Import Question JSON

Current Question (ID: 19837)

Question:

$\text{An HCl molecule has rotational, translational and vibrational motions.}$ $\text{If the rms velocity of HCl molecules in its gaseous phase is } \vec{v}, m \text{ is its}$ $\text{mass and } k_B \text{ is Boltzmann constant, then its temperature will be:}$

Options:

1. $\frac{mv^2}{7k_B}$
2. $\frac{mv^2}{6k_B}$
3. $\frac{mv^2}{5k_B}$
4. $\frac{mv^2}{3k_B}$

Solution:

$\text{Hint: Energy of molecules = } \frac{f}{2} kT$ $\text{Energy of molecules = } \frac{f}{2} kT$ $\text{For translational } \frac{1}{2} mV^2 = \frac{3}{2} kT$ $T = \frac{mv^2}{3k}$ $\text{According to Translational equation}$ $\text{Ans should be (4) } \frac{mv^2}{6K}$ $\text{NTA has given } \frac{mv^2}{6K} \text{ (2)}$ $\text{So NTA should correct this ans}$

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
}