Import Question JSON

Current Question (ID: 19850)

Question:

$\text{According to the kinetic theory of gases,}$ $\text{(A) the motion of the gas molecules freezes at } 0^\circ\text{C.}$ $\text{(B) the mean free path of gas molecules decreases if the density of molecules is increased.}$ $\text{(C) the mean free path of gas molecules increases if the temperature is increased keeping the pressure constant.}$ $\text{(D) average kinetic energy per molecule per degree of freedom is } \frac{3}{2} k_B T \text{ (for monoatomic gases).}$ $\text{Choose the most appropriate answer from the options given below:}$

Options:

1. $\text{(A) and (C) only}$
2. $\text{(B) and (C) only}$
3. $\text{(A) and (B) only}$
4. $\text{(C) and (D) only}$

Solution:

$\text{Hint: } \lambda = \frac{kT}{\sqrt{2}\pi d^2 P}$ $\text{Explanation: The mean free path of a gas is inversely proportional to the density and directly proportional to the pressure.}$ $\text{Therefore the mean free path of gas molecules decreases if the density of molecules is increased and increases if the temperature is increased by keeping the pressure constant.}$

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
}