Import Question JSON

Current Question (ID: 19841)

Question:

$\text{Consider a gas of triatomic molecules. The molecules are assumed to be triangular, composed of massless rigid rods with atoms at the vertices. The internal energy of a mole of the gas at temperature } T \text{ is:}$

Options:

1. $3RT$
2. $\frac{5}{2}RT$
3. $\frac{9}{2}RT$
4. $\frac{3}{2}RT$

Solution:

$\text{Hint: } U = \frac{f}{2}nRT$ $\text{Step: Find the internal energy of a mole of the gas at temperature } T.$ $\text{we know that the internal energy is given as;}$ $U = \frac{f}{2}nRT$ $\text{For a gas of triatomic molecules the degree of freedom, } f = 6.$ $\Rightarrow U = \frac{6}{2}nRT = 3RT$ $\text{Hence, option (1) is the correct answer.}$

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
}