Import Question JSON

Current Question (ID: 17930)

Question:

$\text{An element with a molar mass of } 2.7 \times 10^{-2} \text{ kg mol}^{-1} \text{ and density } 2.7 \times 10^{3} \text{ kg m}^{-3} \text{ forms a unit cell with an edge length of } 405 \text{ pm. The type of unit cell is-}$

Options:

1. $\text{Simple cubic cell.}$
2. $\text{Face-centered cubic cell.}$
3. $\text{Body-centered cubic cell.}$
4. $\text{None of the above.}$

Solution:

$\text{HINT: } d = \frac{Z \times M}{N_A \times a^3}$ $\text{Explanation:}$ $\text{STEP 1:}$ $\text{The given values are as follows:}$ $\text{The density of the element, } d = 2.7 \times 10^3 \text{ kg m}^{-3}$ $\text{Molar mass, } M = 2.7 \times 10^{-2} \text{ kg mol}^{-1}$ $\text{Edge length, } a = 405 \text{ pm} = 405 \times 10^{-12} \text{ m} = 4.05 \times 10^{-10} \text{ m}$ $\text{STEP 2:}$ $\text{Calculate the value of } Z \text{ is as follows:}$ $z = \frac{d \times N_A \times a^3}{M}$ $= \frac{2.7 \times 10^3 \text{ kg m}^{-3} \times (4.05 \times 10^{-10} \text{ m})^3 \times 6.023 \times 10^{23} \text{ mol}^{-1}}{2.7 \times 10^{-2} \text{ kg mol}^{-1}}$ $\Rightarrow z = 4$ $\text{The unit cell is FCC (Face-centered cubic cell) as four atoms are present per unit cell.}$

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
}