Import Question JSON

Current Question (ID: 11159)

Question:

$\text{A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per } \text{O}_2 \text{ molecule to that per } \text{N}_2 \text{ molecule is:}$

Options:

1. $1 : 1$ (Correct)
2. $1 : 2$
3. $2 : 1$
4. $\text{depends on the moments of inertia of the two molecules}$

Solution:

$\text{1. Average kinetic energy per molecule per degree of freedom} = \frac{1}{2} k\text{T}$ $\text{Since both the gases are diatomic and at the same temperature (300 K), both will have the same number of rotational degrees of freedom i.e. two.}$ $\text{Therefore, both the gases will have the same average rotational kinetic energy per molecule } \left(= 2 \times \frac{1}{2}\right) k\text{T} = k\text{T}$ $\text{Thus } \frac{E_1}{E_2} = \frac{1}{1}$

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
}