Import Question JSON

Current Question (ID: 19839)

Question:

$\text{A gas mixture consists of } 3 \text{ moles of oxygen and } 5 \text{ moles of argon at temperature } T. \text{ Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of } RT) \text{ of the mixture is:}$ $1.\ 11$ $2.\ 15$ $3.\ 20$ $4.\ 13$

Options:

1. $11$
2. $15$
3. $20$
4. $13$

Solution:

$\text{Hint: } U = \frac{fnRT}{2}$ $\text{Step: Find the total internal energy of the mixture.}$ $\text{The number of degrees of freedom for diatomic oxygen considering the oxygen bond is rigid:}$ $f_1 = 5$ $\text{The number of degrees of freedom for monoatomic argon:}$ $f_2 = 3$ $\text{The total internal energy of the mixture of gas is given by:}$ $U = \frac{1}{2} n_1 f_1 RT + \frac{1}{2} n_2 f_2 RT$ $\text{Substitute the known values we get;}$ $U = \left( \frac{1}{2} \times 3 \times 5 + \frac{1}{2} \times 5 \times 3 \right) RT$ $\Rightarrow U = 15RT$ $\text{Hence, option (2) is the correct answer.}$

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
}