Import Question JSON

Current Question (ID: 7427)

Question:

$\text{The volume occupied by one water molecule (density} = 1 \text{ g cm}^{-3}\text{) is:}$

Options:

1. $9.0 \times 10^{-23} \text{ cm}^3$
2. $6.023 \times 10^{-23} \text{ cm}^3$
3. $3.0 \times 10^{-23} \text{ cm}^3$
4. $5.5 \times 10^{-23} \text{ cm}^3$

Solution:

$\text{HINT:}$ $\text{Explanation:}$ $\text{STEP 1:}$ $\text{According to the mole concept,}$ $1\text{ mol of water} = 6.02 \times 10^{23} \text{ molecules of water} = 18\text{ g}$ $\therefore\text{Mass of one molecule of water(by unitary method), m} = \frac{18}{6.023 \times 10^{23}} \text{ g}$ $\text{STEP 2:}$ $\text{Now as, Density (d)} = \frac{m}{V}$ $\text{By rearranging the formula, V} = \text{m/d}$ $(\text{Given, density} = 1 \text{ g cm}^{-3})$ $\text{Hence, } V = \frac{m}{d} = \frac{18}{6.023 \times 10^{23} \times 1} = 3 \times 10^{-23} \text{ cm}^3$ $\text{Thus, option 3 is the correct answer.}$

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
}