Import Question JSON

Current Question (ID: 11157)

Question:

$\text{A gas mixture consists of 2 moles of } \text{O}_2 \text{ and 4 moles of Ar at temperature } T. \text{ Neglecting all the vibrational modes, the total internal energy of the system is:}$

Options:

1. $15RT$
2. $9RT$
3. $11RT$ (Correct)
4. $4RT$

Solution:

$\text{Hint: } U_{\text{total}} = U_{\text{O}_2} + U_{\text{Ar}}$ $\text{Step 1: Find the degree of freedom for each gas.}$ $f_{\text{O}_2} = 5$ $f_{\text{Ar}} = 3$ $\text{Step 2: Find internal energy for each gas.}$ $U = \frac{nfRT}{2}$ $U_{\text{O}_2} = \frac{2 \times 5 RT}{2} = \frac{10RT}{2} = 5RT$ $U_{\text{Ar}} = \frac{4 \times 3 \times RT}{2} = \frac{12RT}{2} = 6RT$ $\text{Step 3: Find the total internal energy.}$ $U_{\text{total}} = U_{\text{O}_2} + U_{\text{Ar}} = 5RT + 6RT = 11RT$ $\text{Hence, option (3) is the correct answer.}$

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
}