Import Question JSON

Current Question (ID: 11164)

Question:

$\text{Which of the following statements about degrees of freedom are correct?}$ $\text{(A) A molecule with } n \text{ degrees of freedom has } n^2 \text{ different ways of storing energy.}$ $\text{(B) Each degree of freedom is associated with an average energy of } \frac{1}{2}RT \text{ per mole.}$ $\text{(C) A monoatomic gas molecule has 1 rotational degree of freedom whereas a diatomic molecule has 2 rotational degrees of freedom.}$ $\text{(D) } \text{CH}_4 \text{ has a total of 6 degrees of freedom.}$ $\text{Choose the correct option from the options given below:}$

Options:

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

Solution:

$\text{Hint: Methane molecule is tetrahedron.}$ $\text{Step 1: Find the energy associated with each degree of freedom.}$ $\text{According to the law of equipartition of energy, each degree of freedom is associated with } \frac{1}{2}RT \text{ average energy per mole.}$ $\text{Step 2: Find the number of degrees of freedom for } \text{CH}_4\text{.}$ $\text{A methane molecule is a tetrahedron molecule.}$ $\text{Degree of freedom due to rotation } = 3$ $\text{Degree of freedom due to translation } = 3$ $\text{So, the total degree of freedom for } \text{CH}_4 \text{ molecule is } = 6\text{.}$ $\text{Therefore, the correct statements are (B) and (D).}$ $\text{Hence, option (2) is the correct answer.}$

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
}