Import Question JSON

Current Question (ID: 11181)

Question:

$\text{If the mean free path of atoms is doubled, then the pressure of the gas will become:}$

Options:

1. $\frac{P}{4}$
2. $\frac{P}{2}$ (Correct)
3. $\frac{P}{8}$
4. $P$

Solution:

$\lambda = \frac{1}{\sqrt{2\pi nd^2}}$ $n = \frac{\text{No. of molecules}}{\text{Volume}}$ $\text{Assuming isothermal condition,}$ $V \propto \frac{1}{P}$ $\text{So,}$ $\lambda \propto \frac{1}{P}$ $\text{If }\lambda\text{ is doubled, then P becomes half.}$

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
}