Import Question JSON

Current Question (ID: 17975)

Question:

$\text{A compound forms a hexagonal close-packed structure. The total number of voids in } 0.5 \text{ moles}$ $\text{of the compound will be -}$

Options:

1. $9.033 \times 10^{23}$
2. $3.011 \times 10^{23}$
3. $6.023 \times 10^{23}$
4. $8.024 \times 10^{23}$

Solution:

$\text{HINT: The number of octahedral voids is equal to the number of atoms in a lattice.}$ $\text{STEP 1: Calculate the number of tetrahedral void and octahedral voids is as follows:}$ $\text{Number of close-packed particles} = 0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$ $\text{Therefore, number of octahedral voids} = 3.011 \times 10^{23}$ $\text{The number of tetrahedral voids is double of octahedral voids.}$ $\text{And, the number of tetrahedral voids} = 2 \times 3.011 \times 10^{23} = 6.022 \times 10^{23}$ $\text{STEP 2: Calculate the total voids are as follows:}$ $\text{Therefore, total number of voids} = 3.011 \times 10^{23} + 6.022 \times 10^{23} = 9.033 \times 10^{23}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

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
}