Import Question JSON

Current Question (ID: 17938)

Question:

$\text{Ice crystallizes in a hexagonal lattice having the volume of the unit cell as } 132 \times 10^{-24} \text{ cm}^3. \text{ If the density is } 0.92 \text{ g/cm}^3 \text{ at a given temperature, then the number of } \text{H}_2\text{O} \text{ molecules per unit cell is:}$

Options:

1. $1$
2. $2$
3. $3$
4. $4$

Solution:

$\text{STEP 1:}$ $\text{Moles of } \text{H}_2\text{O} = \frac{\text{Mass}}{18}$ $\text{Molecules of } \text{H}_2\text{O} = \text{Avogadro number} \times \text{ moles}$ $\text{Mass of ice} = \text{volume} \times \text{density}$ $= 132 \times 10^{-24} \text{ cm}^3 \times 0.92 \text{ g/cm}^3 \approx 121.5 \times 10^{-24}$ $\text{STEP 2:}$ $\text{No. of moles} = \frac{121.5 \times 10^{-24}}{18} = 6.7 \times 10^{-24}$ $\text{No. of molecules of } \text{H}_2\text{O} = 6.7 \times 10^{-24} \times 6.023 \times 10^{23} = 4$

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
}