Import Question JSON

Current Question (ID: 8198)

Question:

With 100% increase in temperature, the average velocity of a gaseous molecule increases by -

Options:

1. $2.8$ times
2. $4.0$ times
3. $1.4$ times
4. $2.0$ times

Solution:

Hint: Average velocity = $\sqrt{\frac{8RT}{\pi M}}$\n\nStep 1:\n\nThe formula of average velocity is as follows:\n\nAverage velocity = $\sqrt{\frac{8RT}{\pi M}}$\n\n$V_{av} \propto \sqrt{T}$\n\nStep 2:\n\nCalculate the average velocity of a gaseous molecule when 100% increase in temperature occurs\n\nor $(V_{av})_2 / (V_{av})_1 = \sqrt{\frac{2T}{T}} = 1.4$

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
}