Import Question JSON

Current Question (ID: 19886)

Question:

$\text{A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:}$

Options:

1. $\frac{1}{32}$
2. $\frac{1}{2\sqrt{2}}$
3. $\frac{1}{4}$
4. $\frac{2\sqrt{2}}{1}$

Solution:

$\text{The root mean square speed is given by } v_{rms} = \sqrt{\frac{3kT}{m}}. $ $\text{For helium and oxygen, the ratio is } \frac{v_{rms, \text{He}}}{v_{rms, \text{O}_2}} = \sqrt{\frac{m_{\text{O}_2}}{m_{\text{He}}}}. $ $\text{Given } m_{\text{He}} = 4 \text{ u and } m_{\text{O}_2} = 32 \text{ u, we have } \frac{v_{rms, \text{He}}}{v_{rms, \text{O}_2}} = \sqrt{\frac{32}{4}} = \sqrt{8} = 2\sqrt{2}. $

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
}