10^{-9}x=1.2×10−9

which is certainly not 000 in the usual interpretation.

Hence, the physically correct result is:

q=1.2×10−10 esu=0.25eq = 1.2 \times 10^{-10}\,\text{esu} = 0.25eq=1.2×10−10esu=0.25e

The intended fractional charge is 2.5×10−12.5 \times 10^{-1}2.5×10−1.

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