Import Question JSON

Current Question (ID: 17963)

Question:

$\text{An element crystallizes in a structure having FCC unit cell of an edge length 200 pm. If 200 g of this element contains } 24 \times 10^{23} \text{ atoms, the density of the element is -}$

Options:

1. $50.3 \text{ g/cc}$
2. $63.4 \text{ g/cc}$
3. $41.6 \text{ g/cc}$
4. $34.8 \text{ g/cc}$

Solution:

$\text{Density formula} = \frac{\text{Mass of substance}}{\text{Volume of substance}}$ $\text{STEP 1: Calculate the volume of FCC unit cell as follows:}$ $a \text{ (edge length)} = 200 \text{ pm} = 2 \times 10^{-8} \text{ cm}$ $V \text{ (volume of FCC unit cell)} = a^3$ $= 8 \times 10^{-24} \text{ cm}^3$ $\text{STEP 2: Calculate the amount of one FCC unit cell as follows:}$ $\text{Amount of } 24 \times 10^{23} \text{ atoms} = 200 \text{ g}$ $\text{Amount of 1 atom in FCC} = \frac{200}{24 \times 10^{23}}$ $1 \text{ FCC unit cell contains 4 atoms,}$ $\text{Amount of 1 unit cell} = \frac{200}{24 \times 10^{23}} \times 4$ $= 33.3 \times 10^{-23} \text{ g}$ $\text{STEP 3: Calculate the density is as follows:}$ $\text{density} = \frac{m}{v}$ $= \frac{33.3 \times 10^{-23}}{8 \times 10^{-24}}$ $= 41.6 \text{ g/cc}$ $\text{Hence, the density of the element is 41.6 g/cc}$

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
}