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Current Question (ID: 8022)

Question:
A diatomic molecule has a dipole moment of $1.2 \text{ D}$. If its bond length is equal to $10^{-10} \text{ m}$, then the fraction of an electronic charge on each atom will be:
Options:
  • 1. $42\%$
  • 2. $52\%$
  • 3. $37\%$
  • 4. $25\%$ (Correct)
Solution:
$\text{HINT: Dipole moment = charge } \times \text{ distance} \text{Explanation:} \text{First, convert the given dipole moment from Debyes to esu-cm:} $1 \text{ Debye} = 10^{-18} \text{ esu-cm}$ $\mu = 1.2 \text{ D} = 1.2 \times 10^{-18} \text{ esu-cm}$ \text{Next, convert the bond length from meters to centimeters:} $1 \text{ m} = 100 \text{ cm} = 10^2 \text{ cm}$ $\text{d} = 10^{-10} \text{ m} = 10^{-10} \times 10^2 \text{ cm} = 10^{-8} \text{ cm}$ \text{The formula for dipole moment is } \mu = \text{q} \times \text{d} \text{, where q is the charge and d is the distance.} \text{We want to find the charge q (fraction of electronic charge). So, } \text{q} = \frac{\mu}{\text{d}} \text{Step I: Calculate the charge (q) in esu.} $\text{q} = \frac{1.2 \times 10^{-18} \text{ esu-cm}}{10^{-8} \text{ cm}} = 1.2 \times 10^{-10} \text{ esu}$ \text{Step II: The charge of an electron (e) in esu is approximately } 4.8 \times 10^{-10} \text{ esu.} \text{Step III: Calculate the percentage of electronic charge.} $\% \text{charge} = \frac{\text{Calculated value of charge}}{\text{Theoretical value of charge}} \times 100\%$ $\% \text{charge} = \frac{\text{q}}{\text{e}} \times 100\%$ $\% \text{charge} = \frac{1.2 \times 10^{-10} \text{ esu}}{4.8 \times 10^{-10} \text{ esu}} \times 100\%$ $\% \text{charge} = \frac{1.2}{4.8} \times 100\% = 0.25 \times 100\% = 25\%$ \text{So, the fraction of an electronic charge on each atom is } 25\%.}$

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Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}