Import Question JSON

Current Question (ID: 8233)

Question:

$\text{At }27^{\circ} \text{ C, the ratio of root mean square speeds of ozone to oxygen is-}$

Options:

1. $\sqrt{(3/5)}$
2. $\sqrt{(4/3)}$
3. $\sqrt{(2/3)}$
4. $0.25$

Solution:

$\text{Hint: }v_{\text{rms}} = \sqrt{\frac{3\text{RT}}{\text{M}}}$ $\text{Step 1:}$ $\text{The formula of }v_{\text{rms}}\text{ is as follows:}$ $v_{\text{rms}} = \sqrt{\frac{3\text{RT}}{\text{M}}}$ $v_{\text{rms}}\text{ O}_3 = \sqrt{\frac{3\text{RT}}{\text{M}_{\text{O}_3}}}$ $v_{\text{rms}}\text{ O}_2 = \sqrt{\frac{3\text{RT}}{\text{M}_{\text{O}_2}}}$ $\frac{v_{\text{rms}}\text{ O}_3}{v_{\text{rms}}\text{ O}_2} = \sqrt{\frac{\text{M}_{\text{O}_2}}{\text{M}_{\text{O}_3}}}$ $\text{Step 2:}$ $\text{Calculate the ratio of root mean square speeds of ozone to oxygen is as follows:}$ $= \sqrt{\frac{32}{48}}$ $= \sqrt{\frac{2}{3}}$

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
}