Import Question JSON

Current Question (ID: 11152)

Question:

$\text{The rms speed of oxygen atoms is } v. \text{ If the temperature is halved and the oxygen atoms combine to form oxygen molecules, then the rms speed will be:}$

Options:

1. $\frac{v}{\sqrt{2}}$
2. $v\sqrt{2}$
3. $2v$
4. $\frac{v}{2}$ (Correct)

Solution:

$\text{Hint: The rms speed depends on temperature and molecular mass of gas.}$ $\text{Step 1: Relate initial } v_{\text{rms}} \text{ to conditions.}$ $v = \sqrt{\frac{3RT}{M}}$ $\text{Step 2: Find final conditions in terms of initial conditions.}$ $M_2 = 2M$ $T_2 = \frac{T}{2}$ $\text{Step 3: Find the final } v_{\text{rms}}.$ $v_2 = \sqrt{\frac{3RT_2}{M_2}} = \frac{v}{2}$

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
}