Import Question JSON

Current Question (ID: 20789)

Question:

$\text{What is the ratio of the number of molecules of oxygen to nitrogen in a specific gaseous mixture if their mass ratio is } 1:4?$

Options:

1. $7:32$
2. $1:8$
3. $3:16$
4. $1:4$

Solution:

$\text{Hint: 1 mole of a substance contains } N_A \text{ number of molecules}$ $\text{Step 1:}$ $\text{The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is } 1:4.$ $\text{Let the mass of oxygen } = x \text{ g}$ $\text{Let the mass of nitrogen } = 4x \text{ g}$ $\text{The formula for calculating the number of molecules in a given mass is as follows:}$ $\text{Number of molecules} = \frac{\text{amount of substance}}{\text{Molar mass of substance}} \times N_A$ $\text{Number of molecules of oxygen} = \frac{x}{32} \times N_A$ $\text{Number of molecules of nitrogen} = \frac{4x}{28} \times N_A$ $\text{Step 2:}$ $\text{The ratio of the number of molecules of } \text{O}_2 \text{ and } \text{N}_2 \text{ is as follows:}$ $\frac{\frac{x N_A}{32}}{\frac{4x N_A}{28}} = \frac{28}{128} = \frac{7}{32}$ $\text{Hence, option 1 is the correct answer.}$

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
}